Simplified Solution Research Articles

Rapid virtual fractional flow reserve using 3D computational fluid dynamics.

Over the last ten years, virtual Fractional Flow Reserve (vFFR) has improved the utility of Fractional Flow Reserve (FFR), a globally recommended assessment to guide coronary interventions. Although the speed of vFFR computation has accelerated, techniques utilising full 3D computational fluid dynamics (CFD) solutions rather than simplified analytical solutions still require significant time to compute. This study investigated the speed, accuracy and cost of a novel 3D-CFD software method based upon a graphic processing unit (GPU) computation, compared with the existing fastest central processing unit (CPU)-based 3D-CFD technique, on 40 angiographic cases. The novel GPU simulation was significantly faster than the CPU method (median 31.7 s (Interquartile Range (IQR) 24.0-44.4s) vs. 607.5 s (490-964 s), P < 0.0001). The novel GPU technique was 99.6% (IQR 99.3-99.9) accurate relative to the CPU method. The initial cost of the GPU hardware was greater than the CPU (£4080 vs. £2876), but the median energy consumption per case was significantly less using the GPU method (8.44 (6.80-13.39) Wh vs. 2.60 (2.16-3.12) Wh, P < 0.0001). This study demonstrates that vFFR can be computed using 3D-CFD with up to 28-fold acceleration than previous techniques with no clinically significant sacrifice in accuracy.

Dimensional analysis of vapor bubble growth considering bubble–bubble interactions in flash boiling microdroplets of highly volatile liquid electrofuels

Electrofuels (e-fuels) produced from renewable electricity and carbon sources have gained significant attention in recent years as promising alternatives to fossil fuels for the transportation sector. However, the highly volatile e-fuels, such as short-chain oxymethylene ethers (OMEx) are prone to flash vaporization phenomena, which is associated with the formation and growth of vapor bubbles, followed by explosive bursting of the liquid jet. This phenomenon is important in many practical applications, for example, superheated liquid sprays in gasoline direct injection engines as well as cryogenic engines. The simulation of a flash boiling spray of such highly volatile liquid fuels is numerically challenging due to several reasons, including (1) the complexity of the bubble growth process in the presence of multiple vapor bubbles and (2) the need to use an extremely small time step size to accurately capture the underlying physics associated with the flash boiling process. In this paper, we first present a bubble growth model in flash boiling microdroplets considering bubble–bubble interactions along with the finite droplet size effects. A dimensional analysis of the newly derived Rayleigh–Plesset equation (RPE) with bubble–bubble interactions is then performed for Reynolds numbers of different orders of magnitude to estimate the relative importance of different forces acting on the bubble surface. Based on this analysis, a simplified nondimensional semi-analytical solution for bubble growth, which also includes the bubble–bubble interactions, is derived to estimate the bubble growth behavior with reasonable accuracy using the larger time step sizes for a wide range of operating conditions. The derived semi-analytical solution is shown to be a good approximation for describing the bubble growth rate over the whole lifetime of the bubble, thus making it useful for simulations of superheated sprays with large numbers of droplets and even more bubbles. The bubble–bubble interactions are found to have a significant impact on the bubble growth dynamics and result in delaying the onset of droplet bursting due to the slower growth of the vapor bubble compared to the bubble growth without bubble–bubble interactions. Furthermore, in a comparison with DNS results, the proposed bubble growth model is shown to reasonably capture the impact of bubble interactions leading to smaller volumetric droplet expansion.

Oxidative dissolution of Cr-doped UO2 nuclear fuel

Alternative UO2 nuclear fuels, incorporating Cr as a dopant, are currently in use in light–water reactors. Dissolution experiments using Cr-doped UO2, performed as a function of Cr content in a simplified groundwater solution and under oxic conditions, established that the addition of Cr to the UO2 matrix systematically reduced the normalised dissolution rate of U at 25 and 40 °C. This effect was most notable under dilute solution conditions, and is the result of galvanic coupling between Cr and U, resulting from the presence of Cr2+ in the UO2 matrix, as corroborated by activation energy determination. Under conditions of solution saturation, where schoepite ((UO2)8O2(OH)12·(H2O)12) and Na2U2O7·6H2O were identified as secondary phases, the rate of U dissolution was invariant with Cr content. Moreover, at 60 °C, the trend was reversed and the rate of U dissolution increased with increasing Cr content. Under these conditions, other factors, including U solubility or bicarbonate-surface interactions, exert a stronger influence on the U dissolution kinetics than Cr. Increased grain size, a feature of Cr-doped UO2 fuel, was also found to reduce the normalised dissolution rate of U. In establishing the mechanisms by which Cr dopants influence UO2 fuel dissolution, it can be concluded that, overall, Cr-doped UO2 nuclear fuel possesses similar dissolution kinetics to undoped UO2 fuel, giving confidence for its eventual disposal in a geological facility.

Simplified Solution of Time-Cost Trade-off Problem for Building Constructions by Linear Scheduling

Time-cost trade-off is an important optimization problem for contractors, because its optimum solution minimizes the total project cost. Formation of the time-cost trade-off problem causes an important workload, since the problem requires preparation of different construction cost and duration alternatives of the activities. Previous studies focused on the optimum solution of the problem and ignored the difficulties of the preparation of the different construction alternatives for the activities, which is a very difficult task for contractors. In this study, the creation of construction alternatives consisting of different time and cost values is automated. Quantity take-off of construction items is computed by user-defined dimensions of structural elements. Workmanship and material requirements are computed by pre-defined job descriptions and quantity take-off values. Different construction alternatives are formed by assigning different crew sizes and the corresponding construction durations are computed by estimating the job efficiency of the crew by regression models derived from the literature. Precedence relationships of the main construction items are pre-defined and the construction schedule is formed by a line of balance in terms of work days. The problem is optimized by a genetic algorithm the parameters of which are fine-tuned by experimental design. The developed approach is implemented on a spreadsheet application and the total optimization process including data entry is completed in one and a half hour on a desktop computer with i5 CPU. This study contributes to relevant literature by proposing a systematic approach for the formation of construction alternatives of the time-cost trade-off problem. The proposed approach can be beneficial for contractors and project managers to form and solve the time-cost trade-off problem with minimum endeavor and cost. KEYWORDS: Time-cost trade-off, Genetic algorithm, Line of balance, Optimization, Experimental design.

Rotating detonation combustors for propulsion: Some fundamental, numerical and experimental aspects

Propulsion systems based on the constant-pressure combustion process have reached maturity in terms of performance, which is close to its theoretical limit. Technological breakthroughs are needed to develop more efficient transportation systems that meet today’s demands for reduced environmental impact and increased performance. The Rotating Detonation Engine (RDE), a specific implementation of the detonation process, appears today as a promising candidate due to its high thermal efficiency, wide operating Mach range, short combustion time and, thus, high compactness. Following the first proofs of concept presented in the 1960s, the last decade has seen a significant increase in laboratory demonstrators with different fuels, injection techniques, operating conditions, dimensions and geometric configurations. Recently, two flight tests of rocket-type RDEs have been reported in Japan and Poland, supervized by Professors Kasahara (Nagoya University) and Wolanski (Warsaw University), respectively. Engineering approaches are now required to design industrial systems whose missions impose efficiency and reliability constraints. The latter may render ineffective the simplified solutions and configurations developed under laboratory conditions. This requires understanding the fundamentals of detonation dynamics relevant to the RDE and the interrelated optimizations of the device components. This article summarizes some of the authors’ experimental and numerical work on fundamental and applied issues now considered to affect, individually or in combination, the efficiency and reliability of the RDE. These are the structure of the detonation reaction zone, the detonation dynamics for rotating regimes, the injection configurations, the chamber geometry, and the integration constraints.

How ploughing and frictional melting regulate ice-skating friction

The slipperiness of ice is well known while, for ice skating, its mechanism still needs further investigation, where the complex interactions including the thermal conduction of the skate—meltwater—ice system, the ploughing and the frictional melting of ice to the friction force are still unclear. This study presents a theoretical framework and a simplified analytical solution to unveil the friction mechanism when a curved skate sliding on ice. The theory is validated by experiments and the effects of these various factors, including the sliding velocity, the ice temperature, the supporting weight, and the geometry of the skate blade to the friction are revealed in detail. This study finds that the contribution of friction force from the ploughing deformation through skate indentation and that from the fluid friction through the shear motion of the meltwater layer is comparable with each other, which thus clarifies how the ploughing deformation of the ice substrate together with its frictional melting regulates the friction during skating.

Determination of mixed-mode stress intensity factors for axial crotch corner cracks at cylindrical vessel to nozzle intersections under internal pressure and nozzle loads

In this study, Stress Intensity Factors (SIF) of quarter circle and semi elliptic cracks at the crotch corner of the intersection between a cylindrical pressure vessel and a radial nozzle have been computed for combinations of the actions of internal pressure and external forces on the nozzle. Until now, practitioners have used simplified solutions for SIFs available from the literature, such as the Newman-Raju equations for the mode I SIF produced by an internal longitudinal semi-elliptical crack in a cylinder, to approximate the SIF produced at a crotch corner crack. These equations do not take into account the effect of the opening of the cylinder for the nozzle and the resulting stress distribution along the cylinder. As a result, there is uncertainty about the validity of using these simplified solutions in engineering critical assessments and a more exact determination of the SIFs for crotch corner cracks would be beneficial.The mode I, II and III stress intensity factors have been determined for crotch corner cracks for a single size of vessel and are presented as a function of variables such as location on the crack front, crack size and aspect ratio (a/c), crack angle with respect to the axis of the vessel, and the magnitude of internal pressure and external forces. The results are presented in graphical form. The study concludes with the recommendation that the analysis be extended to a wider range of vessel and nozzle parameters.

The Combined Bearing Capacities of Anchor Chain Segment by Considering Its Actual Geometry and Roughness

The soil resistances along the embedded ground chain affect the pull-out capacity of anchor as they determine the magnitude and direction of tension at the padeye. To facilitate analyses, the chain was usually simplified as a cylindrical line. The chain segment with actual geometry, buried deeply in clayey soil, is studied using a large deformation finite element approach to overcome severe distortion of soil elements around the chain. The uniaxial resistances obtained by the large deformation analyses are verified by comparison with the existing model tests and simplified solutions, followed by presentation of the yield envelope against combined loading. Both the probe test and swipe test are used to form the yield envelopes, and their results have good consistency. The influence of roughness of chain–soil interface on the soil resistances is quantified as well. It is found that the envelope of the chain segment with actual geometry is smaller than that against the simplified cylindrical shape; therefore, the most convenient design may not be the safest option.

Simplified analytical solutions to the yaw dynamics of modular floating structures

Climate change has necessitated the development of modular floating structures (MFS) as a sustainable solution to enhance the resiliency of coastal cities against flooding and sea level rise. Hence, it is imperative that simplified methods of analysis are introduced to the design community. This technical note presents closed-form expressions parameterizing the response amplitude operators (RAO) of rectangular pontoons subject to yaw (rotation about the vertical z axis) to complement solutions derived by Wang (2022) for the five remaining degrees of freedom. Following validation, a parametric investigation was implemented to assess the influence of pontoon geometry on the yaw response of an idealized MFS exposed to realistic sea states. It was identified that pontoons exhibiting a characteristic width smaller than the wavelength are generally more resistant to yaw excitation as they become squarer in shape. Conversely, while larger pontoons are less sensitive to geometric effects, they exhibit heightened sensitivity to changes in wave conditions. The simplified analytical approach thus provides an accessible pathway towards the structural or architectural design of floating structures as a precursor to detailed computational modeling.

Optimal Pricing Strategy of New Products and Remanufactured Products Considering Consumers’ Switching Purchase Behavior

Due to income constraints, increased awareness of environmental protection and preference for new products, consumers generate switching purchases between new and remanufactured products, which often lead to a “cannibalization effect” in the market, and make sellers fall into a vicious circle of price reduction. Considering consumers’ switching purchase behavior, this study examines the pricing problem of new products and remanufactured products in the competitive market environment. Based on two-period duopoly asymmetric price game models, there has been less research on the effectiveness of the price matching strategy and the traditional dynamic pricing strategy, which is the issue that this paper is dedicated to discussing. This study analyzes the equilibrium profits and their influencing factors under the dynamic pricing and price matching strategies of sellers, and discusses the simplified solution of the model. The results show that consumer learning costs, initial consumers and product differences can affect the sellers’ pricing decisions. Consumers’ learning costs of products reduces the equilibrium profit of the manufacturer and increases that of the remanufacturer. Initial consumers are not always advantageous for sellers’ profitability. Product differences affect the determination of the seller’s equilibrium strategy. In the optimal strategy, the remanufacturer should insist on price matching, while the manufacturer should choose dynamic pricing or price matching according to the product differences. This study provides sellers with insights to choose appropriate and custom pricing strategies to maximize profit as well as prevent the majority of consumers switching purchase.

Prediction of Three-Dimensional Consolidation Settlement: Observational Method and Its Applicability

This paper presents a closed form of the simplified three-dimensional (3D) (vertical and radial) consolidation solution, which has negligible errors for practical cases. Based on the simplified solution, two observational methods (namely, 3D modified curve fit and linear rule methods) that could predict the actual 3D consolidation settlement behaviors by reflecting the effect of sampling range were newly developed. The appropriateness of the proposed methods was verified by using 3D and two-dimensional (2D) theoretical data. Then, the proposed methods were applied to three case records. Back-analyzed results (i.e., the end of consolidation settlement S100 and consolidation coefficient ch(n)) were slightly affected by the differently approached methods and the inputted value of vertical consolidation coefficient (cv). S100 and ch(n) values obtained from the 3D modified methods were close to those secured from the 2D modified methods due to the insignificant effect of vertical drainage for the cases. Owing to incomplete measurement (93%–98% of S100, i.e., no consideration of sampling range effect), an existing 3D method and the original 2D Asaoka and exponential methods predicted a lower S100 and higher ch(n) than those predicted by the 3D or 2D modified curve fit methods. Therefore, the proposed 3D methods can be recommended for practical applications.

Wave–Tide Interaction for a Strongly Modulated Wave Field

Abstract Observations from Coastal Data Information Program (CDIP) moored buoys off the coast of Florida reveal tidally driven wave–current interactions that modify significant wave heights by up to 25% and shift peak periods by up to a second. A case study at Fernandina Beach, Florida, shows surface waves steepening on following tidal currents and becoming less steep on opposing tidal currents, with the largest modulations occurring in the long-period swell band. To better understand tidal modulations as a function of the phase of the tide, we use simplified analytical and numerical solutions to the equations of geometrical optics and conservation of wave action under the assumption of a one-dimensional tide acting as a progressive shallow-water wave. The theoretical frameworks allow us to identify parameters that characterize the magnitude of variation in surface waves due to tidally induced currents and changes in water depth. We compute modulations to the omnidirectional and directional wave spectrum (between 0.05 and 0.15 Hz), as well as characteristic bulk parameters such as significant wave height and peak period. The theory is corroborated using directional wave and surface current observations from the Fernandina Beach CDIP station (located in water of average depth of 16 m). We find that the numerical results reproduce the observed wave modulations due to tidal currents and changes in water depth. Specifically, surface waves traveling in the direction of the tide are strongly modulated, and the relative speeds between the tide and surface waves set the sign and magnitude of these modulations. Given knowledge of tidal currents, water-depth variations, and wave climatology, theoretical and numerical predictions may be used to provide both statistical and instantaneous estimates of wave-height variations due to tides. Because operational forecasts and nowcasts do not routinely include tides or currents, these findings can help to accurately represent nearshore surface wave variability.

Different Strategies for the Microfluidic Purification of Antibiotics from Food: A Comparative Study.

The presence of residual antibiotics in food is increasingly emerging as a worrying risk for human health both for the possible direct toxicity and for the development of antibiotic-resistant bacteria. In the context of food safety, new methods based on microfluidics could offer better performance, providing improved rapidity, portability and sustainability, being more cost effective and easy to use. Here, a microfluidic method based on the use of magnetic microbeads specifically functionalized and inserted in polymeric microchambers is proposed. The microbeads are functionalized either with aptamers, antibodies or small functional groups able to interact with specific antibiotics. The setup of these different strategies as well as the performance of the different functionalizations are carefully evaluated and compared. The most promising results are obtained employing the functionalization with aptamers, which are able not only to capture and release almost all tetracycline present in the initial sample but also to deliver an enriched and simplified solution of antibiotic. These solutions of purified antibiotics are particularly suitable for further analyses, for example, with innovative methods, such as label-free detection. On the contrary, the on-chip process based on antibodies could capture only partially the antibiotics, as well as the protocol based on beads functionalized with small groups specific for sulfonamides. Therefore, the on-chip purification with aptamers combined with new portable detection systems opens new possibilities for the development of sensors in the field of food safety.

Generalized hydrodynamic coefficients of a circular SFT in finite water depth

In this work, a numerical model is developed for calculating the generalized hydrodynamic coefficients of a horizontal vibrating cylinder representative of a submerged floating tunnel in finite water depth. In this model, the whole computational domain is divided into three sub-domains and the velocity potential for describing the fluid motion in each sub-domain is solved separately using different approaches. In the inner domain bounding the cylinder, a simple Green function is utilized to form a boundary integral equation, which is solved by the boundary element method (BEM), and the technique of eigenfunction expansion is applied in the outer domains away from the cylinder. The eigenfunctions in the outer domains indicate that there exists a critical vibration frequency below which no propagating wave can be generated and thus the radiation damping is zero. Characteristics of the generalized hydrodynamic coefficient in a wider range of the submergence depth, the vibration frequency and the axial wavenumber are explored. It is found that the generalized hydrodynamic coefficients in the vicinity of the critical vibration frequency experience abrupt changes, characterised by a ‘sharp peak’ profile. Generally, the generalized (horizontal and vertical) added mass increases firstly with the vibration frequency to its maximum value at the critical frequency, and then decreases with the further increase in the vibration frequency. However, behaviours are rather different in terms of the vertical added mass if the cylinder is fully submerged; a discontinuity at the critical frequency is observed, and the value jumps from positive to negative here. Afterwards the vertical added mass starts to increase quickly and becomes positive again with the further increase of the vibration frequency. This phenomenon of discontinuity may be associated with the fact that the radiation force changes its direction suddenly at the critical frequency; from being ‘out-of-phase’ to ‘in-phase’ with the cylinder motion. In addition, semi-analytical solutions are derived for approximating the generalized added mass in a high frequency range, which suggests that the generalized added mass decreases with the axial wavenumber, and with the presence of free surface, especially when the axial wavenumber is small. While for a deeply submerged cylinder, the effect of the free surface is negligible and then further simplified solutions are provided.

Multicriteria Optimization of Design Solutions for Microclimate Systems for Rooms with Artificial Ice

Рurpose of research. The most energy-intensive facilities for holding sports and cultural events are indoor ice rinks and ice arenas. Simplified technical solutions when designing the systems for providing the microclimate of these structures lead to significant operating costs and can lead to serious negative consequences in a relatively short period. In this regard, the problem of developing methods for choosing the optimal design solution for these systems is becoming ever more urgent. The purpose of the article is to develop a mathematical model for multi-criteria optimization of design solutions for systems providing the microclimate of rooms with artificial ice.Methods. Determining the optimal design solution for microclimate systems in terms of several parameters, each of which can be decisive, is an applied task of system analysis, the basic principles and patterns of which were taken into account when solving the problem of multicriteria optimization.Results. A list of particular optimality criteria reflecting the qualitative and quantitative characteristics of design solutions has been determined. The method of vector criterion convolution has been used to search for the optimal solution for the selected particular criteria. An optimization model based on the principles of system analysis has been developed.Conclusion. The developed mathematical model of multicriteria optimization makes it possible to provide priority to more important particular criteria by increasing their weights. In this case, it should be remembered that particular criteria must be commensurate, and, therefore, reduced to a dimensionless form. Since the absolute values of the criteria are essential in the optimization task under consideration, for the chosen vector of parameters, it is necessary to choose exactly the additive method of folding the generalized criterion.

Distribution of Currents in 2 × 25 kV Electric Railway Systems under Normal Conditions

This article shows a detailed analysis of the distribution of currents in 2 × 25 kV electric railway systems under normal conditions. The network equations are clearly formulated in a way that enables the presentation of a novel simplified analytical solution as well as the traditional numerical solution of the equation set. The simplified analytical solution is obtained when the transformer impedances are neglected, and under these conditions: (a) the distributions of currents are analytically deduced for cases with only one train; (b) the distribution of currents among autotransformers and between catenary and feeder can be easily understood, as well as the effect of the train position on the distribution of currents; and (c) the superposition method is applied for cases with multiple trains in order to clearly explain the distribution of currents from the results with only one train. On the other hand, the network equations are also numerically solved, including autotransformer impedances, and it is shown that their effect is very low, especially because these impedances are typically small. Therefore, the proposed analytical method is a good tool to obtain an easy and approximate solution for the distribution of currents in these systems, as well as an excellent tool to facilitate the understanding of that distribution.

Compressive performance of welded hollow spherical joints with external triangular ribs

This study addresses the axial compressive performance of welded hollow spherical (WHS) joints with external triangular ribs. External triangular ribs are able to postpone the local buckling of the joint during axial loading, and thus strengthen the compressive capacity of it. A simplified analytical model is proposed to elucidate the stress distribution on the hollow sphere of axial-loaded WHS joints with external triangular ribs. Then a simplified solution for the yield strength of axial-loaded WHS joints is deduced based on the elastic thin shell theory. The simplified solution indicates that the yield strength of WHS joints with external triangular ribs can be expressed by a coefficient related to the specifications of the ribs and the joints multiply by that of WHS joints without external ribs. Compression tests on 6 full-scale specimens of WHS joints with varied configurations of triangular ribs are conducted. It shows that the failure mode and the strength enhancement of the specimens vary as the specification of the triangular ribs change, and the triangular ribs enhance the strength of the joints up to 77 %. A refined FE model is established and calibrated against the findings from the experiments. Parametric studies on the design parameters which may affect the compressive response of the WHS joints with triangular ribs are fully investigated. It is shown that the compressive yield strength of the joint rises with the increase of the number, height and thickness of the triangular ribs, and decreases with the increase of the angle-of-elevation of the triangular ribs. It is also shown that the effect of the ratio of the diameter of the sphere to that of the steel tube on the compressive yield strength of the joint is much lighter than the others, and deemed as negligible. Regression analysis on the experimental and numerical data is carried out to obtain a practical formula for the compressive capacity of WHS joints with external triangular ribs. This formula is incorporated with the previously developed formula for the compressive capacity of WHS joints with external trapezoidal ribs, to form a general formula applicable for WHS joints with either external triangular ribs or external trapezoidal ribs.

Comparison of Propagation Models and Forward Calculation Methods on Cellular, Tissue and Organ Scale Atrial Electrophysiology.

The bidomain model and the finite element method are an established standard to mathematically describe cardiac electrophysiology, but are both suboptimal choices for fast and large-scale simulations due to high computational costs. We investigate to what extent simplified approaches for propagation models (monodomain, reaction-Eikonal and Eikonal) and forward calculation (boundary element and infinite volume conductor) deliver markedly accelerated, yet physiologically accurate simulation results in atrial electrophysiology. We compared action potential durations, local activation times (LATs), and electrocardiograms (ECGs) for sinus rhythm simulations on healthy and fibrotically infiltrated atrial models. All simplified model solutions yielded LATs and P waves in accurate accordance with the bidomain results. Only for the Eikonal model with pre-computed action potential templates shifted in time to derive transmembrane voltages, repolarization behavior notably deviated from the bidomain results. ECGs calculated with the boundary element method were characterized by correlation coefficients 0.9 compared to the finite element method. The infinite volume conductor method led to lower correlation coefficients caused predominantly by systematic overestimations of P wave amplitudes in the precordial leads. Our results demonstrate that the Eikonal model yields accurate LATs and combined with the boundary element method precise ECGs compared to markedly more expensive full bidomain simulations. However, for an accurate representation of atrial repolarization dynamics, diffusion terms must be accounted for in simplified models. Simulations of atrial LATs and ECGs can be notably accelerated to clinically feasible time frames at high accuracy by resorting to the Eikonal and boundary element methods.

THIRLWALL’S BPCG MODEL WITH CAPITAL FLOWS AND DISAGGREGATED IMPORTS SECTORS USING A SIMPLIFIED * GENERAL SOLUTION (SGS): THE CASE OF TURKEY, 1998-2019

In this paper, we considered an extended version of the BPCG model incorporating both the capital inflows and some possible structural changes by disaggregating total imports into intermediate, consumption and capital imports for the 1998-2019 period to study the Turkish economy. We calculated the rate of growth of Turkish income for the extended BPCG model based on a Simplified General Solution (SGS) using the estimated income and price elasticities of demands for three types of imports separately and the time-varying shares of exports earnings in total imports expenditures and the time-varying shares of intermediate, consumption and capital imports sectors. The time-varying shares are introduced in order to capture some structural changes in the composition of imports and the type of financing the trade deficit in addition to the changes in the composition of manufactured imports. We observed that the economic growth in Turkey was almost always accompanied with heavy capital inflows which helped the financing of the merchandise trade deficits. Even though the real exports increased by an average of 6.01% during 1998-2019 period, its relatively small contribution to the rate of growth of income was found to be due to the fact that we took into account the rise in intermediate imports attributable to an increase in manufactured exports confining the BP-Equilibrium growth rate of Turkish income. Moreover, we also found that an average of 0.49% deterioration in the real exchange rate (RER) had a very small effect. We also pointed out that the short-run variations may be more important from a policy perspective, where the policy-makers may be more concerned for the next two or three years by taking into account the short run influences of especially those of expected abrupt changes in capital flows. Finally, we noticed that a first stylized fact for the Turkish economy seemed to be abrupt decreases in capital flows before/during the recessions like those in 2001 and 2009 and a second stylized fact that the Turkish economy grows during the periods when heavy capital inflows increase, generally after the recessions.

Partial-inductance retarded partial coefficients: Their exact computation based on the Cagniard–DeHoop technique

The Partial Element Equivalent Circuit (PEEC) method is a well recognized integral-equation (IE) technique to solve Maxwell’s equations. Similarly to the method of moments (MoM), the electromagnetic (EM) interactions between currents and between charges are described in terms of integrals. In contrast to the standard MoM, the PEEC method keeps the electric and magnetic coupling phenomena separate, which leads to different interaction integrals to be computed. These integrals admit simplified solutions for the case of the static free-space Green’s function and orthogonal geometries but their applicability is limited to electrically small problems only. When the full-wave free-space Green’s function is considered, the integrals are typically computed in the frequency domain (FD) by resorting to Gaussian quadrature schemes. The accuracy and efficiency of such schemes is a delicate issue. Therefore, recent works have investigated the possibility of applying the Cagniard–DeHoop (CdH) technique to calculate the interaction integrals for zero-thickness elementary domains. In this paper, we close the loop and shall apply the CdH technique to calculate the partial-inductance between two elementary bricks as prescribed by the PEEC technique exactly in the time domain (TD). The analytical approach is demonstrated on the interaction between two bricks as it occurs in the modeling of the magnetic field coupling between volumetric currents. The accuracy of the proposed approach is (successfully) tested for two representative cases.