Use Of Boundary Conditions Research Articles

Structural appraisal of baja prototype using resistive strain gauges and linear potentiometer

Every machine or structural component undergoes a certain elastic deformation when exposed to some type of load or force. Furthermore, when it comes to the design and validation of components, a structural analysis plays a fundamental role, given the need to guarantee the integrity of the designed parts. To achieve this, reliable data is essential so that the entire process can be carried out in a coherent manner, based on engineering criteria. Therefore, the present study seeks to acquire dynamic or static loads and forces, which are present in main and critical components in a BAJA-type prototype, from the KomiKeto Baja Team - UFSJ, aiming to acquire data for the use of boundary conditions in numerical simulations, in addition to dynamic capture of loading cycles for subsequent fatigue analysis.

Including Shield Wires in the Analysis of Transient Processes Occurring in HVAC Transmission Lines

The article presents an analysis of electromagnetic transient processes in long ultra-high voltage transmission lines, taking into account shield wires. It was shown that EMTP and Matlab/Simulink software are currently widely used in the study of transient processes in power lines. The EMTP software package uses the finite element method when integrating the equation that mathematically models the distributed parameter transmission line. The Matlab/Simulink software uses the d’Alembert method. In both cases, it is not known how the boundary conditions for the partial differential equation that mathematically models the transmission line are determined. The power line is analyzed as a distributed parameter system, described by a second-order partial differential equation. The advantage of the proposed method of calculating the boundary conditions for the abovementioned equation is the use of boundary conditions of the second and third types of Neumann and Poincaré, which allowed us to take into account the mutual influence of shield wires and phase conductors of the line in one power system. On this basis, the methodology for obtaining time domain graphs, spatial distributions, and traveling wave distributions of voltages and currents for phase conductors and line shielding wires is presented. The results of a computer simulation of transient processes when switching on the power line, taking into account controlled phase commutation and under single-phase earth fault conditions, are presented. All calculation results of transient processes presented in the article were obtained exclusively using numerical methods.

Bag Boundaries for Quasispinor Confinement Within Nanolanes on a Graphene Sheet

AbstractThe problem of bag boundary conditions within a field‐theoretic approach is revisited to study confinement of massless Dirac quasispinors in monolayer graphene. While no‐flux bag boundaries have previously been used to model lattice termination sites in graphene nanoribbons, a generalized setting is considered in which the confining boundaries are envisaged as arbitrary straight lines drawn across a graphene sheet and the quasispinor currents are allowed to partially permeate (leak) through such boundaries. Specifically focus is on rectangular nanolanes defined as areas confined between a pair of parallel lines at arbitrary separation on an unbounded lattice. It is shown that such nanolanes exhibit a considerable range of bandgap tunability depending on their widths and armchair, zigzag, or intermediate orientation. The case of nanoribbons can be derived as a special limit from the nanolane model. In this case, certain inconsistencies are clarified in previous implementations of no‐flux bag boundaries and show that the continuum approach reproduces the tight‐binding bandgaps accurately (within just a few percent in relative deviation) even as the nanoribbon width is decreased to just a couple of lattice spacings. This accentuates the proper use of boundary conditions when field‐theoretic approaches are applied to graphene systems.

Microconvection of MHD solarized nanofluid in the presence of double slip and surface suction

Refrigeration systems are becoming more efficient as a result of nanofluids. Cooling and heating process improvements can lead to enhanced industrial efficiency, reduced processing times, energy conservation, and improved heating and cooling processes. A study is being conducted on the effects of magnetohydrodynamics (MHD) in nanofluids by adding double slip and thermal radiation to the governing model. It is numerically simulated using bvp4c code in MATLAB. Analyzing temperature, concentration, and velocity requires the evaluation of multiple parameters. A more uniform distribution of temperatures can be achieved by increasing the Biot number, thermal radiation, and thermophoretic motion parameters. The use of suction is an effective method of controlling the rate of temperature reduction in various manufacturing processes. A product's mechanical properties and overall quality can be enhanced if one is able to control how quickly it cools during the process of melting and condensing raw materials. As a consequence of the emergence of quadratic and linear slip factors, the flow velocity decreases. A distinguishing feature of this research is the use of boundary conditions that are tailored to the geometry that is being investigated.

A robust collision source method for rank adaptive dynamical low-rank approximation in radiation therapy

Deterministic models for radiation transport describe the density of radiation particles moving through a background material. In radiation therapy applications, the phase space of this density is composed of energy, spatial position and direction of flight. The resulting six-dimensional phase space prohibits fine numerical discretizations, which are essential for the construction of accurate and reliable treatment plans. In this work, we tackle the high dimensional phase space through a dynamical low-rank approximation of the particle density. Dynamical low-rank approximation (DLRA) evolves the solution on a low-rank manifold in time. Interpreting the energy variable as a pseudo-time lets us employ the DLRA framework to represent the solution of the radiation transport equation on a low-rank manifold for every energy. Stiff scattering terms are treated through an efficient implicit energy discretization and a rank adaptive integrator is chosen to dynamically adapt the rank in energy. To facilitate the use of boundary conditions and reduce the overall rank, the radiation transport equation is split into collided and uncollided particles through a collision source method. Uncollided particles are described by a directed quadrature set guaranteeing low computational costs, whereas collided particles are represented by a low-rank solution. It can be shown that the presented method is L2-stable under a time step restriction which does not depend on stiff scattering terms. Moreover, the implicit treatment of scattering does not require numerical inversions of matrices. Numerical results for radiation therapy configurations as well as the line source benchmark underline the efficiency of the proposed method.

Крутильні пружні хвилі. Деякі аспекти нелінійного аналізу

The features of the use of boundary conditions in the nonlinear problem of torsional wave propagation for an elastically deformable medium with an external boundary are analyzed. The formulation and wave analysis in the linear (classical) approach are briefly described, since the linear solution is used in the work as a first approximation in the nonlinear approach. The first feature for a torsional wave is a significant complication in the nonlinear approach of the boundary conditions due to the difference between the shape of the boundary before and after the deformation (in the linear approach, the shape of the boundary does not change). The second feature is the significant complication of the mathematical representation of the boundary conditions due to the appearance of additional nonlinear terms. For a torsional wave, it was found that the use of the condition of absence of stresses on the boundary surface (assumption of a free boundary) may not be completely correct.

A Solution to Linear Black-Scholes Second-order Parabolic equation in sobolev space

In this paper, a set of functions were constructed that transforms Black-Scholes partial differential equation into weak formulations. The analytical solutions: existence, uniqueness and other estimates were also obtained in weak form with the use of boundary conditions to establish the effects of its financial implications in Sobolev spaces. The regularity conditions of the problem were considered which the coefficients, the boundary of the domain are all smooth functions. To this end, the definitions, assumptions which paved way to useful assertions are illustrated in this paper.

Surface ground vibration of a tunnel embedded in soil layer of cold regions to a moving point load

The vibration characteristics of tunnel buried in seasonal frozen soil is considered as a two-dimensional model in which a moving unit vertical load is applied to an infinite beam. The beam is regarded as the Euler Bernoulli model and the unsaturated frozen soil is treated as a poroelastic medium. The analysis of the influence of dynamic response of tunnel in cold region on the ground surface in frequency-wavenumber domain can be obtained through the conservation of momentum, mass and energy of unsaturated frozen soil, as well as the use of boundary conditions. The analytical solution in transformed domain is obtained by Fourier transform. The critical velocity of frozen soil in cold region under different saturation and frozen ratio is obtained by means of the dispersion curve, and the influence of its change on the critical velocity is also analyzed. The effects of changes in parameters of seasonal frozen soil on the dynamic response are studied. It indicates that the typical parameters like saturation, frozen ratio, and critical velocity etc. in unsaturated frozen soil have a great influence on the vertical and horizonal displacement caused by the load. In addition, this paper raises several unresolved issues to highlight the need for further research in this rapidly expanding field.

Modular Approach for Modelling Warming up Process in Water Installations with Flow-Regulating Elements

The paper presents a new method for modelling the warming up process of a water system with elements regulating the flow in a stochastic manner. The paper presents the basic equations describing the work of typical elements which the water installation is composed of. In the proposed method, a new computational algorithm was used in the form of an iterative procedure enabling the use of boundary conditions that can be stochastically modified during the warming-up process. A typical situation, when such a modification is processed, is the regulation of the medium flow through two-way or three-way valves or applying additional heat source. Moreover, the presented method does not require the transformation of the differential equations, describing the operation of individual elements, into a linear form, which significantly facilitates analytical work and makes it more flexible. The example of analysis of the operation of water installation used for controlling temperature of the process gases in a chemical installation shows the functionality and flexibility of the method. The adopted calculation schematics enable changing the direction of the heat flow while the heat exchanger is in operation. Additionally, the sequence of calculation processed in modules describing operation of installation elements is elective (there is no situation that output parameters from one element are used as input parameters for other element in the same calculation step).

Dynamic response of an elastic plate on a transversely isotropic viscoelastic half-space with variable with depth moduli to a rectangular moving load

The dynamic response of a flexural elastic plate on a transversely isotropic half-space with elastic constants varying with depth to a rectangular load moving with constant speed is determined analytically. Soil viscoelasticity via hysteric damping and plate viscous damping is also considered. Use is made of the method of the complex Fourier series involving the two horizontal coordinates and the time. Because the load speed is constant, only a double series expansion of the response functions is required. Employment of this method reduces the partial differential equations of motion for the soil and the plate to ordinary differential equations with variable coefficients and an algebraic equation, respectively. Those ordinary differential equations are solved by the method of Frobenius. Use of boundary conditions and equilibrium and compatibility at the soil-plate interface help to determine the constants of integration and obtain the soil and plate response in closed form. Verification of the obtained solution is done by using it to determine the response of simpler cases to moving loads for which there are analytical results in the existing literature. Parametric studies are finally conducted to assess the effects of viscoelasticity, cross-anisotropy and non-homogeneity of soil, of stiffness of the plate, as well as of load speed on the plate response.

On the use of boundary conditions and thermophysical properties of nanoparticles for application of nanofluids as coolant in nuclear power plants; a numerical study

In the first part of the present study, a thermal-hydraulic subchannel code hereafter called ‘SUBTHAC’ is developed to evaluate the enhancement effects of nanoparticles in core heat transfer. The first version of SUBTHAC (V1.0) can analyze the steady state flow of coolant with Al2O3, TiO2 or CuO as nanoparticles (other types of nanoparticles can be added by the user). Different output profiles can be selected such as fluid temperature, pressure and velocity for each subchannel, clad outside temperature for each fuel rod, axial and lateral mass flow, etc. SUBTHAC uses a dedicated algorithm to solve the subchannel equations and, unlike many other codes, allows for thermophysical parameters of nanoparticles to be a function of the temperature, leading to improvement the accuracy of results. Results computed by SUBTHAC for base fluid (pure water) are validated against those obtained by COBRA-EN code. In the next step, with the aim of validating the capability of nanofluid analysis of SUBTHAC code, its nanofluids results have been validated against reference CFD simulations. After the validation, comprehensive numerical comparisons are conducted to assess the enhancement of thermal-hydraulic parameters by using nanofluids. It is shown that, among Al2O3, TiO2 and CuO nanofluids with volumetric concentration in the range of 1–5%, TiO2-3% and CuO-3% are the best choices to increase fluid outlet temperature and decrease clad temperature, respectively. Using nanofluids with a concentration higher than 3% volumetric is not justifiable as the core pressure drop increases up to more than 20%.In the second part of the manuscript, some relevant remarks are put forward on the assignment of boundary conditions (BC, i.e. inlet velocity/inlet mass flux/inlet Reynolds number) and the adoption of reliable values for specific heat capacity of nanoparticles in operational temperature of NPPs. The effects of using the above boundary conditions and incorrect values of the specific heat (as adopted in the literature so far) are depicted by presenting some profiles of coolant and clad temperature. Selecting different BCs and incorrect values of specific heat for nanoparticles can jeopardize the results of calculations.

Excision and avoiding the use of boundary conditions in numerical relativity

A procedure for evolving hyperbolic systems of equations on compact computational domains with no boundary conditions was recently described in Bieri et al (2019 (arXiv:1905.08657 [gr-qc])). In that proposal, the computational grid is expanded in spacelike directions with respect to the outermost characteristic and initial data is imposed on the expanded grid boundary. We discuss a related method that removes the need for imposing boundary conditions: the computational domain is excised along a direction spacelike or tangent to the innermost going characteristic. We compare the two methods, and provide example evolutions from a code that implements the excision method: evolution of a massless self-gravitating scalar field in spherical symmetry.

Benchmarking transcranial electrical stimulation finite element models: a comparison study

Objective. To compare field measure differences in simulations of transcranial electrical stimulation (tES) generated by variations in finite element (FE) models due to boundary condition specification, use of tissue compartment smoothing filters, and use of free or structured tetrahedral meshes based on magnetic resonance imaging (MRI) data. Approach. A structural MRI head volume was acquired at 1 mm3 resolution and segmented into ten tissue compartments. Predicted current densities and electric fields were computed in segmented models using modeling pipelines involving either an in-house (block) or a commercial platform commonly used in previous FE tES studies involving smoothed compartments and free meshing procedures (smooth). The same boundary conditions were used for both block and smooth pipelines. Differences caused by varying boundary conditions were examined using a simple geometry. Percentage differences of median current density values in five cortical structures were compared between the two pipelines for three electrode montages (F3-right supraorbital, T7-T8 and Cz-Oz). Main results. Use of boundary conditions commonly used in previous tES FE studies produced asymmetric current density profiles in the simple geometry. In head models, median current density differences produced by the two pipelines, using the same boundary conditions, were up to 6% (isotropic) and 18% (anisotropic) in structures targeted by each montage. Tangential electric field measures calculated via either pipeline were within the range of values reported in the literature, when averaged over cortical surface patches. Significance. Apparently equivalent boundary settings may affect predicted current density outcomes and care must be taken in their specification. Smoothing FE model compartments may not be necessary, and directly translated, voxellated tissue boundaries at 1 mm3 resolution may be sufficient for use in tES FE studies, greatly reducing processing times. The findings here may be used to inform future current density modeling studies.

A Simple Method of Constructing Binary Black Hole Initial Data

By applying a parabolic-hyperbolic formulation of the constraints and superposing Kerr-Schild black holes, a simple method is introduced to initialize time evolution of binary systems. As the input parameters are essentially the same as those used in the post-Newtonian (PN) setup the proposed method interrelates various physical expressions applied in PN and in fully relativistic formulations. The global ADM charges are also determined by the input parameters, and no use of boundary conditions in the strong field regime is made.

Particle tracing modeling of ion fluxes at geosynchronous orbit

The first results of a coupled MHD/particle tracing method to evaluate particle fluxes in the inner magnetosphere are presented. This setup is capable of capturing the earthward particle acceleration process resulting from dipolarization events in the tail region of the magnetosphere. On the period of study, the MHD code was able to capture a dipolarization event and the particle tracing algorithm was able to capture the results of these disturbances and calculate proton fluxes in the night side geosynchronous orbit region. The simulation captured dispersionless injections as well as the energy dispersion signatures that are frequently observed by satellites at geosynchronous orbit. Currently, ring current models rely on Maxwellian-type distributions based on either empirical flux values or sparse satellite data for their boundary conditions close to geosynchronous orbit. Despite some differences in intensity and timing, the setup presented here is able to capture substorm injections, which represents an improvement regarding a reverse way of coupling these ring current models with MHD codes through the use of boundary conditions.

Magnetic Spin-Wave Properties of Ferromagnetic Nanosystems of Various Shapes. Peculiarities of the Border Conditions Accounting in the Process of the Wavenumber Values Spectrum Finding

Background. The paper continues the investigation of linear dipole-exchange spin waves in ferromagnetic nanosystems started by the author in previous papers. The known papers investigating dipole-exchange spin waves obtain their spectral characteristics only for a narrow range of special cases. In the presented paper, an approach that allows expanding substantially this range of cases is described and applied. Objective. The aim of the paper is to develop a method – based on the use of boundary conditions – for obtaining the spectral characteristics of dipole-exchange spin waves in a number of nanosystems’ configurations as well as an application of this method to specific configurations. Methods. A method for obtaining a values’ spectrum of the wavenumbers for dipole-exchange spin waves in ferromagnetic nanosystems of a series of typical configurations is proposed. The method does not require specific assumptions, e.g. the absence of transverse spin excitations or the presence of a high-conductivity metal outside the ferromagnet. The method uses imposition of boundary conditions for the magnetic field and the magnetization on the boundary of the ferromagnetic medium for a linear spin wave in the magnetostatic approximation. This method allows obtaining the above-mentioned spectral characteristics for a wider range of cases compared to the known previous papers. Results. The results of the paper are conditions for the magnetic potential – that imply from the above-mentioned boundary conditions – of a linear spin wave on the boundary of a ferromagnetic nanosystem as well as the spectrum of the wavenumbers’ values of such wave for the investigated nanosystems (in the implicit form). In particular, for a ferromagnetic nanosystem of an arbitrary cross section with a one-dimensional translational symmetry, the conditions specifying this spectrum are found. Such conditions are specified – and an implicit expression for this spectrum is obtained – for the case when such nanosystem is a nanotube with a circular cross section. The analysis of the obtai­ned results is carried out. Conclusions. The obtained expressions for the spectrum of the values of the investigated spin waves’ wavenumbers can be used for a wider range of cases than the ones obtained in the previous papers dedicated to the investigated configurations of nanosystems. For a nanotube of the circular cross-section with small (compared to the inverse characteristic size of the nanotube cross-section) values of the longitudinal wave number, the dependence of the latter on the transverse wave number is weak, as well as for the big longitudinal to transverse wavenumber component ratio. The obtained dependence is also represented graphically.

Vulcanizing Hydraulic Press Heating System for Tempering Metal and Alloy Objects

A fundamentally new press heating system has been developed for tempering metal objects that provides formation of a required temperature profile within treated objects with prescribed heating and cooling rates and provides hydraulic press system safe operation. Modernization of mathematical description for transient heating processes is proposed in a heated plate – heat insulation – press system providing the use of boundary conditions that imitate the effect of press structural elements in heating plate and heat insulation plate temperature fields.

A simplified method for the numerical calculation of nonstationary heat transfer through a flat wall

The nonstationary operation modes of power equipment lead to the nonstationary regimes of heat exchange, in particular heat transfer. The transient processes, related to the accumulation of energy in the heat-transmitting surfaces, which manifest themselves in this case, may affect manageability of the work of equipment. Although in many cases, with a proper approximation, the heat exchange surfaces can be represented in the form of a simple variant of an infinite plate, the existing methods and tools for solving the problems on nonstationary heat transfer are built from the positions of universalism, introducing unjustified complications and hampering the generalization of numerical results obtained. We developed a simplified discrete analog to solve the one-dimensional problems on nonstationary heat transfer through an infinite plate. The realized approach allowed us to obtain the analog and results of calculations based on it in the dimensionless form, which substantially facilitates their generalization. A high stability of computational process is demonstrated relative to the selection of a number of nodes in computational grid and calculation step by time. The possibility of using the maximally small computational grids (3 nodes) makes it possible, at the current calculation step by time. To obtain an analytical solution for determining the temperatures at the surfaces of the plate at initial use of boundary conditions of the third kind. As a result, accumulated energy can be defined as a difference in the heat fluxes at the surfaces of the plate. Performing the calculations on the maximally small grids might be useful to solve the inverse problems on thermal conductivity.

Surface transport processes in charged porous media

Surface transport processes are very important in chemistry, colloidal sciences, engineering, biology, and geophysics. Natural or externally produced charges on surfaces create electrical double layers (EDLs) at the solid-liquid interface. The existence of the EDLs produces several complex processes including bulk and surface transport of ions. In this work, a model is presented to simulate bulk and transport processes in homogeneous porous media comprising big pores. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A volume averaging technique is used to derive the averaged transport equations in the limit of thin electrical double layers. Description of the EDL between the electrolyte solution and the charged wall is accomplished using the Gouy-Chapman-Stern (GCS) model. The surface transport terms enter into the average equations due to the use of boundary conditions for diffuse interfaces. Two extra surface transports terms appear in the closed average equations. One is a surface diffusion term equivalent to the transport process in non-charged porous media. The second surface transport term is a migration term unique to charged porous media. The effective bulk and transport parameters for isotropic porous media are calculated solving the corresponding closure problems.

Physical interpretation of the spectral approach to delocalization in infinite disordered systems

In this paper we introduce the spectral approach to delocalization in infinite disordered systems and provide a physical interpretation in context of the classical model of Edwards and Thouless. We argue that spectral analysis is an important contribution to localization problems since it avoids issues related to the use of boundary conditions. Applying the method to 2D and 3D numerical simulations with various amount of disorder W shows that delocalization occurs for W ≤ 0.6 in 2D and for W ≤ 5 for 3D.