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1

Temporal and spatial heterogeneity of the Ailaoshan–Song Ma–Song Chay ophiolitic mélange, and its significance on the evolution of Paleo-Tethys

Lin Wei, Liu Fei, Wang Ying, Meng Lingtong, Faure Michel, Chu Yang, Nguyen Vuong Van, Wu Qinying, We Wei, Thu Hoai Luong Thi, Vu Tich Van

Geotourism / Geoturystyka

|

2023

|

nr 1-2 (72-73)

42--43

EN

The ophiolite is the direct evidence to restore the oceanic evolution, and it is used to identify the convergence boundary of the plates. Compared with ophiolite, ophiolitic mélange, especially its matrix, contains more information about the evolution of ocean. The evolution of eastern Paleo-Tethys, between the South China and Indochina blocks, recorded the whole process of rifting from Gondwana and their northward migration and convergence. To understand the tectonic implications from matrix of ophiolitic mélange, the Mesozoic Paleo-Tethys Ailaoshan–Song Ma–Song Chay suture zone located in the North Vietnam–Southeast Yunnan region acts as an ideal study area. Based on the structural geology, we reviewed previous zircon U-Pb dating and Lu-Hf isotopic analyses on the detrital zircon from the Ailaoshan–Song Ma–Song Chay ophiolitic mélange. Accordingly, we subdivide the matrix of these ophiolitic mélange into four parts (M1, M2, M3, and M4; Fig. 1). M1 is mainly located in the middle segment of the Ailaoshan–Song Ma belt. It shows age peaks of 440 Ma and 960 Ma with εHf(t) values of −19.6 ~ +10.3. M2 is mainly located in the NW segment of the Ailaoshan–Song Ma belt, showing a dominant age peak of ~260 Ma. Particularly, it has εHf(t) values of −28.9 ~ +8.1. M3 is mainly located in the SE segment of the Ailaoshan–Song Ma belt, showing the peaks at ~250 Ma, 440 Ma, and 960 Ma with εHf(t) values of −21.9 ~ +10.1. M4 is mainly located in the Song Chay belt, showing the peaks at ~310 Ma, 470 Ma, 610 Ma, 770 Ma, and 965 Ma with εHf(t) values of −28.2 ~ +10.8. The geochronological data of the detrital zircon from the matrix of the Ailaoshan– Song Ma–Song Chay ophiolitic mélange zone, documents a temporal heterogeneity between the M1, M2, M3, and M4 units, which formed at 310–270 Ma, 265–250 Ma, 245–240 Ma, and 310–255 Ma, respectively. The different components and provenances of each unit reflect a strike-parallel heterogeneity (Fig. 1). The M1 unit was mainly sourced from the Paleozoic sedimentary rocks of the Indochina Block (IB). The main provenance for the M2 unit is Emeishan Large Igneous Province (ELIP). The magmatic arc developed in the IB provided the materials for the M3 unit, and the detrital materials of the M4 were mainly sourced from the South China Block (SCB) (Fig. 1). The Cenozoic strike-slip deformation led to an inverted geometry of the M1, M2, and M3 units, accounting for a strike-perpendicular heterogeneity straight to the strike of the orogenic belt. The temporal, strike-parallel, and strike-perpendicular heterogeneity help us to decipher the tempo-spatial evolution of the Paleo-Tethys. The M1, M2, M3, and M4 units contain information from different evolutionary stages, likely recording the comprehensive history of the ancient oceanic basin. Importantly, our results demonstrate that both the active continental margin of the IB and the passive continental margin of the SCB acted as provenance sources that supplied significant amount of detrital material in the ophiolitic mélange matrix, indicating that the Paleo-Tethys Ocean was a “narrow” or “limited” ocean rather than the archipelagic ocean proposed before.

2

Maximum simulated likelihood: don't stop believin'?

Schrey Christopher

Annals of Computer Science and Information Systems

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2021

|

Vol. 26

175--180

EN

Unobserved heterogeneity may complicate model estimation in econometrics. To integrate out the effect of unobserved heterogeneity via maximum simulated likelihood (MSL) estimation, assumptions regarding the underlying distribution need to be made. Researchers seldomly discuss these assumptions. This raises the question, to what extent estimation results in the MSL-context are robust to potential distributional mismatch. This work-in-progress derives the research question from the literature. A simulation study is conducted that underpins the relevance of this matter, where results imply that mismatch may introduce significant bias. Intended future work to properly address and answer this question is defined and discussed.

3

Influence of the heterogeneity of a dump soil on the assessment of its selected properties

Olesiak Sebastian

Studia Geotechnica et Mechanica

|

2020

|

Vol. 42, nr 3

263--275

EN

This article concerns the assessment of selected physical and mechanical properties of a dump soil. The dump soil is a specific soil with a very heterogeneous internal structure. Next to each other, there may be lumps and crumbs of cohesive soils mixed with non-cohesive soils accompanied by a very diverse admixture of organic substance. In addition, the soil in the waste dump, in spatial terms, may significantly differ in consistency and density. This is the result of the process of forming a dump soil, which takes place in three stages: excavation, transport and dumping. A heterogeneous soil deposited within the waste dump is subject to further processes: consolidation, compaction and creeping. Changes occurring in the course of these processes have a significant impact on the development of the properties of the dump soil. Due to the large diversity of the tested soils, the results of their properties were divided into two groups, based on type and consistency of soil. This allows us to estimate the selected properties of the dump soil only on the basis of their macroscopic analysis.

4

Numerical simulation of elastic wave propagation in masonry compared with acoustic emission experimental results

Livitsanos G., Shetty N., Verstrynge E., Wevers M., Van Hemelrijck D., Aggelis D. G.

Archives of Civil and Mechanical Engineering

|

2020

|

Vol. 20, no. 1

236--246

EN

It has been shown in acoustic emission literature that the distance between a possible cracking event and a receiver is affecting the signal parameters providing a wrong image of the real fracture characteristics. In this study, lab-scale experimental tests on masonry components are performed in order to determine the disturbance of the acoustic emission wave properties and verify the experimental observations via numerical wave propagation analysis. The investigation is extended to different geometries including “couplets,” “triplets” and masonry walls. The simulations allow to understand, verify and predict the acoustic emission signal properties alterations in many different types of masonry experiments as well as the correct characterization of the fracture mode.

5

Increasing the reusability of IoT-aware business processes

Wehlitz Robert, Jauer Florian, Rößner Ingo, Franczyk Bogdan

Annals of Computer Science and Information Systems

|

2020

|

Vol. 22

17--22

EN

The Internet of Things (IoT) is based on connected devices which are often heterogeneous in terms of supported communication protocols, interfaces and message formats. IoT-aware business processes, which are executed by process engines, are often bound to specific device types. This decreases their reusability when they are ought to be deployed in multiple IoT scenarios where the ability of supporting different device types is an important requirement. In this paper, we introduce a novel approach on how to overcome the heterogeneity of IoT devices, thus increasing the reusability of IoT-aware business processes. The contribution of this work to information systems research is twofold: First, we present a device abstraction model as the basis to define business process tasks across heterogeneous device types without the need of dealing with their technical implementations. Secondly, we propose a system architecture which supports the modeling, deployment, execution and reuse of IoT-aware business processes.

6

Organizational boundaries – contribution to conceptualization

Pachura P.

Scientific Journal of the Military University of Land Forces

|

2018

|

Vol. 50, No. 4(190)

152--161

EN

The issue of organizational boundaries is a problem discussed from the beginning of the development of the theory of management sciences. Today, it seems that this issue should be subjected to a new conceptualization due to the growing importance of multidimensional spaces in which enterprises operate and the erosion of traditionally interpreted boundaries. At the same time, the notion of a boundary itself is an ambigous concept that derived from and rooted mainly in non-management sciences. Therefore, research on organizational boundaries requires an interdisciplinary approach. In the Polish management science environment, the discussion on border issues is clearly visible, although this is not a question that dominates the mainstream. The aim of the article is to contribute to a scientific discussion in the field of conceptualization of organizational boundaries in the context of a changing reality. The article consists of an introduction, a part devoted to the analysis of organizational boundaries in the perspective of heterogeneous spaces and a part related to presenting the problem of the emergence of “new” boundaries. The whole is concluded with a summary. The article is a review based on interdisciplinary literature research.

7

Modele matematyczne podwójnej przewodności hydraulicznej i ich zastosowanie do interpretacji testów piezometrycznych na obszarze KWB Bełchatów

Wolny F., Jamróz M., Gasiński J., Marciniak M., Kaczmarek M.

Biuletyn Państwowego Instytutu Geologicznego

|

2018

|

nr 471, Hydrogeologia, z. 15

193--199

PL

Testy identyfikacyjne typu slug test lub Paramex realizowane w piezometrach generują oscylacyjną lub wykładniczą reakcję zwierciadła wody. Zgodnie z założeniami teoretycznymi w ośrodku jednorodnym ruch zwierciadła wody ma w większości przypadków charakter wykładniczy. Jednak podczas badań terenowych rejestrowano także dwuwykładniczy charakter ruchu zwierciadła wody, co może świadczyć o podwójnej przewodności hydraulicznej T utworów, w których zafiltrowano badany piezometr. W artykule zaproponowano dwa modele matematyczne podwójnej przewodności, które wykorzystano do identyfikacji parametrów hydrogeologicznych niejednorodnych utworów wodonośnych. Przedstawiono podstawy teoretyczne, algorytmy interpretacyjne oraz przykłady identyfikacji podwójnej przewodności hydraulicznej. Estymacje przewodności wykonano z wykorzystaniem programu Paramex 4 oraz środowiska obliczeniowego MATLAB. Zaprezentowano wyniki estymacji przewodności hydraulicznej dla wybranych piezometrów zafiltrowanych w utworach niejednorodnych na terenie Kopalni Węgla Brunatnego Bełchatów. Przeanalizowano także ograniczenia proponowanych algorytmów interpretacyjnych.

EN

Piezometric tests such as the slug test or PARAMEX test usually result in observing damped oscillations or exponential movement of the water level. However, during some tests, a bi-exponential response of the water table has been recorded. Bi-exponential movement may indicate the presence of a dual-permeability medium around the piezometer screen. Such medium is composed of two subdomains, each characterized by different hydraulic properties (including transmissivity, T). The paper aims to present two mathematical models – the piecewise exponential model and the bi-exponential model – which were applied in order to interpret the results of slug test conducted in heterogeneous sediments of the Bełchatów Lignite Mine. Theoretical background, interpretation algorithms and examples of dual transmissivity estimation for several chosen piezometers are presented. All necessary calculations were performed using Paramex 4 and MATLAB software. Furthermore, the limitations of the interpretation algorithms are discussed.

8

Wpływ niejednorodności struktury zginanych belek z drewna klejonego na efekt ich wzmocnienia

Wdowiak A., Kroner A.

Materiały Budowlane

|

2017

|

nr 1

87--89

PL

Artykuł opisuje doświadczalne badania pojedynczych modeli belek z drewna klejonego, pochodzących z Małopolskiej Krainy Przyrodniczo-Leśnej, wzmocnionych za pomocą taśm węglowych. Zastosowana tarcica konstrukcyjna została przesortowana wytrzymałościowo metodą wizualną zgodnie z PN-EN 14081-1:2016-03 [13]. Celem tych badań było sprawdzenie skuteczności wzmocnienia belek z drewna z defektami. Eksperymentalny program badawczy obejmował określenie nośności na zginanie niezbrojonych i zbrojonych belek klejonych, wykonanych z tarcicy sosnowej.

EN

This article describes the experimental laboratory testing of individual models of glued laminated timber beams derived from Little Poland Nature and Forest Land, strengthened with the use of carbon tapes. The endurance of used timber construction was graded visually according to PN-EN 14081-1:2016-03 [13]. The aim of this study was to verify the effectiveness of the strengthening defective timber beams. The experimental research programme included evaluation of capacity for bending of unreinforced and reinforced glued laminated timber beams, which were made of pine timber.

9

The effect of viscosity and heterogeneity on propagation of G-type waves

Gupta S., Smita

International Journal of Applied Mathematics and Computer Science

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2017

|

Vol. 27, no. 2

253--260

EN

Earthquakes yield motions of massive rock layers accompanied by vibrations which travel in waves. This paper analyses the possibility of G-type wave propagation along the plane surface at the interface of two different media which is assumed to be heterogeneous and viscoelastic. The upper layer is considered to be viscoelastic and the lower half space is considered to be an initially stressed heterogeneous half space. The dispersion equation, as well as the phase and group velocities, is obtained in closed form. The dispersion equation agrees with the classical Love type wave. The effects of the nonhomogeneity of the parameters and the initial stress on the phase and group velocities are expressed by means of a graph.

10

Magnetoelastic shear wave propagation in pre-stressed anisotropic media under gravity

Kumari N., Chattopadhyay A., Singh A. K., Sahu S. A.

Acta Geophysica

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2017

|

Vol. 65, no. 1

189--205

EN

The present study investigates the propagation of shear wave (horizontally polarized) in two initially stressed heterogeneous anisotropic (magnetoelastic transversely isotropic) layers in the crust overlying a transversely isotropic gravitating semi-infinite medium. Heterogeneities in both the anisotropic layers are caused due to exponential variation (case-I) and linear variation (case-II) in the elastic constants with respect to the space variable pointing positively downwards. The dispersion relations have been established in closed form using Whittaker’s asymptotic expansion and were found to be in the well-agreement to the classical Love wave equations. The substantial effects of magnetoelastic coupling parameters, heterogeneity parameters, horizontal compressive initial stresses, Biot’s gravity parameter, and wave number on the phase velocity of shear waves have been computed and depicted by means of a graph. As a special case, dispersion equations have been deduced when the two layers and half-space are isotropic and homogeneous. The comparative study for both cases of heterogeneity of the layers has been performed and also depicted by means of graphical illustrations.

11

Badanie zmienności i niejednorodności zawartości popiołu i siarki w pokładzie 308 KWK Ziemowit

Paszek M., Auguścik J., Mucha J.

Zeszyty Naukowe Instytutu Gospodarki Surowcami Mineralnymi i Energią PAN

|

2016

|

nr 96

229--239

PL

Stosując metody statystyczne i geostatystyczne opisano liczbowo zmienność oraz zbadano niejednorodność zawartości popiołu oraz siarki w pokładzie 308 złoża KWK Ziemowit. Podstawę badań stanowiły wyniki analiz chemicznych prób bruzdowych pobranych w wyrobiskach górniczych. Analiza statystyczna obu parametrów wykazała ich dużą zmienność, znaczące odstępstwa rozkładów empirycznych od teoretycznego rozkładu normalnego i występowanie licznych wartości odstających. Zaproponowano dwa geostatystyczne modele zmienności parametrów: sferyczny dla zawartości popiołu oraz Gaussa dla zawartości siarki. W strukturze zmienności parametrów stwierdzono wyraźnie zaznaczony nielosowy charakter zmian ich wartości. Na podstawie map semiwariogramów kierunkowych (indykatrysy zmienności) ujawniono wyraźną anizotropię zmienności parametrów w zakresie odległości 1000–1500 m. Przy użyciu testu wielokrotnych porównań Gamesa-Howella wykazano niejednorodność rozmieszczenia badanych parametrów, mającą wpływ na ich dużą zmienność.

EN

The variability and heterogeneity of ash and sulphur contents in bituminous coal with seam no. 308 from the “Ziemowit” coal mine have been studied. The data stems from channel samples collected in mine works. The statistical analysis of both parameters showed big variability, significant deviations of empirical distributions from the theoretical normal distribution and occurrence of numerous outliers. Two geostatistical variability models were proposed: spherical for ash content and Gaussian for sulphur content. Anisotropy was revealed based on directional semivariogram maps. The heterogeneity of above-mentioned parameters was proven using a test of multiple comparisons (Games-Howell test).

12

Analiza heterogeniczności utworów syluru i ordowiku z rejonu syneklizy bałtyckiej na podstawie wyników badań laboratoryjnych

Krakowska P., Jarzyna J., Puskarczyk E., Wawrzyniak-Guz K.

Prace Naukowe Instytutu Nafty i Gazu

|

2016

|

nr 209 wyd. konferencyjne

565--568

PL

Analiza heterogeniczności utworów syluru i ordowiku z rejonu syneklizy bałtyckiej z przykładowego otworu „B” została przeprowadzona na podstawie wyników badań laboratoryjnych: petrofizycznych i geochemicznych. Utwory formacji iłowców z Pasłęka, ogniwa iłowców bitumicznych Jantaru, a także formacji szarozielonych margli z Ornety zostały podzielone na grupy o zbliżonych własnościach fizycznych i chemicznych. Wydzielenia uzyskano na drodze analizy statystycznej heterogeniczności skał (Heterogeneity Rock Analysis Clustering (HRA)), na którą składa się najpierw analiza składowych głównych (Principal Component Analysis), a następnie klastrowa (Cluster Analysis).

EN

Heterogeneity analysis of Silurian and Ordovician deposits from the Baltic Syneclise in the exemplary well „B” was made on the basis of the petrophysical and geochemical results of laboratory measurements. The Pasłek Formation with the Jantar Bituminous Black Claystone Member, as well as the Orneta Grey-Green Marls Formation were divided into groups with similar physical and chemical properties. Clusters were obtained by statistical analysis called Heterogeneity Rock Analysis Clustering (HRA), which firstly consists of the Principal Component Analysis and next – Cluster Analysis.

13

Modelling of SH-waves in a fiber-reinforced anisotropic layer over a pre-stressed heterogeneous half-space

Kakar R., Kakar S.

Journal of Theoretical and Applied Mechanics

|

2016

|

Vol. 54 nr 2

463--475

EN

Modelling of SH-waves in an anisotropic fiber-reinforced layer provides a great deal of support in the understanding of seismic wave propagation. This paper deals with the propagation of SH-waves in a fiber-reinforced anisotropic layer over a pre-stressed heterogeneous half-space. The heterogeneity of the elastic half-space is caused by linear variations of density and rigidity. As a special case when both media are homogeneous and stress free, the derived equation is in agreement with the general equation of the Love wave. Numerically, it is observed that the velocity of SH-waves decreases with an increase in heterogeneity-reinforced parameters and decrease in initial stress.

14

Distributed web service repository

Nawrocki P., Mamla A.

Computer Science

|

2015

|

Vol. 16 (1)

55--73

EN

The increasing availability and popularity of computer systems has resulted in a demand for new language- and platform-independent ways of data exchange. This demand has, in turn, led to significant growth in the importance of systems based on Web services. Alongside the growing number of systems accessible via Web services came the need for specialized data repositories that could offer effective means of searching the available services. The development of mobile systems and wireless data transmission technologies has allowed us to use distributed devices and computer systems on a greater scale. The accelerating growth of distributed systems might be a good reason to consider the development of distributed Web service repositories with built-in mechanisms for data migration and synchronization.

15

Influence of mixed boundary conditions and heterogeneity on the vibration behavior of orthotropic truncated conical shells

Sofiyev A. H., Huseynov S. E., Kuruoglu N.

Archives of Mechanics

|

2015

|

Vol. 67, nr 4

331--348

EN

This paper presents the vibration behavior analysis of heterogeneous orthotropic conical shells with mixed boundary conditions. Basic equations of heterogeneous orthotropic truncated conical shells are derived using Donnell–Mushtari shell theory. Employing the separation of variables and Galerkin’s method, the expressions for frequency of heterogeneous orthotropic conical shells with two mixed boundary conditions are obtained. The results are validated through numerical comparisons with available results in the literature. The influences of truncated shell characteristics, heterogeneity, material orthotropy and mixed boundary conditions on dimensionless frequency parameters are investigated.

16

Pollutant’s Horizontal Dispersion Along and Against Sinusoidally Varying Velocity from a Pulse Type Point Source

Singh M. K., Mahato N. K., Kumar N.

Acta Geophysica

|

2015

|

Vol. 63, no. 1

214--231

EN

An analytical solution of a two-dimensional advection diffusion equation with time dependent coefficients is obtained by using Laplace Integral Transformation Technique. The horizontal medium of solute transport is considered of semi-infinite extent along both the longitudinal and lateral directions. The input concentration is assumed at an intermediate position of the domain. It helps to evaluate concentration level along the flow as well as against the flow through one model only. The source of the input concentration is considered to be of pulse type. In the presence of the source, it is assumed to be decreasing very slowly with time, and just after the elimination of the source it is assumed to be zero. The dispersion coefficient and the advection parameter are considered directly proportional to each other. The analytical solution may be used to predict the solute concentration level with position and time in an open medium as well as in a porous medium. The effect of heterogeneity on the solute transport may also be predicted.

17

Niejednorodność złóż w świetle badań geostatystycznych

Kokesz Z.

Przegląd Górniczy

|

2014

|

T. 70, nr 1

62--73

PL

W pracy scharakteryzowano zjawisko niejednorodności złóż polegające na obszarowym zróżnicowaniu średnich wartości parametrów złożowych oraz zróżnicowaniu struktury ich zmienności opisanej za pomocą semiwariogramów. Zwrócono w nim uwagę na niestabilność struktur zmienności parametrów złożowych. Stwierdzono, że obserwowane różnice w przebiegu semiwariogramów sporządzonych dla różnych części złoża rzadko są wywołane tzw. efektem proporcjonalności, a obszarowe zróżnicowanie struktury zmienności parametrów złożowych znajduje najczęściej wytłumaczenie w budowie geologicznej złóż. Wyniki badań sugerują, że małe fragmenty złóż mogą stanowić quasi-homogeniczne rejony. Badania wskazują na potrzebę głębszego analizowania struktur zmienności złóż i uwzględniania jej wyników przy prognozowaniu jakości kopaliny i szacowania zasobów metodą krigingu.

EN

The results of geostatistical studies of variability structures of the Polish mineral deposits have been presented. Special attention has been paid to the heterogeneity of variability structures of deposit parameters. It has been pointed that the variability of the parameters can be marked by different types of heterogeneity. It is interesting to note that non-homogeneity most frequently finds its explanation in deposit geology. It has been emphasized that the variability structures of the parameters should be analysed more deeply. When heterogeneity is evident it should be taken into account during determination of the quality of mineral raw materials and estimation of resources/reserves by kriging.

18

In-situ testing and heterogeneity of UFG Cu at elevated temperatures

Petrenec M., Král P., Dvořák J., Svoboda M., Sklenička V.

Journal of Achievements in Materials and Manufacturing Engineering

|

2014

|

Vol. 62, nr 2

69--74

EN

Purpose: The motivation of present investigation is the study of deformation-induced processes during in-situ tensile and compression test at elevated temperature in order to elucidate the role of the microstructure changes during creep testing. Design/methodology/approach: Experiments were conducted to investigate deformation-induced processes during in-situ tensile test at elevated temperature. Findings: It was found that creep resistance of UFG pure Al and Cu is considerably improved after one ECAP pass in comparison with coarse grained material, however, further repetitive pressing leads to a noticeable deterioration in creep properties of ECAP material. Researches limitations/implications: In the present work was found that ultrafine-grained microstructure is instable and significant grain growth has already occurred during heating to the testing temperature. Originality/value: The experiments conducted on pure Al and Cu found that their creep resistance is considerably improved after one ECAP pass in comparison with unpressed material.

19

Anizotropia i niejednorodność złóż w świetle badań geostatystycznych

Kokesz Z.

Zeszyty Naukowe Instytutu Gospodarki Surowcami Mineralnymi i Energią PAN

|

2013

|

nr 85

181--197

PL

W artykule przedstawiono wyniki geostatystycznych badań struktury zmienności złóż kopalin stałych. Szczególną uwagę zwrócono na kierunkowe i obszarowe zróżnicowanie zmienności parametrów złożowych. Stwierdzono, że złoża mogą cechować się różnym typem anizotropii i niejednorodnością. Anizotropia, jak i obszarowe zróżnicowanie struktury zmienności parametrów złożowych, znajdują najczęściej wytłumaczenie w budowie geologicznej złóż. Badania wskazują na potrzebę głębszego analizowania struktur zmienności złóż i uwzględniania jej wyników przy projektowaniu prac rozpoznawczych, ocenie jakości kopaliny, szacowaniu zasobów, a także przy prowadzeniu eksploatacji.

EN

The results of geostatistical studies of variablility structures of selected mineral deposits have been presented in the paper. Special attention has been paid to anisotropy and heterogeneity of variability structures of deposit parameters. It has been pointed out that the variability of the parameters can be marked by different types of anisotropy and also by heterogeneity. It is interesting to note that directional differentiation of the variabilities and non-homogeneity most frequently finds its explanation in geology. It has been emphasized that the variability structures of the parameters should be analysed more deeply. When anisotropy or heterogeneity is evident, it should be taken into account in planning of geological exploration, determination of quality of raw materials, resources/reserves estimation, projecting of raw materials exploitation.

20

Metody badań niejednorodności energetycznej powierzchni katalizatorów i adsorbentów

Woszczyński P.

Wiadomości Chemiczne

|

2013

|

[Z] 67, 7-8

635--664

EN

The knowledge of the properties and a surface structure of catalysts and adsorbents is of great importance in the selection of these materials to the relevant objectives. Interesting structural information can be obtained in many ways, for example: with the use of spectroscopic or microscopic techniques or in direct examination of the adsorption isotherms. This article focuses on these last-mentioned methods, which can be a source of information on energy heterogeneity of the catalyst or adsorbent surface. Heterogeneity is usually determined by measuring adsorption isotherms of a selected adsorbate on the examined adsorbent, which is dependent of adsorbate coverage on the adsorbent relative to the equilibrium pressure under isothermal conditions. Among the many mathematical models describing this relationship particularly interesting is the adsorption isotherm model described by generalized integral Fredholm equation. The solution of this equation is density function with the assumed local isotherm model. There are different ways to solve the Fredholm equation, depending on measurement methods of obtained adsorption isotherms. For example, an application of static techniques (gravimetric or volumetric) needs to use advanced, sophisticated numerical methods for directly solving integral equations, other techniques (e.g. such as calorimetric or chromatographic) provide specific values that simplify these calculations. The resulting energy density function allows to observe active centers as peaks or inflections of the curve on the energy spectrum graph.