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1

Subdiffusive Behavior in Crowded Environments: Impact of Obstacle Mobility and Spatial Restrictions

Polanowski Piotr, Sikorski Andrzej

Computational Methods in Science and Technology

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2023

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Vol. 29, No. 1-4

27--35

EN

Biological systems are generally dense reaction-diffusion systems. Therefore, determining the mechanism of motion in such systems is of crucial importance in understanding their dynamics. Subdiffusive behavior is very common in biological systems but its origin usually does not have a clear explanation. One attempt to explain this behavior is the presence of randomly placed stationary obstacles in a medium filled with molecules of a certain medium. With an appropriate concentration of obstacles, the molecules of the medium cease to perform classic Brownian motions and motion becomes subdiffusive. This mechanism seems to be well documented in both simulations and experiments. The question arises whether a similar effect can be obtained in systems where obstacles are not stationary, but their mobility is drastically reduced comparing to medium molecules, or the reduction in mobility is combined with a limitation in movement (the movement of obstacles resembles, for example, the Orestein-Ulhenbeck movement). Is it possible to observe subdiffusion behavior in such a situation? We try to answer this question on the basis of Monte Carlo simulations based on the Dynamic Lattice Liquid (DLL) model. Based on the concept of cooperative movements, this model has a unique feature that allows one to take into account the correlation of movements between the elements that make up the examined system, which is important in the case of high densities due to the strict correlation of movements between the moving elements. The tests concern systems where obstacles were single beads whose mobility was changed with additional restrictions imposed on the displacement. It was shown that no entrapment of medium molecules was observed and a slight deviation from normal diffusion was also shown.

2

Experimental and Mesoscopic Lattice Numerical Investigation of Increase of Chloride Diffusivity Coefficient during Uniaxial Loading Model

Bui Truong Son, Pham Duc Tho, Tran The Truyen, Nguyen Thi Nu, Vu Minh Ngoc

Inżynieria Mineralna

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2020

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no. 2, vol. 1

23--30

EN

This paper presents experimental and simulation results of the change in the chloride diffusion coefficient of concrete C40 (f’c=40 MPa) during axial loading. Test Method for Electrical Indication was used to measure the chloride diffusivity of the concrete sample during the axial loading. A mesoscopic lattice model is proposed to describe the variation of chloride diffusion coefficient versus damage variable. In such a model, the domain of material is discretized randomly by using Voronoi tessellation for the transport element and Delaunay triangulation for a mechanical element. At the mesoscale, the concrete is constituted by three phases: aggregate, cement paste and ITZ, in which aggregate is assumed to be elastic while cement matrix and ITZ are represented by a damage model with softening. The experimental and numerical results show that in the first stage, without crack (s < 40%smax), the chloride diffusion coefficient remains almost constant, however in the crack initiation and propagation stage (s = 60-80%smax) chloride diffusion coefficient increases significantly. An empirical power model is also proposed to describe the increase of the chloride diffusion coefficient versus stress level and damage variable.

PL

W artykule przedstawiono wyniki doświadczalne i symulacyjne zmiany współczynnika dyfuzji chlorków betonu C40 (f’c = 40 MPa) podczas obciążenia osiowego. Do pomiaru dyfuzyjności chlorków próbki betonu podczas obciążenia osiowego wykorzystano metodę badania wskazań elektrycznych. Zaproponowano mezoskopowy model sieci krystalicznej w celu opisania zmiany współczynnika dyfuzji chlorków w funkcji zmiennej uszkodzenia. W takim modelu domena materiału jest dyskretyzowana losowo przy użyciu teselacji Voronoia dla elementu transportowego i triangulacji Delaunaya dla elementu mechanicznego. W mezoskali beton składa się z trzech faz: kruszywa, zaczynu cementowego i ITZ, w których zakłada się, że kruszywo jest elastyczne, natomiast osnowa cementowa i ITZ są reprezentowane przez model uszkodzenia ze zmiękczeniem. Wyniki eksperymentalne i numeryczne pokazują, że w pierwszym etapie, bez pęknięcia ((σ<40%σmax), współczynnik dyfuzji chlorków pozostaje prawie stały, natomiast w fazie inicjacji i propagacji pęknięcia (σ=60-80% σmax) współczynnik dyfuzji chlorków znacznie wzrasta. Zaproponowano również empiryczny model mocy opisujący wzrost współczynnika dyfuzji chlorków w funkcji poziomu naprężenia i zmiennej uszkodzenia.

3

Monte-Carlo Simulations of Two-Dimensional Polymer Solutions with Explicit Solvent Treatment

Polanowski P., Jeszka J. K., Sikorski A.

Computational Methods in Science and Technology

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2017

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Vol. 23, No. 4

305--316

EN

The static properties of two dimensional athermal polymer solutions with explicit solvent molecules were studied by Monte Carlo lattice simulations using the cooperative motion algorithm (CMA). The simulations were performed for a wide range of polymer chain length N (from 16 to 1024) and polymer concentration (from 0.0156 to 1.00). The results obtained for short chains (N < 256) were in good agreement with theoretical predictions and previous simulations. For the longest chains (512 or 1024 beads) some unexpected behavior in the dilute and semidilute regimes was found. A rapid change in the concentration dependence of the end-to-end distance, the radius of gyration and the chain asphericity was observed below a critical concentration of the microphase separation, ϕc = 0.6 (for N = 1024). At concentrations lower than _c, the chains tends to be more rod-like. Single chain scattering structure factors showed changes in the fractal dimension of the chain as a function of the polymer concentration. The observed phenomena can be related to the excluded volume of solvent molecules, which leads to a modification of chain statistics in the vicinity of other chains.

4

Spring method for modelling of particulate solid composed of spherical particles and weak matrix

Zabulionis D., Kačianauskas R., Rimša V., Rojek J., Pilkavičius S.

Archives of Civil and Mechanical Engineering

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2015

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Vol. 15, no. 4

775--785

EN

In the present paper, a possibility of an approximation of elastic particulate composite with a network of elastic springs that undertake only axial forces is considered. It is assumed that the springs are equivalent to two hemispheres interacting through a weaker interface member. In a frame of the suggested approach, the description of the composite is limited to translational degrees of freedom, therefore, only a normal interaction between the spheres was considered. The methodology for calculation of the axial stiffness of the elastic springs and obtained solutions of the stiffness in explicit form are the main novelty of the article. A comparison of the stiffnesses of the springs obtained by the proposed methodology and by the three dimensional Finite Element Method (FEM) has shown a good agreement between them in a wide range of the ratio of the modulus of elasticity of the particles and matrix at four different distances between surfaces of the particles. A possibility of the approximation of particulate composite by springs was tested and discussed in details by comparing results of a mechanical response of a sample (under three different loading cases) modelled as a three dimensional solid and as a system comprised of the springs. The solutions were obtained by the FEM.

5

Mechanical unfolding of Ddfln4 studied by coarse-grained knowledge-based cabs model

Kouza M., Jamroz M., Gront D., Kmiecik S., Koliński A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2014

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Vol. 18, No 4

373--378

EN

Mechanical unfolding of the fourth domain of Distyostelium discoideum fi lamin ( DDFLN 4) was studied using a CABS – coarse-grained knowledge-based protein model. Our study demonstrates that CABS is capable of reproducing the unfolding free energy landscape of protein unfolding and highlights an important role of non-native interacti ons in the protein unfolding process. The obtained three peaks in the force-extension profile suggest a four-state picture of DDFLN 4 protein unfolding and correspond reasonably to the results of the all-at om simulation in explicit solvent.

6

Effect of steel fibres on concrete behavior in 2D and 3D simulations using lattice model

Kozicki J., Tejchman J.

Archives of Mechanics

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2010

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Vol. 62, nr 6

465-492

EN

Quasi-static simulations of a concrete behaviour with steel fibres under uniaxial tension were carried out using a discrete irregular lattice model. Fibrous concrete was described at a meso-scale as a three-phase material composed of aggregate, cement matrix, steel fibres and interfacial zones between cement matrix and aggregate, and between cement matrix and steel fibres. The effect of the fibre interface strength, fibre volume, fibre orientation, fibre length and specimen size on the concrete behaviour was investigated. The results of two- and three-dimensional analyses were compared.

7

2D Lattice Model for Fracture in Brittle Materials

Kozicki J., Tejchman J.

Archives of Hydro-Engineering and Environmental Mechanics

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2006

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Vol. 53, nr 2

137-154

EN

The numerical simulations show the potential of a lattice discrete approach to model fracture during brittle materials in different two-dimensional quasi-static processes of loading behaviour. The 2D calculations were carried out for brittle specimens subject to uniaxial compression, uniaxial extension and shear. The effect of the specimen size on the global stress-strain diagram during uniaxial tension was also investigated. The advantages and disadvantages of the model were outlined.

8

The prediction of thermodynamic properties of systems formed by chain-like molecules using a cell-hole group contribution model

Hofman T.

Prace Naukowe Politechniki Warszawskiej. Chemia

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2003

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z. 71

3-165

EN

A group contribution model is developed for predicting of the configurational properties of the pure chain-like compounds and their mixtures. In the first sections a detailed description of the existing lattice models of fluids is given. A special attention is put to the hole models. As the first step in the model development, the Smirnova-Victorov model36 is applied for predicting of the properties of pure n-alkanes, aliphatic monoethers and 1-chloroalkanes and their mixtures with ^z-alkanes. The properties include: densities as the functions of pressure and temperature for liquids and gases, saturated vapor pressures, enthalpies of vaporization, mixing functions, phase equilibria in binary systems. An inability to predict liquid densities under high pressures properly, has lead to a formulation of a new cell-hole model. It has been tested for the above mentioned data. A significant improvement is observed for the high-pressure liquid densities, saturated vapor pressures and the high-pressure vapor-liquid equilibria. Keywords: thermodynamics, equation of state, group contribution, prediction, lattice model, cell model, hole model, fluid-phase equilibrium, mixing functions, P-p-T properties

PL

Głównym celem pracy było stworzenie modelu termodynamicznego, umożliwiającego przewidywanie pełnego zbioru właściwości konfiguracyjnych czystych substancji złożonych z cząsteczek łańcuchowych i ich mieszanin. W pierwszej części podsumowano aktualny stan wiedzy na temat siatkowych modeli płynów, ze szczególnym uwzględnieniem modeli dziurowych. Dyskusja możliwości istniejących teorii została oparta na modelu Smimowej i Wiktorowa36, którego użyto do przewidywania szeregu właściwości czystych n-alkanów, monoeterów alifatycznych i 1-chloroalkanów oraz ich mieszanin z n-alkanami (gęstości w funkcji ciśnienia i temperatury dla cieczy i gazów, prężności pary nasyconej, entalpii parowania, funkcji mieszania, równowag fazowych w układach dwuskładnikowych). Wypływające stąd wnioski, a przede wszystkim nieprawidłowy opis gęstości cieczy pod bardzo wysokimi ciśnieniami, doprowadziły do zdefiniowania nowego modelu, łączącego cechy modeli dziurowych i komórkowych. Jego wyprowadzenie, zastosowanie do tego samego zbioru danych oraz dyskusja wyników, są zawarte w trzech kolejnych rozdziałach. Nowy model daje zdecydowanie lepszą dokładność przede wszystkim dla wysokociśnieniowych gęstości cieczy, prężności pary nasyconej i równowag ciecz-para pod wysokimi ciśnieniami. Słowa kluczowe: termodynamika, równanie stanu, udziały grupowe, przewidywanie, model siatkowy, model komórkowy, model dziurowy, równowaga fazowa, funkcje mieszania, właściwości P-p-T.

9

Self-Assembling Systems in Restricted Geometry

Ciach A., Tasinkevych M.

Polish Journal of Chemistry

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2001

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Vol. 75, nr 1

1-28

EN

Results obtained within Ciach-Hoye-Stell model of oil-water-surfactant mixtures in restricted geometry are reviewed. Special attention is paid to ordering effects of a surface (or two parallel surfaces) close to phase boundaries between lamellar and microemulsion or water-rich phases. Relations between the structure of the confined self-assembling system and the measurable quantities are discussed. Predictions of the Ciach-Hoye-Stell model are compared with Landau-Ginzburg and membrane theories and with experimental results.

10

Models of the Hydrophobic Attraction

Widom B.

Polish Journal of Chemistry

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2001

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Vol. 75, nr 4

507-515

EN

Some recently proposed models of hydrophobic attraction, equivalent to the Ising model of ferromagnetism, are described and their properties reviewed. They are such that the accommodation of a hydrophobic solute in the solvent is energetically favorable but even more unfavorable entropically, which is believed to be the basic mechanism of hydrophobicity in water solution. The effective attraction between pairs of solute molecules as mediated by the solvent is calculated, as is the deviation from additivity in the interactions among three or more. The very low solubilities of the solutes in the model solvents are also calculated. In a different model, based on a phenomenological free energy leading to a closed-loop solubility curve in the temperature-composition plane, one finds the same very great increase in heat capacity on dissolving a hydrophobic solute as is found in experiment.

11

Lattice Cluster Theory for Copolymer Blends : General Theory in the Incompressible System, Long Chain Limit

Dudowicz J., Freed K. F.

Polish Journal of Chemistry

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2001

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Vol. 75, nr 4

527-545

EN

The lattice cluster theory is developed for binary blends of two structured monomer copolymers in the simplifying limit of an incompressible system and high molecular weights. The major advance in the present theory is the inclusion of nonrandom mixing effects that lead to a monomer sequence dependence of the Helmholtz free energy without the introduction of new adjustable parameters beyond those present in descriptions of binary homopolymer blends formed from the constituent monomers. Equivalently, the sequence dependent contributions are shown to emerge from a proper determination of the "surface fractions" in individual copolymer chains. The general theory applies to blends of random copolymer, diblock copolymers, alternating copolymers, as well as of copolymers with kinetically controlled monomer sequences. The theory is illustrated for purely random copolymer blends of deuterated and hydrogenated polybutadienes, where the computed phase boundaries depart qualitatively from those predicted by random copolymer Flory-Huggins theory.

12

Diffusion ona Silicalite Lattice Model

Bellemans A., Bouyermaouen A.

Polish Journal of Chemistry

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2001

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Vol. 75, nr 4

501-506

EN

A lattice model is proposed for describing the diffusion of small molecules in silicalite, as a special example of zeolite. The lattice structure matches the interlacing of the silicalite channels and the molecules hop randomly from site to site according to simple rules. The diffusion of a single molecule is treated exactly. The ability of the model to meet more complicated situations is briefly discussed.