Calculation Algorithm Research Articles

Triply Bifurcations and Metric Universalities in 1D Trimodal Maps

The famous Feigenbaum’s constants such as scaling factor and convergence rate can be measured and recomputed in unimodal maps, one of the methods is by the n-tupling bifurcations to chaos and parameter calculation algorithm which are called star transformation and word-lifting technique respectively. In the paper, we presented a kind of simple triply star transformation rule and the corresponding proof of admissible three super-stable kneading sequences (TSSKS), a few of TSSKS to chaos by triply bifurcations and the metric universalities are investigated.

Efficient quantum mechanical minimum free energy path calculation by combining path integral hybrid Monte Carlo and climbing image nudged elastic band methods, and its application to the addition reaction of hydrogen isocyanide to formaldehyde.

We propose an efficient algorithm for a minimum free energy path calculation based on the path integral hybrid Monte Carlo (PIHMC) method by combining the climbing image-nudged elastic band (CI-NEB) and the thermodynamic integration (TI) methods. Here, the CI-NEB and the TI methods are used to find a transition state along the reaction path and evaluate the free energy path, respectively. Our algorithm is applied to the Walden inversion reaction of the hydronium ions (H3O+). The numerical results show that the computational effort by our algorithm is significantly reduced compared to that of the previously proposed algorithm combining PIHMC without losing accuracy. We also demonstrate the importance of temperature and isotope effects on the addition reaction of hydrogen isocyanide to formaldehyde. In this reaction, the nuclear quantum effect causes the structural change at the TS and decreases the energy barrier.

RASCBEC: Raman spectroscopy calculation via born effective charge

We present a reformulated algorithm for ab initio calculations of Raman spectra for large systems by applying an external electric field, and complement it by a code implementation we name RASCBEC. With the RASCBEC code, we have successfully benchmark crystalline materials and compute Raman spectra of large molecules, and amorphous oxides. Our results demonstrate a remarkable level of agreement with the results from other commonly used codes as well as the experimental data. The electric field approach for Raman spectra calculation is designed to overcome the computational challenges associated with the conventional method, which requires calculating the macroscopic dielectric tensor at numerous molecular geometries. This approach is favored because it can significantly reduce computational time. We reformulated this method by obtaining the Raman intensity from the first-order derivative of the Born Effective Charge (BEC), which is computed directly from vasp (the Vienna Ab Initio Simulation Package). This differs from other electric field-based methods that calculate Raman intensities as the second-order derivative of force with respect to the electric field. By reducing the order of derivatives, we can avoid numerical noise and accuracy concerns. Additionally, since forces are often very small numbers, taking the derivative of BEC is numerically more stable, allowing our method to be applied to a broader range of material parameters. This advantage makes RASCBEC particularly beneficial for large molecules and extensive amorphous systems.

К РАСЧЕТУ ЖИДКОСТНЫХ ТАРЕЛЬЧАТЫХ СЕПАРАТОРОВ С ПАРАБОЛИЧЕСКИМИ ВСТАВКАМИ

The object of the study is liquid disk separators with curvilinear inserts, which are described by equations of the type . The study was conducted to study the effect of the insert shape on the intensity of the centrifugal force on the liquid flow, as well as on the length of the sedimentation path (or float) of dispersed medium particles. The efficiency of clarification of dispersed media is predetermined by two design characteristics of the device - the length of the particle sedimentation path and the direction of the centrifugal force relative to the walls of the curved channel. For parabolic inserts, the distance between them and the angle of inclination of the walls are variable quantities. To calculate these quantities, nonlinear equations are constructed and an algorithm for numerical calculations is proposed. The calculation results are presented as graphical dependencies of the above parameters along the channel length. The calculations were performed for paraboloids of revolution with degrees m=2, 3 and 4 at coefficient a=2, 3 and 4. As the coefficient a increases, the distance between the inserts decreases. The influence of the exponent m on the gap between the paraboloids of revolution is more complex. The gap size along the channel length decreased from 3 cm to several millimeters. The angle of inclination of the walls relative to the rotation axis decreased in the range from 70 to 10 degrees. As the parameters a and m increase, this angle decreases, therefore, the component of the centrifugal force directed perpendicular to the channel wall increases. The equations of motion of the liquid system were solved by the method of equal flow surfaces, according to which the flow is represented as several layers with their own velocities. At the inlet section, the velocity diagram develops from a flat profile to a parabolic form. As a result of the action of the centrifugal force, an asymmetry of the velocity profile is observed. The obtained results can be used to justify the geometric characteristics of a plate separator with parabolic inserts and to coordinate them with the flow regime parameters.

Evaluation of Dose Calculation Algorithms Accuracy for ISOgray Treatment Planning System in Motorized Wedged Treatment Fields

Abstract Background: Different dose calculation methods vary in accuracy and speed. While most methods sacrifice precision for efficiency Monte Carlo (MC) simulation offers high accuracy but slower calculation. ISOgray treatment planning system (TPS) uses Clarkson, collapsed cone convolution (CCC), and fast Fourier transform (FFT) algorithms for dose distribution. This study’s primary goal is to evaluate the dose calculation accuracy for ISOgray TPS algorithms in the presence of a wedge. Methods: This study evaluates the dose calculation algorithms using the ISOgray TPS in the context of radiation therapy. The authors compare ISOgray TPS algorithms on an Elekta Compact LINAC through MC simulations. The study compares MC simulations for open and wedge fields with ISOgray algorithms by using gamma index analysis for validation. Results: The percentage depth dose results for all open and wedge fields showed a more than 98% pass rate for points. However, there were differences in the dose profile gamma index results. Open fields passed the gamma index analysis in the in-plane direction, but not all points passed in the cross-plane direction. Wedge fields passed in the cross-plane direction, but not all in the in-plane direction, except for the Clarkson algorithms. Conclusion: In all investigated algorithms, error increases in the penumbra areas, outside the field, and at cross-plane of open fields and in-plane direction of wedged fields. By increasing the wedge angle, the discrepancy between the TPS algorithms and MC simulations becomes more pronounced. This discrepancy is attributed to the increased presence of scattered photons and the variation in the delivered dose within the wedge field, consequently impacts the beam quality. While the CCC and FFT algorithms had better accuracy, the Clarkson algorithm, particularly at larger effective wedge angles, exhibited greater effectiveness than the two mentioned algorithms.

Effect of water on asphaltene-precipitation behavior of CO2-crude oil mixtures during CCUS processes

Water can extensively exist in reservoirs. Since the solubility of CO2 in water is not negligible under reservoir conditions, the aqueous phase should also be considered during the phase-behavior simulations of the CO2 flooding process. With the presence of an asphaltene phase and an aqueous phase, four phases (i.e., a vapor phase, a hydrocarbon phase, an asphaltene phase, and an aqueous phase) can coexist at a given thermodynamic equilibrium. In this study, a robust and efficient four-phase vapor–liquid-liquid-aqueous equilibrium calculation algorithm is applied to conduct four-phase vapor–liquid-asphaltene-aqueous equilibrium calculations by assuming asphaltene is a dense liquid phase. The algorithm is first validated by comparing the calculated asphaltene precipitation data with the presence of water against the experimental asphaltene precipitation data documented in the literature. The validation shows that the calculation results agree well with the experimental data, indicating that such algorithm can make reliable predictions of asphaltene precipitation with the presence of water. The validated algorithm is subsequently used to construct pressure–temperature (PT) and pressure-composition (Px) phase diagrams to study the effect of water on asphaltene precipitation under different pressure/temperature conditions and under the injection of CO2. We can conclude from the calculated results that although adding water to the reservoir fluid can cause obvious changes in the PT phase diagrams, it does not have a noticeable influence on the asphaltene precipitation onsets. However, it can be seen from the calculated Px phase diagrams that the presence of water during the CO2 flooding process can make asphaltene precipitated more easily. The maximum amount of asphaltene precipitation is decreased by the presence of water due to the fact that a considerable amount of CO2 is dissolved in the aqueous phase instead of the liquid hydrocarbon phase.

Enhancing the global and local robustness of networks: A network motif-based approach

In the real world, both natural and artificial networks, may experience degradation or failure due to faults or external perturbations, which may negatively impact people's lives. Therefore, optimizing network robustness to maintain functionality under such conditions is a crucial research area. With the deepening of network robustness research, more and more studies have found that the local robustness of networks is related to network motifs. Considering the optimization of the robustness based on the global network properties (global robustness) and local robustness of the network, this paper proposes a motif-based edge rewiring algorithm (MBER), which includes the Edge Selection Algorithm, Edge Rewiring Algorithm, Simplified Calculation Algorithm for the Number of Major Network Motifs and Adjusted Nondominated Sorting Algorithm. We optimize four synthetic networks and four real-world networks using MBER and four other optimization algorithms, respectively. The results demonstrate that the MBER algorithm is more effective in enhancing the global and local robustness of networks. Additionally, we analyse the time complexity of MBER and four other optimization algorithms, revealing that the MBER algorithm exhibits the highest time complexity due to its consideration of local robustness. This paper can provide a reference for enhancing the robustness of real-world networks more comprehensively and enriches the research on network robustness enhancement.

Formulations and numerical techniques for computation of acoustic pressure and its gradient by integral method

Starting from the Ffowcs Williams-Hawkings surface integral formulation for a moving medium, the article proposes rather simple expressions for the radiated pressure and its gradient in the time domain, that are valid for solid or porous, fixed or moving integration surfaces. Moreover, these original expressions allow calculations with integration surfaces in supersonic motion (such as rotating surfaces around propellers or rotors). Versions dedicated to fixed integration surfaces are also proposed. The usual locally compact and the fully non-compact integration techniques are recalled, with, for both, a detailed description of efficient calculation algorithms. Particular attention is devoted to the order of precision of the calculations. The time derivation techniques and integration schemes used in this study lead to a theoretical second order that can easily be increased for the locally compact integration method. The results of these expressions and integration methods are compared to the analytical solution for the case of a fixed monopole and for that of a rotating monopole. They clearly show the benefit of the direct gradient calculation over a calculation by finite differences of the pressure around the observation point, particularly for broadband signals.

Identifying the parameters and operation modes of the cavitation apparatus taking into account the influence of the processing material

The object of this study is dynamic pressure that takes into account the main parameters of technological process. Under real conditions of cavitation apparatus operation, a discrepancy between actual and calculated parameters of 30–50 % was found, which significantly reduces the efficiency and quality of material processing. The problem was solved through a joint study of the movement of the acoustic apparatus and the technological environment as a single structured system taking into account the influence of materials. This is a peculiarity of the approach and distinctive features of the results in comparison with existing ones, in which the research was conducted separately for the processing material and the cavitation apparatus. The model proposed in the work reflects the elastic, inertial, and dissipative parameters in the equations of motion, provided that their changes are taken into account, both in the acoustic apparatus and in the technological material. This approach has made it possible to reveal the physical essence of the interaction and analytically describe their joint movement. The resulting analytical dependences made it possible to calculate and propose numerical values of vibration amplitudes in the range of 4.0...20.0 μm, sound pressure values in the range of 5.0...30.0∙105 Pa for media with a viscosity of (10–200)∙10-3 Pa∙s. With the set value of the amplitude, it is possible to assign the necessary parameters for the implementation of the cavitation process. The developed calculation algorithm ensures the reliability of the accepted models and parameters of the cavitation apparatus. The proposed approach of joint study of the movement of the acoustic apparatus and the environment is expedient to use for the practical implementation of ultrasonic treatment. In particular, such processes as dispersion, emulsification, mixing, extraction, and others, in order to increase their efficiency

Scalar and vectorized implementations of the density functional theory via Geant4 and GeantV project

In this paper, we present the implementation of the Density Functional Theory (DFT) method using the Geant4-DNA framework in the Single Instruction Single Data (SISD) mode. Furthermore, this implementation is improved in terms of execution time within the GeantV project with vectorization techniques such as Single Instruction Multiple Data (SIMD). Within this framework, a set of SIMD strategies in molecular calculation algorithms such as one-electron operators, two-electron operator, quadrature grids, and functionals, was implemented using the VecCore library. The applications developed in this work implement two DFT functionals, the Local Density Approximation (LDA) and the General Gradient Approximation (GGA), to approximate the molecular ground-state energies of small molecules and amino acids. To assess the performance of the implementations, a standard test simulation was performed in multiple CPU platforms. The SIMD vectorization strategy significantly accelerates DFT calculations, leading to time ratios ranging from 1.6 to 5.4 in either individual steps or entire implementations when compared with the scalar process within Geant4.

New algorithm of three-phase equilibrium calculations for CO2-hydrocarbon-water systems

In this century, global warming caused by the accumulation of atmospheric carbon dioxide has become an essential concern. The industry has two main decarbonization options: CO2 capture for permanent storage in geological formations and CO2 utilization for enhancing oil recovery (EOR). Both methods require accurate reservoir simulation to correctly describe the fluids flowing process and design an optimal injection plan. However, existing reservoir simulation practices often neglect the interaction and dissolution of CO2 and hydrocarbon components in water, leading to inaccurate predictions. Neglecting CO2 dissolution in water undermines storage estimation for capture and results in unreliable EOR descriptions. Therefore, to address this, our study focuses on developing a reliable and accurate phase equilibrium calculation package for hydrocarbon-CO2-water three-phase systems, which meets the demanding efficiency and robustness criteria of reservoir simulation. In this paper, we first introduce the methodology of the three-phase equilibrium calculation algorithm, then illustrate the numerical techniques employed to improve computational efficiency and finally demonstrate superior robustness of this algorithm through comprehensive case studies. Our research contributes three key improvements. First, we have increased the reliability of phase behavior descriptions by considering the dissolution of CO2 and hydrocarbon components in water. Second, we have enhanced the robustness of the three-phase equilibrium calculations algorithm, enabling accurate determination of three-phase statuses and fluid behaviors where standard commercial software may fail. Third, our algorithm exhibits notable efficiency improvements, ensuring its suitability for three-phase compositional simulations. The findings of this research provide valuable insights into the accurate modeling of hydrocarbon-CO2-water three-phase systems and offer practical solutions for designing effective CO2 reduction strategies.

Improved heterogeneity handling in the collapsed cone dose engine for brachytherapy.

Model-based dose calculation algorithms (MBDCA), such as the Advanced Collapsed cone Engine (ACE) in Oncentra Brachy® can be used to overcome the limitations of the TG-43 formalism. ACE is a point kernel superposition algorithm that calculates the total dose separated into primary, first-scatter, and multiple-scatter dose. Albeit ACE yields accurate results under most circumstances, several studies have reported underestimations of the dose to cortical bone. These underestimations are likely caused by approximations in the handling of multiple-scatter dose for non-water media. Such would result in noticeable deviations where the multiple-scatter is a considerable fraction of the total dose, that is, at greater distances from the source. To improve and test the accuracy of the multiple-scatter dose component in the ACE algorithm to remedy its inaccuracy for non-water geometries. A careful analysis of the transport and absorption of the multiple-scatter energy fluence revealed an inconsistency in the scaling of energy absorption ratios for non-water media of the multiple-scatter kernel. We implemented an updated algorithm version, ACEcorr, and tested it for three different geometries. All had a single 192Ir-source at the center of a cubic water phantom with a box-shaped heterogeneity of either cortical bone or air, positioned at different distances from the source. Dose distributions for the three cases were calculated with ACE and ACEcorr and compared to Monte Carlo simulations, using the percentage dose difference ratio as figure-of-merit. All dose calculation methods scored separately the dose deposited by primary, first-scattered, and multiple-scattered photons. The accuracy of the updated algorithm ACEcorr was superior to ACE. In the cortical bone heterogeneity, the mean percentage dose difference ratio for the total dose improved from to (in the worst case) by our update. Less impact was seen in the air heterogeneity, where both ACE and ACEcorr deviated less than 2% from the Monte Carlo results. The algorithm update mainly concerns the multiple-scattered dose component, but an accompanying data processing update also had a small effect ( 0.5% difference) on the primary and first-scattered dose. The calculation times were not affected. The updates to ACE improved the accuracy of multiple-scatter dose calculation for non-water media, without increasing calculation times.

Associations between biomarkers and P-wave indices in patients with heart failure

Abstract Background Atrial structural abnormalities linked to the risk of atrial fibrillation (AF), as indicated by P-wave indices on surface ECG, are associated with the fibrotic transformation of the atrial myocardium. To what extent incident AF can be predicted by ECG characteristics in patients with advanced atrial structural remodeling, such as patients with heart failure (HF), is less well studied. Purpose To evaluate the association between P-wave indices and biomarkers implicated in cardiac fibrosis, and incident AF in patients with HF. Methods Patients with new-onset or worsening of HF were prospectively recruited in a observational study (n=501) and followed-up for 5 years. Blood samples were collected for analysis using proximity extension assay that included a subset of biomarkers that were associated with fibrosis development (TIMP-2, MMP-2, MMP-3, MMP-9, ST-2, GDF-15, Gal-3). All ECGs ever recorded in the hospital catchment area were exported in digital format and processed using Glasgow algorithm for calculation of the P-wave indices (P-wave duration [PWD], P-wave terminal force in V1 [PTFV1] and P-wave axis [Paxis]) and rhythm identification. AF diagnosis was ascertained by manual ECG review. Only patients who did not have AF reported or ECG documented at enrolment were included in the analysis. Of those subjects, 121 patients also had biomarkers of fibrosis analyzed. Cox-regression analyses were used to assess biomarkers’ and p-wave indices’ associations with incident AF. Results After exclusion of patients with prevalent AF (n=317), 184 patients comprised the study group (mean age of 71 years, 33.2% women, 121 patients with biomarker data available). During follow-up, incident AF was observed in 39 patients. At enrolment, PWD>120 ms was observed in 38.7%, abnormal PTFV1>40 mm*ms in 24.5% and Paxis<0° in 5.4%. Among the seven biomarkers assessed, five demonstrated significant associations with incident AF in adjusted analyses: TIMP4 (HR 1.78; 95%CI 1.03-3.05; p=0.037); MMP2 (HR 1.97; 95%CI 1.03-3.80; p=0.042), MMP3 (HR 1.39; 95%CI 1.03-1.88; p=0.031); ST2 (HR 1.91; 95%CI 1.29-2.83; p=0.001) and GDF-15 (HR 2.56; 95%CI 1.50-4.35; p=0.001) (Figure 1). However, none of the tested P-wave variables (P-wave duration, P-wave terminal force, and P-wave axis) were associated to incident AF. Conclusions In this prospective long-term follow-up study of patients admitted for acute HF, biomarkers with proven associations to fibrosis were strongly associated with incident AF. P-wave indices used for prediction of AF in epidemiological cohorts appear to have limited value in patients with HF who have high prevalence of ECG atrial abnormalities at baseline.

Математична модель камери згоряння газотурбінного двигуна, який працює на етанолі

Ethanol is one of the most promising alternative fuels for Ukraine. To convert existing projects of power and cogeneration plants based on gas turbine engines (GTEs) operating on petroleum products and natural gas to ethanol, as well as for their design and performance calculation, it is necessary to have a mathematical model of the working process of GTE combustor. The object of the study is the working process of the GTE combustor fueling on ethanol. The subject of the study is a mathematical model of the working process of GTE combustor fueling on ethanol. The work aims to improve a mathematical model of the working process of a GTE combustor fueling on ethanol by changing the algorithm for calculation of the fuel air ratio, considering thermal dissociation, and a correctly formulated equivalent chemical reaction path of the combustion process. To achieve the aim, the following tasks were solved: based on the use of experimental values of specific isobaric heat capacities of combustion products, which are a function of temperature and pressure, a mathematical model of the working process of the GTE combustor was improved ("simplified" mathematical model); based on the solution of the system of equations of chemical thermodynamics, a mathematical model of the working process of the GTE combustor was developed ("complex" mathematical model); the results of calculation by "simplified" mathematical model of the working process of the GTE combustor were compared with the "complex" one. The following results were obtained: the difference in the calculation of the combustion products' thermodynamic parameters between the developed mathematical models was less than 1.2% for the three modes of the General Electric CF6-80A engine. Conclusion: the "simplified" mathematical model of the working process of the GTE combustor fueling on ethanol was improved. A feature of the model is the implicit consideration of the effect of thermal dissociation and correctly formulated equivalent chemical reaction path of the combustion process by using experimental values of specific isobaric heat capacities of combustion products. This will improve the accuracy of fuel air ratio calculation and other thermodynamic parameters of GTE combustor mathematical models fueling on ethanol, without significantly complicating the model algorithm.

The dosimetric accuracy of a commercial model-based dose calculation algorithm in modeling a six-groove direction modulated brachytherapy tandem applicator

Objective.With advancements in high-dose rate brachytherapy, the clinical translation of intensity modulated brachytherapy (IMBT) innovations necessitates utilization of model-based dose calculation algorithms (MBDCA) for accurate and rapid dose calculations. This study uniquely benchmarks a commercial MBDCA, BrachyVision ACUROSTM(BVA), against Monte Carlo (MC) simulations, evaluating dose distributions for a novel IMBT applicator, termed as thesix-grooveDirection Modulated Brachytherapy (DMBT) tandem, expanding beyond previous focus on partially shielded vaginal cylinder applicators, through a novel methodology.Approach.The DMBT tandem applicator, made of a tungsten alloy with six evenly spaced grooves, was simulated using the GEANT4 MC code. Subsequently, two main scenarios were created using the BVA and reproduced by the MC simulations: 'Source at the Center of the Water Phantom (SACWP)' and 'Source at the Middle of the Applicator (SAMA)' for three cubical virtual water phantoms (20 cm)3, (30 cm)3, and (40 cm)3. A track length estimator was utilized for dose calculation and 2D/3D scoring were performed. The difference in isodose surfaces/lines (i.e. coverage) at each voxel,ΔDIsodose Levels/Lines, was thus calculated for relevant normalization points (rref).Results.The coverage was comparable, based on 2D scoring, between the BVA and MC isodose surfaces/lines for the region of clinical relevance, (i.e. within 5 cm radius from the source) withΔDIsodose Lines(rref: 1 cm from the source) falling within 2% for the two scenarios for all phantom sizes. For the phantom (20 cm)3,ΔDIsodose Levels(3D scoring) recorded the range [-3.0% +6.5%] ([-7.4% +7.3%]) for 95% of the voxels of the same scoring volume for the SACWP (SAMA) scenario.Significance.The results indicated that the BVA could render comparable coverage as compared to the MC simulations in the region of clinical relevance for different phantom sizes.ΔDIsodose Linesmay offer an advantageous metric for evaluation of MBDCAs in clinical setting.

Design and tension distribution optimization of a 9-DOF cable-driven parallel spray-painting robot with 3 degrees of redundancy

This paper presents a 9-DOF cable-driven parallel spray-painting robot (CDPSR) with 3 ° of redundancy (DORs) for automated spraying on large, curved surfaces and proposes a feasible cable tension region (FCTR) calculation algorithm for multi-redundant robots. The end effector of the CDPSR consists of two moving platforms connected by a spherical hinge and driven by 12 cables, enabling 9 DOFs of motion (3 for translation and 6 for rotation). Given that the CDPSR has three DORs, a multi-dimensional FCTR vertex calculation algorithm is introduced. The FCTR is an adjacent, continuous, and closed convex hull in every dimension; therefore, the vertices of the FCTR can be determined sequentially and dimensionally. For DOR=3, the vertices on one face of the convex polyhedron are first determined and then extended to adjacent faces until the polyhedron is closed. An experimental prototype of the proposed robot was constructed and experiments on spray trajectory planning and FCTR calculation validation were conducted. The results of the simulations and experiments verified the motion performance of the CDPSR and the accuracy and efficiency of the FCTR calculation algorithm.

Implementation and validation of a very-high-energy electron model in the matRad treatment planning system.

While electron beams of up to 20 MeV are commonly used in radiotherapy, the use of very-high-energy electrons (VHEEs) in the range of 100-200 MeV is now becoming a realistic option thanks to the recent advancements in accelerator technology. Indeed, VHEE offers several clinically attractive features and can be delivered using various conformation methods (including scanning, collimation, and focussing) at ultra-high dose rates. To date, there is a lack of research tools for fast simulation of treatment plans using VHEE beams. This work aims to implement and validate a simple and fast dose calculation algorithm based on the Fermi-Eyges theory of multiple Coulomb scattering for VHEE radiation therapy, with energies up to 200 MeV. A treatment planning system (TPS) toolkit with VHEE modality would indeed allow for further preclinical investigations, including treatment plan optimization and evaluation, and thus contribute to the gradual introduction of VHEE radiotherapy in clinical practice. A VHEE pencil beam scanning double Gaussian model was introduced into the open-source TPS matRad environment along with new functions and options dedicated to VHEE dose calculations. Various geometries and field configurations were then calculated in matRad (up to 200 MeV and 15×15 cm2, with complex bone or lung heterogeneities) and the results were compared to Monte Carlo simulations in the TOPAS/Geant4 toolkit. Two types of beam model (divergent or focused) were also tested. Examples of clinical treatment plans were computed, and the results were compared between the two codes. VHEE modality was fully implemented in matRad with GUI capabilities while preserving all original TPS features. New relevant options such as the importation of specific spot-lists or adjustment of the lateral dose calculation cutoff to optimize the calculation speed were validated. Single spot and square field dose distributions were validated in water alone as well as in clinically relevant inhomogeneities. Dose maps from the VHEE model in matRad were in good agreement with TOPAS (2D gamma index [2%/1mm] with passing rates superior to 90%, <6% mean dose differences), except for large interface heterogeneities. This work describes the implementation of a simple but efficient VHEE simulation model in matRad. A few configurations were studied in order to validate the model against accurate Monte Carlo simulations, demonstrating its usefulness for carrying out preliminary studies involving VHEE radiotherapy.

Development of the Views of Yu.N. Rabotnov on Strength Criteria of Composites

Besides the well-known fundamental works of Yu.N. Rabotnov in the field of hereditary elasticity and creep theory, one of the aspects of his scientific activity was the mechanics of composite materials and, in particular, a new class of strength criteria for structurally anisotropic composites proposed by him. The main feature of Yuri Rabotnov’s approach was not an attempt to construct a uniform smooth limiting surface in the stress-space, but taking into account real fracture mechanisms, which, as a rule, are directional in nature. Now such approaches become crucial in calculation algorithms modeling the fracture process with taking into account the degradation of elastic and strength properties, but in the period of the first Yu.N. Rabotnov’s papers they were pioneering and caused certain discussions. Development and application of some of Rabotnov’s proposed types of strength criteria for fiber-reinforced composites in tension, compression and complex stress state are discussed in this anniversary paper.

Estimating Risk of Debt Instruments Using the CreditMetrics&amp;lt;SUP&amp;gt;TM&amp;lt;/SUP&amp;gt; Method: On the Example of JSCMB ‘Ipoteka-Bank’, Uzbekistan

In the article, credit risk assessment metric of a debt financial instrument, in particular a corporate Eurobond, is studied within the framework of the relevance of risk assessment in the financial sector due to the dangers and complexities of time. Joint-Stock Commercial Mortgage Bank ‘Ipoteka-Bank’, operating in the banking sector of the Republic of Uzbekistan, which is considered one of the important links of the financial sector of the Republic, was selected as the object of analysis. As input data for the analysis, statistical data of the bank provided in its official web-site’s open sources, in particular, data on Eurobonds issued and placed by the bank in London Stock Exchange, are used. At the same time, one of the advantages of the research is the described and disclosed in details and widely used global benchmarking data, published by Standard&amp;Poor&amp;apos;s rating agency, as part of the methodology requirement. According to the methodology, credit risk assessment analysis was performed following a strict and detailed calculation algorithm for debt instrument risk assessment. The calculation of credit risk assessment of one debt instrument, especially the Eurobond, according to this procedure followed with the authors’ discussion, conclusion and recommendation is also reflected in the article.

Heuristic algorithm for calculating the component composition of recombination gas without an adapted equation of state

Background. To conduct laboratory research of projects of gas enhanced oil recovery methods, a large volume of reservoir system is required. Often its replenishment by depth and/or separator samples is not economically feasible. Therefore, the task of fluid recombination from wellhead liquid sample and natural gas simulator arises. Objective. To calculate the component composition of recombination gas under the conditions of the task. Materials and methods. The heuristic calculation algorithm uses the tools of: modeling, inverse problems of physics, set theory, mathematical programming. Special focus is given to its empirical and theoretical justification. Results. The paper considers the limitations of the thermodynamic method. The conditions of the problem to be solved are outlined and justified. The applied algorithm of the solution is formulated and derived. The efficiency of the algorithm for oil systems is experimentally confirmed. Conclusions. The work will be of interest for specialists in the field of laboratory research projects of gas enhanced oil recovery methods. The issues of improving the accuracy of the applied algorithm and its further development are still under discussion.