Simple Boundary Conditions Research Articles

Calculation Models of Radiopharmaceutical Activities of An Open 4-Compartment Model using The MIRD Method

An open 4-compartment model has been created which includes heart, thyroid, kidney, and liver organs using the MIRD method. Based on the compartment model, models of differential equations can be made as a function of the activities of the four organs. By ignoring the absorption function of radiopharmaceuticals from breast organs (absorption of radiopharmaceuticals by breast organs is very small) and using boundary conditions of the radiopharmaceutical activities function that enters or goes out of the heart organ has the same exponential factor function and ignores all disturbance, we get model of the activity equation is obtained from the heart, thyroid, kidney and liver organs. This activity equation model is only at the conceptual stage of a simple model through simple boundary conditions as well. This model is very difficult to apply to patients because there are many disturbing factors to the dose flow pattern such as organ function abnormalities, internal disease, internal and external disorders, etc.

Harmonic chains and the thermal diode effect.

Harmonic oscillator chains connecting two harmonic reservoirs at different constant temperatures cannot act as thermal diodes, irrespective of structural asymmetry. However, here we prove that perfectly harmonic junctions can rectify heat once the reservoirs (described by white Langevin noise) are placed under temperature gradients, which are asymmetric at the two sides, an effect that we term "temperature-gradient harmonic oscillator diodes." This nonlinear diode effect results from the additional constraint-the imposed thermal gradient at the boundaries. We demonstrate the rectification behavior based on the exact analytical formulation of steady-state heat transport in harmonic systems coupled to Langevin baths, which can describe quantum and classical transport, both regimes realizing the diode effect under the involved boundary conditions. Our study shows that asymmetric harmonic systems, such as room-temperature hydrocarbon molecules with varying side groups and end groups, or a linear lattice of trapped ions may rectify heat by going beyond simple boundary conditions.

On three-dimensional dynamics of fibre-reinforced functionally graded plates when fibres resist bending

This communication aims to initiate an investigation towards understanding the influence that fibre bending stiffness has on the three-dimensional dynamic behaviour of fibrous composites with embedded functionally graded stiff fibres. In this context, it (i) formulates the general dynamical problem of a rectangular plate with embedded a single family of straight fibres that possess bending resistance and are distributed in a controlled, functionally graded manner through the plate thickness, and (ii) for simple support boundary conditions, it solves the free relevant vibration problem. The problem formulation is based on principles of polar linear elasticity and leads to a high-order set of Navier-type partial differential equations with variable coefficients. For simply supported edge boundaries, solution of these equations is achieved with the use of a computationally efficient semi-analytical (so-called fictitious layer) mathematical method. Two types of possible inhomogeneous distributions of straight fibres are considered for computational and numerical result presentation purposes. These are both regarded as possible, realistic types of inhomogeneous redistributions of stiff fibres that in previous studies have been assumed homogeneously distributed throughout the plate body. The presented numerical results examine to a considerable extent the manner that either of the employed types of inhomogeneous fibre redistribution, in conjunction with the fibre ability to resist bending, affects the dynamic behaviour of the fibrous composite plate of interest.

Oscillatory porous medium ferroconvection with Maxwell-Cattaneo law of heat conduction

The scheme of small perturbation is used to address the problem of buoyancy driven convection of Darcy-Brinkman type in a ferromagnetic fluid invoking the Maxwell-Cattaneo law. An analytical solution of the eigenvalue problem involved, encompassing stationary and overstable modes, is obtained by adopting simplified boundary conditions. The mathematical application package MATHEMATICA is adopted to determine the eigenvalue expressions and the critical numbers. It is established that the threshold of Darcy-Brinkman ferroconvection is amplified through the stresses of magnetic and second sound mechanisms and the opposite influence is found to be true due to the presence of porous medium. It is delineated that both the critical frequency of oscillations and aspect ratio of cells of convective heat transfer are susceptible to the different parameters of the study. It is also shown that, as long as the Cattaneo and Prandtl numbers are pretty high, the oscillatory mode of instability is preferred to the stationary mode of ferroconvection.

Two-Channel System Dynamics of the Outer Weser Estuary—A Modeling Study

In this paper, we unravel the mechanisms responsible for the development of the two-channel system in the Outer Weser Estuary. A process-based morphodynamic model is built based on a flat-bed approach using simplified boundary conditions and accelerated morphological development. The results are analyzed in two steps: first, by checking for morphodynamic equilibrium in the simulations and second, by applying a newly developed method that interprets simulations based on categorization of the two-channel system and cross-sectional correlation analysis. All simulations reach a morphodynamic equilibrium and develop two channels that vary considerably over time and between the simulations. Variations can be found in the location and depth of the two channels, the development of the dominant channel over time and the alteration in the dominance pattern. The conclusions are that the development of the two-channel system is mainly caused by the tides and the basin geometry. Furthermore, it is shown that the alternation pattern and period are dependent on the dominance of the tides compared to the influence of river discharge.

Space-time asymptotic expansion method for transient thermal conduction in the periodic composite with temperature-dependent thermal properties

Space-time asymptotic expansion method (AEM) is a rigorous method for solving the multiscale transient thermal conduction problem in periodic composites. However, the AEM is still difficult to model the thermal behavior in composites when temperature-dependent material properties are taken into account. Besides, its complex and costly implementation also restricts the usage of AEM. A space–time AEM for multiscale transient thermal analysis is comprehensively studied in this study to address these issues properly. After the constitutive equation of temperature-dependent characteristic temperature tensor and effective thermal properties in the transient thermal conduction is deduced from the solid theoretical base, a new implementation approach comprised of both homogenization and localization is developed. It can directly model the characteristic temperature tensor within a representative volume element model under simple periodic boundary conditions and linear temperature loads, differing from conventional AEM, which requires complex location-related heat flux loads. Moreover, a new characteristic heat flux tensor is proposed to replace the characteristic temperature tensor in the localization of heat flux. All these contributions simplify the localization in the new implementation. The thermal behavior of A fiber-reinforced composite during the forming process is investigated using the space–time AEM and multiscale finite element method. The comparison results between space–time AEM and multiscale finite element method indicate that the space–time AEM is accurate and efficient as the differences of local temperature and heat flux are 0.0051 °C and 7.2 × 10-5 W/mm2, and the total nodes in space–time AEM is only about half of the multiscale finite element method.

Scaled boundary finite element method for hydrodynamic bearings in rotordynamic simulations

The behavior of rotor systems with hydrodynamic bearings can be affected crucially by the nonlinear bearing forces. These forces are incorporated in rotordynamic simulations by solving the Reynolds equation in every step of a time integration scheme. Since closed-form analytical solutions of the Reynolds equation are known only for simplified boundary conditions, numerical methods and look-up table approaches are applied. To obtain accurate and convergent results, numerical solutions require a fine discretization, while the look-up tables require a fine grid of interpolation points. In both cases, the numerical effort of the rotordynamic simulation is dominated by the computation of the bearing forces.In this study, a semi-analytical solution of the Reynolds equation based on the Scaled Boundary Finite Element Method (SBFEM) is developed to reduce the numerical effort of the overall simulation. In contrast to a purely numerical solution, the two-dimensional pressure field is discretized in only one coordinate direction, whereas in the other direction, an analytical formulation is used. This results in a system of non-homogeneous ordinary differential equations, which is solved under consideration of the boundary conditions. Since the complexity of the SBFEM model and the resulting numerical effort depend on the modeling of the oil supply groove, three different models are analyzed in this paper. The equations are derived, the solutions are verified, and their numerical efficiency is investigated in comparison to an FEM solution, which is one of the standard numerical approaches.

Continuum modelling of an asymmetric CCRF argon plasma reactor: Influence of higher excited states and sensitivity to model parameters

AbstractPrecise control of capacitively coupled radiofrequency (CCRF) plasma reactors is required to achieve desired outcomes in surface functionalisation and material synthesis processes. This necessitates detailed mapping of the large process parameter space and a thorough understanding of spatial and temporal variations of the plasma throughout the reactor. These goals can only feasibly be achieved with accurate numerical modelling. Previous numerical studies of CCRF discharges have implemented a range of simplifying assumptions to improve numerical tractability, such as small electrode spacing, radial uniformity, fewer active species and simplified boundary conditions, while neglecting self‐bias formation. Although this approach is useful in developing the methodology for continuum plasma modelling, it poses challenges for direct comparison with experimental data and for understanding the behaviour of plasma processes employed in the surface treatment of large, complex objects, or the synthesis of nanoparticles. Here we report the development of a two‐dimensional axisymmetric continuum model for a CCRF reactor with a pure argon 13.56‐MHz discharge using the finite element method. The large electrode spacing and reactor design result in two distinct discharge regions and the formation of a strong DC self‐bias on the powered electrode. The plasma discharge is studied as the pressure is varied from 0.1 to 0.3 Torr, over the radiofrequency input power range of 25–100 W, which leads to consistent enhancements of the electron density and self‐bias. The impact of the electron energy distribution function (EEDF) on the discharge is assessed, with the assumption of a Druyvesteyn EEDF resulting in a bulk electron density and temperature of 3.4 × 1015 m−3 and 3.3 eV, respectively, compared with 8.1 × 1015 m−3 and 1.9 eV in the Maxwellian case. The asymmetric power distribution throughout the reactor is quantified to build a reduced domain model with a lower computational cost. The effect of an electrically floating parallel plate electrode is assessed, resulting in a 42% higher bulk plasma potential as compared with the grounded case. The inclusion of resonant and 2p excited states of argon is shown to have a major impact on the discharge dynamics, leading to an order of magnitude reduction in bulk electron density. This study proposes a robust numerical model of a CCRF argon plasma discharge to facilitate future simulations of more complex discharges with important implications in plasma surface engineering and synthesis of materials.

Analytical algorithm for longitudinal deformation profile of a deep tunnel

To investigate the longitudinal deformation profile (LDP) of a deep tunnel in non-hydrostatic condition, an analytical model is proposed in our study. In this model, the problem is considered as a superposition of two partial models, and the displacement field of the second partial model is the same as that of the concerned problem. Therefore, the problem can be solved by a model with simple boundary conditions. We obtain the solutions for the stress and displacement fields of an infinite body caused by arbitrary surface tractions on the boundary of the coming tunnel (zone inside the tunnel before excavation) by integrating the extended Kelvin solution over the boundary. The obtained stress solution is used to solve the specific surface tractions, which can satisfy the boundary conditions of the second partial model, on the boundary of the coming tunnel in an infinite body. Then, the specific surface tractions are substituted into the obtained displacement solution to solve the displacement on the wall and face of the tunnel. Therefore, the LDP can also be calculated. The proposed solution is verified by both numerical simulation and the LDP functions recommended by other researchers. The major advantage of our analytical model is that it can consider the effects of the axial and horizontal lateral pressure coefficients. It is revealed that the horizontal lateral pressure coefficient majorly affects the LDP behind the tunnel face, while the axial lateral pressure coefficient dominates the LDP ahead of the tunnel face. Furthermore, the deformation characteristics of the LDPs ahead of the face and the unexcavated core are investigated. The axial displacements of the excavation face can be used to predict the crown displacements ahead of the face.

A Semi-Analytical Method for Channel Modeling in Diffusion-Based Molecular Communication Networks

Channel modeling is a challenging vital step towards the development of diffusion-based molecular communication networks (DMCNs). Analytical approaches for diffusion channel modeling are limited to simple and specific geometries and boundary conditions. Also, simulation- and experiment-driven methods are very time-consuming and computationally complex. In this paper, the channel model for DMCN employing the fundamental concentration Green's function (CGF) is characterized. A general homogeneous boundary condition framework is considered that includes any linear reaction systems at the boundaries in the environment. To obtain the CGF for a general DMCN including multiple transmitters, receivers, and other objects with arbitrary geometries and boundary conditions, a semi-analytical method (SAM) is proposed. The CGF linear integral equation (CLIE) is analytically derived. By employing the numerical method of moments, the problem of CGF derivation from CLIE is transformed into an inverse matrix problem. Moreover, a sequential SAM is proposed that converts the inversion problem of a large matrix into multiple smaller matrices reducing the computational complexity. Particle-based simulator confirms the results obtained from the proposed SAM. The convergence and run time for the proposed method are examined. Further, the error probability of a simple diffusion-based molecular communication system is analyzed and examined using the proposed method.

Effects of boundary conditions on stress distribution of hydraulic support: A simulation and experimental study

This paper analyzed the effects of boundary conditions on the stress distribution of hydraulic support with the static finite element (FE) model. Five loading conditions are considered in this study, including: 1) canopy torsional loading, 2) canopy eccentric loading, 3) base torsional loading, 4) base diagonal loading, and 5) base symmetrical loading. In order to verify the simulation results obtained from the FE model, the corresponding experiments have also been performed. Based on the comparison between simulation and experimental results, the effects of pin-joint simplified methods and boundary conditions are evaluated in terms of accuracy and efficiency. Moreover, the new elastic-support boundary is also proposed to improve the simulation accuracy under conditions 2, 3, 4, and 5. The results show that bonded contact between the pin and shaft hole has high efficiency and accuracy compared with the frictional contact. The frictional contact boundary is reasonable under condition 1. However, the elastic-support boundary is suggested to be adopted to improve calculation accuracy for the stress distribution of the constraint components (canopy or base) under conditions 2, 3, 4, and 5.

Nonlinear Dirac Equation for Graphene

The possibility of introducing a nonlinear correction to the Dirac equation for graphene in order to adequately describe collective electronic phenomena is considered. In contrast to the other papers on this topic the interaction term includes the sum of the spinor components’ squares instead of their difference. Particular attention is paid to the equality of the spatial coordinates. We investigate the properties of the obtained nonlinear equation, in order to describe the high-temperature ferromagnetism in graphene without making any assumptions on the key role of defects of the structure in providing the effect. The numerical simulation is carried out for the simple boundary and initial conditions with the Lax–Friedrichs scheme as a result of which information is obtained on the dynamics of the electron density for a number of the simplest initial and boundary conditions.

Modelling laminar diffusion flames using a fast convergence three-dimensional CVFEM code

Laminar diffusion flames have been employed extensively to investigate the effects of physical and chemical-related parameters on combustion phenomena. Attention has been given to improve combustion models while keeping the two-dimensional (2D) axisymmetric approach and simplified boundary conditions. The flow structure due to the discrete jet nature of the reactants claims a more realistic inlet boundary condition for the burner plate which can only be accomplished if the solution domain is 3D. In this work, we present a novel 3D simulation code for the analysis of non-premixed laminar flames of methane and air, considering detailed inlet boundary conditions. The code is based on the control volume finite element method, written in MATLAB environment. To accomplish that a novel flow-oriented upwind scheme was implemented for the advection terms of the conservation equations. Combustion modelling can be carried out by either an enhanced flame sheet model in which an enthalpy equation is integrated in combination with the mixture fraction equation or detailed reaction schemes. Radiative heat losses were accounted for in the added energy equation. Three-dimensional numerical predictions, based on the flame sheet model, were able to simulate the near-wall gas temperature and inflow velocity field of a set of perforated plate burner with different porosities. It was found that the discrete nature of the injection of fuel and oxidiser, inflow boundary condition, plays a significant role on flame shape and length. Much better agreement between published experimental data and numerical predictions was obtained, particularly regarding flame structure, species mass fractions and temperature distribution of non-premixed laminar flames regardless of the adopted simplified combustion model. It was observed that flame length decreased as the burner porosity increased, up to a certain limit. The modified flow-oriented scheme greatly improved solution stability and computational time of the reacting system predictions.

Estimation of the Maximum Efficiency and the Load Power in the Periodic WPT Systems Using Numerical and Circuit Models

The article presents an analysis of the maximum efficiency and maximum load power, which are available to obtain in periodic wireless power transfer (WPT) systems. The numerical computations of the proposed WPT structures are performed using the finite element method and branch current method. Two theoretical models are discussed, i.e., a numerical model with simplified structure and boundary conditions as well as an equivalent circuit model is proposed to solve WPT systems with many magnetically coupled planar coils. A multivariate analysis is performed, which takes into account the variability of the number of turns, distance between a transmitting and receiving coil, and the frequency of an energy source. The outputs, such as overall efficiency, power of the source and power transferred to a load are discussed. The formulas for the load impedance required to maximize the efficiency or load power, which are taking into account the electrical parameters of the system resulting from its geometry, are presented. The results obtained from proposed models are consistent, which confirm the correctness of the adopted circuit model, which is less complex and faster to compute than numerical one. It is also possible to perform a quick assessment of electrical parameters of the analyzed WPT structure, using presented analytical formulas and numerical model or experimental data. The results allow for a detailed discussion of the dependence of the efficiency and power of the WPT system with respect to geometry of spiral coils.

Micromechanical modeling approach with simplified boundary conditions to compute electromechanical properties of architected piezoelectric composites

Architected piezoelectric composites (PCs) have recently gained interest in designing transducers and nondestructive testing devices. The current analytical modeling approach cannot be readily applied to design architected periodic PCs exhibiting elastic anisotropy and piezoelectric activity. This study presents a micromechanical (MM)-model based finite element (FE) modeling framework to predict the electromechanical properties (EMPs) of the architected PCs. As an example, the microstructure with one-dimensional (1–3 PCs) connectivity is considered with different cross-sections of fibers. 3D FE models are developed. The intrinsic symmetry of architected composite is used to derive boundary conditions (BCs) equivalent to periodic BCs (PBCs). The proposed approach is simple and eliminates the need for a tedious mesh generation process on opposite boundary faces on the MM model of architected PCs. The EMPs of 1–3 PCs calculated from the proposed micromechanics-FE models were compared with those obtained from analytical solutions (i.e. based on micromechanics theories), and FE homogenization (i.e. obtained by employing the PBCs available in the literature). A quite good agreement between the proposed modeling approach and the ones obtained using the analytical model was observed. However, an excellent agreement is observed with the MM results that employed PBCs. Hence, we have concluded that the proposed MM modeling approach is equivalent to MM models that employed PBCs. The computed enhanced effective elastic, piezoelectric, and dielectric properties and corresponding figure of merit revealed that 1–3 PCs are suitable in transducer applications.

Investigation on the Analysis of Bending and Buckling for FGM Euler-Bernoulli Beam Resting on Winkler-Pasternak Elastic Foundation

In this paper, Functionally Graded Material (FGM) has been analyzed to examine bending and buckling of simply supported beams. Using Euler-Bernoulli beam theory (EBT), these beams that rested on Winkler-Pasternak elastic foundation are exposed to two types of loads that are axial compressive force and distributed transverse load. Here, based on power-law distributions, the properties of the material of FGM beam is assumed to be varied at the direction of the thickness. The derivation of the FGM beams’ governing equations was done using the total potential energy principle. The transverse deflection and the critical buckling of the FGM beam were determined using the Navier-type solution method with simple boundary conditions. A closure on the effects of the power-law exponent of FGM, and the spring constant with the shear constant of elastic foundation on the transverse deflection and critical buckling load was achieved. A validation study for numerical results was carried out here with previous results from the literature and they are said to be in excellent agreement. It is shown by the numerical results that critical buckling load is decreasing with increasing both, slenderness ratio and values of power-law exponent and vice versa for transverse deflection.

On the influence of inlet perturbations on slug dynamics in horizontal multiphase flow—a computational study

When multiphase flows are modeled numerically, complex geometrical and operational features of the experiments, such as the phase mixing section, are often not resolved in detail. Rather simplified boundary conditions are prescribed, which usually cause less irregular dynamics in the system than present in reality. In this paper, a perturbation that randomly disturbs the secondary components of the velocity vector at the inlet is proposed in order to capture the experimentally observed instabilities at the interface between the phases. This in particular enhances the formation of slugs in the pipe. Different amplitudes of the perturbation are investigated. One observes that, the higher the perturbation amplitude, the earlier the slugs occur. On the other hand, sufficiently far away from the inlet, the flow pattern shows the same dynamics for different perturbation amplitudes. Hence, no specific frequency is imposed by the prescribed perturbation. The simulation results are validated by comparison with liquid level data from a corresponding experiment.

Micromechanical modeling of architected piezoelectric foam with simplified boundary conditions for hydrophone applications

Architected piezoelectric materials with controlled porosity are of interest for applications such as hydrophones, miniature accelerometers, vibratory sensors, and contact microphones. Current analytical modeling approach cannot be readily applied to design architected periodic piezoelectric foams with tunable properties while exhibiting elastic anisotropy and piezoelectric activity. This study presents micromechanical-finite element (FE) models to characterize the electromechanical properties of architected piezoelectric foams. The microstructure with zero-dimension (3-0 foam, spherical porosity) and one-dimensional (3-1 foam, cylindrical porosity) connectivity were considered to analyze the effect of porosity connectivity on the performance of piezoelectric foam. 3D FE models of the 3-0 and 3-1 foams were developed and using the intrinsic symmetry of porous structures simplified mixed boundary conditions (MBCs) equivalent to periodic boundary conditions (PBC) were proposed. The proposed approach is simple and eliminates the need of tedious mesh generation process on opposite boundary faces on the micromechanical model of porous microstructures with PBCs. The results obtained from the proposed micromechanics-FE models were compared with those obtained by means of the analytical models based on micromechanics theories, and FE models with PBCs reported in the literature for both 3-0 and 3-1 type foams. An excellent agreement was observed. The computed effective elastic, piezoelectric and dielectric properties and corresponding figure of merit (FOM) revealed that piezoelectric foams with 3-0 connectivity exhibit enhanced hydrostatic FOM as compared to piezoelectric foams with 3-1 connectivity. It is concluded that spherical porosity is more suitable to hydrophone applications.

Formation mechanism of static pressure circumferential double-peak distribution in a centrifugal compressor under the action of downstream boundary

In the centrifugal compressor applied in the automobile turbochargers, the asymmetric structure of volute causes the non-uniform flow field in the impeller and compressor stall. The non-uniformity of the flow field in the compressor can be reflected by the casing-wall static pressure distribution. In this study, by removing the volute and directly imposing different simplified static pressure boundary conditions at the diffuser outlet, the formation mechanism of casing-wall static pressure circumferential double-peak distribution of the compressor is explored. It is found that the mass flow rate is redistributed at the impeller outlet due to local high static pressure induced by the volute tongue, which results in the formation of two airflow regions with high velocity in the diffuser, ultimately leading to the static pressure circumferential double-peak distribution in the diffuser and the impeller. Noted that because of the existence of the blades, the airflow regions with high and low velocity formed in the diffuser are locked within a limited range of one or more widths of the blade passage. When the number of blades in the compressor is large, the static pressure can appear as multi-peak distribution in the circumferential direction. Moreover, the result of the mass flow rate redistribution at the impeller outlet is determined by the static pressure distribution characteristics at the diffuser outlet.

A hybrid symplectic and high-frequency homogenization analysis for the dispersion property of periodic micro-structured thin plate structures

A hybrid homogenization analysis approach is developed for the dispersion of one- and two-dimensional periodic micro-structured thin plate structures by combining the high-frequency homogenization method and the symplectic method. In the present method, the displacement field of the unit cell which is needed in the high frequency homogenization method is expressed in terms of wave components which are obtained by solving an eigenvalue problem which is first proposed. The eigenproblem developed based on the symplectic method allows the displacement function of the unit cell with arbitrary simple boundary conditions to be obtained rationally, so that the high-frequency homogenization analysis can be more conveniently applied to the dispersion analysis of the periodic micro-structured plate structures. Numerical examples of one-dimensional and two-dimensional periodic structures with various boundary conditions for the unit cell are provided to confirm the utility of the proposed method.