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The self-diffusion of parabens (methylparaben, propylparaben) and tetramethylsilane in the binary solvents carbon tetrachloride – co-solvent (methanol‑d4, acetone‑d6) has been investigated by the pulsed gradient spin-echo nuclear magnetic resonance (PGSE NMR) method in the range of temperatures from 278 to 318 K. The self-diffusion coefficients of paraben and tetramethylsilane increase as the concentration of acetone‑d6 increases and have a minimum for paraben and an inflection point for tetramethylsilane when the methanol‑d4 concentration increases. Based on the Stokes-Einstein equation it is shown that the paraben hydrodynamic radius in the binary solvent acetone‑d6 – carbon tetrachloride is practically independent of the acetone‑d6 concentration and has a maximum in the binary solvent methanol‑d4 – carbon tetrachloride. This behavior in both cases is explained by the paraben self-association degree and the heteroassociation degree of paraben – co-solvent.

Solvation of methylxanthines (caffeine, theophylline, and theobromine) in carbon tetrachloride–methanol mixtures is studied by means of molecular dynamics over the range of concentrations under standard conditions. Methylxanthine molecules form hydrogen bonds with methanol through two oxygen atoms and one nitrogen atom and interact weakly through a hydrogen atom bound to the carbon of the imidazole ring. The distribution of the number of hydrogen bonds formed between different methylxanthine and methanol atoms is independent of the concentration of the polar co-solvent. At low amounts of methanol, methylxanthines tend to form stacking aggregates.

The chemical shifts and self-diffusion coefficients of methylxanthines (caffeine, theophylline and theobromine) and tetramethylsilane in the binary solvent methanol‑d4–carbon tetrachloride have been investigated by 1H NMR and 1H PGSE NMR methods at the temperatures of 298, 303 and 313 K. The concentration dependences of tetramethylsilane self-diffusion coefficients have an inflection point and the concentration dependences of methylxanthines self-diffusion coefficients have a minimum in the region of 0.2–0.4 mol fraction of methanol‑d4. The self-diffusion coefficient values for theophylline and theobromine are the same and lower than the corresponding value for caffeine. It has been found that rise in the methanol concentration leads to an increase in the chemical shifts of the imidazole ring protons (CH) in the methylxanthine molecule, which indicates a change in the methylxanthines molecular association degree. The differences in the concentration dependences of the self-diffusion coefficients were interpreted by taking into account the molecular association within the framework of the Stokes-Einstein equation.

The self-diffusion of p-coumaric and caffeic acids in a binary tetrachloromethane–acetone-d6 solution at low concentrations of the dissolved compound is studied via pulsed field gradient-spin echo 1H NMR at 278 and 298 K. According to the results, the self-diffusion coefficients of caffeic acid are lower than those of p-coumaric acid. The hydrodynamic radii of the acids in tetrachloromethane, calculated using the Stokes–Einstein equation, are lower than those in acetone-d6. This behavior is due to an increase in the degree of acid–acetone heteroassociation. Molecular association is also apparent from changes in the chemical shifts of protons in carboxyl and hydroxyl groups within molecules of the studied acids.

An experimental and theoretical study of the dissolving power of the binary solvent consisting of inert (carbon tetrachloride) and self-associated (methanol) components has been carried out. According to the experimental data, the dependence of the caffeine solubility on the composition of the binary solvent has a maximum in the region of 0.5 mole fraction of the cosolvent. The maximum is also observed for the concentration dependence of the Gibbs energy of solvation calculated within the framework of molecular dynamics (MD) simulation. Within the framework of the ASL (Associated Solution + Lattice) model, it was shown that the main contribution to solubility is made by the caffeine – methanol heteroassociation. The second largest contribution is defined by non-specific intermolecular interactions in the system. A negative contribution is made by the difference in the sizes of the molecules of the mixture components.

The self-diffusion coefficients of acetone and chloroform in a binary acetone–chloroform mixture at 298 K are determined via pulsed field gradient NMR spectroscopy. It is estimated that the hydrodynamic radii of the mixture’s components, calculated using the Stokes–Einstein equation, grow as the concentrations of the components fall. It is shown that such behavior of hydrodynamic radii is due to acetone–chloroform heteroassociation. The hydrodynamic radii of monomers and heteroassociates in a 1: 1 ratio are determined along with the constant of heteroassociation, using the proposed model of an associated solution.

Two approaches to the calculation of air subdomains are compared in this paper, i.e. the use of imaginary points and explicit allocation. They are completely mathematically equivalent to each other, but there is a difference in their complexity of implementation, complexity of parallelization and computational resources needed for performing calculations and their applications. The explicit allocation of air subdomains requires a lot of separated grids, the use of imaginary points requires more memory and calculation time. It is of interest to estimate how important the contribution of interfaces between the grids is. Usually, estimates of the memory and time costs are calculated based on the geometric characteristics of the model under consideration. In this paper, the corresponding formulas are presented for the case of full wave simulation of the impact of seismic waves on a multi-storey building. The question under consideration was whether theoretical estimates of this type are valid. In order to do this we consider 7 building types, i.e. an underground shelter, a barn, barracks, a summer cottage, a residential building of an old building type, a residential building of a new building type, and a skyscraper. We use a solid-state drive memory device. The results of the studies can also be extrapolated to the case of direct problems in geophysics to describe, for example, a geological medium containing gas-saturated pores or karst areas.

Destruction is occurred in wide variety of applied problems: collisions, dynamic load of materials, seismic influence on ground facilities, railway defects, etc. Nowadays, there are a lot of different mechanical models that describe the destruction process. In addition to the failure criteria, it is important to take into account correctly the changes in rheology of destroyed material. Due to these reasons, it is important to have the ability to simulate the process of destruction of arbitrary material. In this paper, the method for simulation is proposed. It is based on the numerical solution of govern system of elastic equations by the grid-characteristic method. After each step of elastic scheme, special corrector was applied to each damaged nodes of numerical grid to describe correctly dynamic behavior of fractured material. To illustrate the application of proposed technique, a set of problems was solved. The problem of collision between the metal hammer and glass plate was successfully solved in 2D and 3D cases. The developed software allows to analyze not only static image of fractured material but to calculate full stress tensor in a sequence moments of time. The extension of this approach may significantly extend the area of application of numerical simulation.

Recent researches have shown that the damaged areas, calculated using various failure criteria for materials with complex heterogeneous structure are not always consistent with physical experiments and with each other. In this paper, we compare two failure criteria, i.e. the principal stress criterion and the von Mises yield criterion. Also, we compare two models of destruction formation, i.e. the model of fractures and sand model. Using the wave dynamics analysis, we explain the difference in the calculated zones of destruction. We indicate what differences in elastic wave phenomena cause the difference in the calculated fracture zones. We assume that further study of the connection between wave phenomena and destruction of materials will allow to develop more precise failure criteria. To carry out the research, we applied numerical modeling of spatial dynamic elastic wave processes in a nuclear power plant and enclosing rocks. We use the grid-characteristic method on combined regular and structural hexahedral grids to describe the complex shape of the dome of the nuclear power plant with minimal computational costs. Moreover, in this work, we consider an approach for calculating the contribution of dynamic elastic wave phenomena to seismic stability of facilities. This technique can be especially useful in the development and testing of seismic insulation of buildings. We propose a failure formation model that takes into account the contribution of static loads and dynamic loads separately.

In this work we measured self-diffusion coefficients of 5 drugs (aspirin, caffeine, ethionamide, salicylic acid, and paracetamol) and 11 biologically active compounds of similar structure in deuterated water and 1-octanol by NMR. It has been found that an increase in the van der Waals volume of the molecules of the studied substances result in reduction of their diffusion mobility in both solvents. The analysis of the experimental data showed the influence of chemical nature and structural isomerization of the molecules on the diffusion mobility. Apparent permeability coefficients of the studied compounds were determined using an artificial phospholipid membrane made of egg lecithin as a model of in vivo absorption. Distribution coefficients in 1-octanol/buffer pH 7.4 system were measured. For the first time the model of the passive diffusion through the phospholipid membrane was validated based on the experimental data. To this end, the passive diffusion was considered as an additive process of molecule passage through the aqueous boundary layer before the membrane and 1-octanol barrier simulating the lipid layer of the membrane.

The self-diffusion of caffeine and methanol in the ternary mixtures methanol–carbon tetrachloride (binary solvent)–caffeine (solute) have been investigated by the pulsed gradient spin-echo nuclear magnetic resonance (PGSE NMR) method at the temperatures of 298 and 313 K. The dependences of self-diffusion coefficients on the composition of binary solvent have a minimum in the region of 0.2 mol fraction of methanol. It has been found that self-diffusion of caffeine is mainly determined by the binary solvent viscosity. As it has been shown, in order to describe the experimental data correctly, the molecular association model of methanol should include cyclic tetramers. The self-association constants, the enthalpies of hydrogen bonds formation and the microfriction factors of the chain associates and the cyclic tetramers of methanol have been estimated.

The study of solvation of three phenolic acids, 3,4,5-trihydroxybenzoic acid (gallic acid), 3,4-dihydroxybenzoic acid (protocatechuic acid), and 4-hydroxy-3,5-dimethoxybenzoic acid (syringic acid), in pure, methanol-modified and acetone-modified (0.03 and 0.06 mol fraction) supercritical (SC) carbon dioxide has been carried out by computational methods. Structural features of hydrogen-bonded complexes formation in modified SC media have been researched by using classical molecular dynamics at different densities corresponding to the experimental pressures 20 and 30 MPa and temperatures from 313 to 333 K. The results obtained have revealed that an increase of fluid density and cosolvent concentration provide increasing the average number of hydrogen bonds formed by the solute with cosolvent. Ab initio calculations of formation energy of hydrogen-bonded complexes solute – cosolvent have been performed. Solvation free energy of the phenolic acids in SC CO2 with and without cosolvents was evaluated by means of the Bennett’s acceptance ratio method. The solvation free energy has been found to be strongly dependent on the number of hydrogen bonds solute – cosolvent. Cosolvent-induced solubility enhancement values were also calculated. The results indicate that the increase in solubility of the phenolic acids is observed by passing from the pure SC CO2 through acetone-modified to methanol-modified solvent. Moreover the order of cosolvent-induced solubility enhancement magnitude depends on the number of hydrogen bonds solute – cosolvent and greatly on the concentration of the latter.

The effect of concentration on the self-diffusion coefficients of acetylsalicylic acid and methyl salicylate in methanol-d4 is investigated in the temperature range of 278–318 K using NMR. It is found that the self-diffusion coefficients increase along with temperature and fall as concentration rises. Within the limit of an infinitely dilute solution, the effective radii of solute molecules, calculated using the Stokes–Einstein equation shrink as the temperature grows. It is shown that the observed reduction of effective radii is associated with an increase in the fraction of solute monomers as the temperature rises. The physicochemical parameters of heteroassociation of acetylsalicylic acid and methyl salicylate with methanol are determined.

Self-diffusion of parabens (methylparaben and propylparaben), phenolic acids (syringic and gallic acids) and their derivative (protocatechualdehyde), hydroxycinnamic acids (caffeic, ferulic, sinapic, and p-coumaric acids), and tetramethylsilane in acetone has been investigated by the pulsed gradient spin-echo nuclear magnetic resonance (PGSE NMR) method and molecular dynamics simulation in ambient conditions. The self-diffusion coefficients obtained by the experimental and theoretical methods are in good agreement with each other. A detailed analysis of the average number of solute – acetone hydrogen bonds has made it possible to trace the influence of the molecular heteroassociation on the self-diffusion of the aromatic compounds. The degree of influence of solute – acetone molecular association on the solute self-diffusion defined as the ratio of the solute self-diffusion coefficient to the self-diffusion coefficient of its monomer has been calculated using the Stokes-Einstein equation. It has been found that for a number of aromatic compounds with the same type and number of functional groups, the parameter expressing the degree of influence of molecular association has similar values. This fact has allowed us to calculate the self-diffusion coefficients of the compounds in the given series at a known self-diffusion coefficient value of one of the series members.

Numerical modeling of dynamic wave processes in heterogeneous media allows to investigate the earthquake stability of different constructions. The aim of this work is to study the earthquakes impact on the ground buildings and underground facilities. The use of grid-characteristic method makes possible to take into account the physics of arising wave processes. The use of systems of hierarchical grids allows to perform a calculation of seismic waves directly from the earthquake source to the ground buildings and underground facilities. The arising area of cracks in this ground building (two-storied houses) at different times from different types of seismic waves is studied. Also the impact of earthquake on the underground facilities is considered. The dynamical arising of cracks and destruction into the underground facilities made from different types of reinforced concrete due to the impact of different types of seismic waves is investigated in this paper. The results demonstrate a possibility of investigation earthquake stability of underground facilities and living buildings using modeling of seismic waves propagation directly from the earthquake centers.

Analysis of the experimental data on the solubility of methylxanthines (theophylline and theobromine) in supercritical (SC) solvent CO2–methanol at various concentrations of methanol within the framework of the ASL model (Associated Solution + Lattice) based on molecular association theory and the simple lattice model is presented. Hetero-association of methylxanthines with the molecules of methanol is studied by means of 1H NMR spectroscopy at 313 K. The contribution of molecular association to the solubility of methylxanthines in the mixed SC solvent CO2–methanol is analyzed. It is shown that the presence of NH group in the molecule of methylxanthine, when passing from caffeine to theophylline or theobromine, leads to an increase of the contribution of the component related to molecular association to solubility.

Hydrogen-bonded complexes of acetylsalicylic acid with polar co-solvents in supercritical carbon dioxide, modified by methanol, ethanol, and acetone of 0.03 mole fraction concentration, are studied by numerical methods of classical molecular dynamics simulation and quantum chemical calculations. The structure, energy of formation, and lifetime of hydrogen-bonded complexes are determined, along with their temperature dependences (from 318 to 388 K at constant density of 0.7 g cm−3). It is shown that the hydrogen bonds between acetylsalicylic acid and methanol are most stable at 318 K and are characterized by the highest value of absolute energy. At higher supercritical temperatures, however, the longest lifetime is observed for acetylsalicylic acid–ethanol complexes. These results correlate with the known literature experimental data showing that the maximum solubility of acetylsalicylic acid at density values close to those considered in this work and at temperatures of 318 and 328 K is achieved when using methanol and ethanol as co-solvents, respectively.

A comprehensive study of the hydrogen-bonded complexes of protocatechualdehyde – acetone formed in an inert solvent was carried out. Concentration dependences of the 1H NMR chemical shifts of protocatechualdehyde in carbon tetrachloride – acetone‑d6 mixtures were obtained. The most probable structures of hydrogen-bonded protocatechualdehyde-acetone complexes were determined by means of all-atomic molecular dynamics simulation. Using the GIAO/DFT (Gauge-Independent Atomic Orbital/Density Functional Theory) approach, the proton chemical shifts of the complexes were calculated within the framework of the (если она не единственная такая, то a) continuum model of the solvent, as well as with an explicit solvent. The parameters obtained from quantum-chemical calculations were used to interpret the experimentally observed dependences. It is shown that protocatechualdehyde forms predominantly hydrogen-bonded complexes with a composition of 1:1 in a binary solvent. The hydrogen atom of the hydroxyl group in the para-position takes part in the formation of the intermolecular hydrogen bond with acetone, while the hydrogen atom of the hydroxyl group in the meta-position is involved in the formation of an intramolecular hydrogen bond.

The tetramethylsilane (TMS) self-diffusion coefficients in the binary solvent carbon tetrachloride (CTC) – acetone-d6 (A-d6) have been obtained by the pulsed gradient spin-echo nuclear magnetic resonance (PGSE NMR) method at 278, 298, and 318 K. The TMS self-diffusion coefficients increase as the A-d6 concentration and temperature become higher. The temperature dependences of the TMS self-diffusion coefficients at various concentrations of the binary solvent have been analysed based on the random discrete displacements model of self-diffusion presented in this paper. Within the framework of the proposed model, it is shown that the Arrhenius type of the temperature dependence of the self-diffusion coefficient (which is observed for TMS in this work) is a special case when the diffusion activation energy ED > kBT. In the opposite case, the temperature dependence of the self-diffusion coefficient tends to the form of the equation obtained for an ideal gas.

The caffeine–methanol association constant at 313 K has been determined by 1H NMR spectroscopy. The caffeine solubility in the supercritical carbon dioxide (SC-CO2)–methanol mixed solvent has been calculated using the association constant experimentally measured by NMR in the framework of the associated solution + lattice (ASL) model, which is based on the theory of molecular association and a simple lattice model. Individual contributions to the solubility have been determined, and the relative role of various factors determining the solubility of caffeine in the mixed solvent has been analyzed. The caffeine solubility as a function of the methanol content of the SC-CO2–methanol system is predicted to pass through a maximum.

In this chapter, the application of the grid-characteristic method to solving seismic prospecting problems is considered. The characteristic seismogeological models, including Marmousi and SEG/EAGE Salt Model, are considered, wave patterns and seismograms are presented. The cases of 2D and 3D modelling, curvilinear boundaries between geological layers, fractured layers taking into account the topology of the Earth’s surface, construction of seismograms for both 2D and 3D seismic survey cases, and vertical seismic profiling are considered. The investigation of the performance of a software complex developed on the basis of a grid-characteristic method for modelling hydrocarbon deposits of various computational complexity was performed. Also, faults zones of a different nature, both about the length of the faults and the type of geological environment inside these faults, was studied. A detailed analysis of spatial dynamic wave patterns is carried out, and predictive conclusions are made about the nature of the seismograms obtained, which were actually confirmed in the respective seismograms. It will be shown in this Chapter that typical analytical tests cannot guarantee that software gives an opportunity for the geologist to develop right conclusions. This problem can be solved only by understanding the physical basis of the phenomena under consideration and the peculiarities of the operation of the difference methods used in the software, simultaneously. This suggests the method called Wave Logica, fragments of which are also given in the Chapter.

A method based on the statements of molecular association theory and a simple lattice model (ASL = Associated Solution + Lattice) is used to calculate the solubility of a series of porphyrin macrocycles (blood porphyrins) in binary solvents (tetrachloromethane-ethyl acetate, tetrachloromethane-methanol). Separate contributions to solubility are identified and the relative role of different factors determining the solubility dependence on the mixed solvent composition is analyzed. The calculated solubility values are in good agreement with the experimental data obtained for the studied systems by the isothermal saturation method with a spectrophotometric control of concentrations.

The problem of numerical modelling elastic wavefields in fractured media plays an important role in interpretation of seismic data. The classical approach is based on the use of the averaged models with elastic parameters depending on the internal structure of the medium. Unfortunately, this approach is limited to the predefined types of periodical structures and it cannot describe the crack-crack interactions. Recently, a new approach based on the direct solution of acoustic equations inside the crack was proposed. However, the main drawback of this method is the enormous computational required even with the use of the modern HPC systems. In this paper, we present a novel approach based on numerical solution of the elastic equations with physically correct conditions on the boundaries of the cracks. This approach allows us to describe randomly oriented thin cracks without a drastic increase of computational time. We have demonstrated that Krauklis waves can be achieved by this approach as well. The results of accurate direct simulation of seismic wavefields in heterogeneous fractured media can be used for improved analysis of the seismic data.

The solubility of CoIII 5,10,15,20-tetra(4-carboxyphenyl)porphyrin and axial complex with methylimidazole in the mixtures of triethyleneglycol-water and tetraethyleneglycol-water was measured in the whole range of polyethyleneglycols (PEG) fractions at 298.2 K using the isothermal saturation method. The composition of the mixture at which the maximal solubility was observed has been revealed. The cosolvent force of PEGs was quantified according to the linear logarithmic model proposed by Yalkowsky applied in the ranges (cosolvent volume fraction, f): 0 ≤ fPEG ≤ 0.24 in triethyleneglycol-water and 0 ≤ fPEG ≤ 0.3 in tetraethyleneglycol-water mixtures. A mathematical approach based on the tenets of the molecular association theory and a simple lattice model (ASL = association solution + lattice) was used to estimate the solubility values of the investigated porphyrins in water-PEG solutions. The ASL model appeared to present a simple means of estimating the solubility of CoIII5,10,15,20-tetra(4-carboxyphenyl)porphyrin and axial complex with methylimidazole in polyethyleneglycol-water mixtures using a single variable parameter.