Simple Boundary Research Articles

Recurrence of the uniform infinite half-plane map via duality of resistances

We study the simple random walk on the Uniform Infinite Half-Plane Map, which is the local limit of critical Boltzmann planar maps with a large and simple boundary. We prove that the simple random walk is recurrent, and that the resistance between the root and the boundary of the hull of radius r is at least of order logr. This resistance bound is expected to be sharp, and is better than those following from previous proofs of recurrence for nonbounded-degree planar maps models. Our main tools are the self-duality of uniform planar maps, a classical lemma about duality of resistances and some peeling estimates. The proof shares some ideas with Russo–Seymour–Welsh theory in percolation.

A non-equilibrium slip wall model for large-eddy simulation with an immersed boundary method

A non-equilibrium wall model for large-eddy simulation with the immersed boundary (IB) method is proposed to reduce the required number of grid points in simulating wall-bounded turbulence. The proposed wall model is presented as an appropriate slip velocity on the wall. The slip velocity is constructed by integrating the simplified turbulent boundary layer (TBL) equation along the wall-normal direction, which enhances the integral momentum balance near the wall on a coarse grid. The effect of pressure gradient on the near wall flow is taken into account by retaining the pressure gradient term in the simplified TBL equation. The proposed model is implemented in the form of a direct-forcing IB method with moving-least-square reconstruction near the wall. The benchmarks of plane channel turbulence and the flows over a backward-facing step are used for validation. The proposed model improves the wall stresses and velocity profiles in the region where the pressure gradient dominates the near wall flows.

Nitrate transport behavior behind subsurface dams under varying hydrological conditions.

The construction of subsurface dams for controlling seawater intrusion triggers the accumulation of nitrate upstream of a dam. This is raising the concerns about nitrate contamination in those regions of coastal aquifers that are supposed to be used as a fresh groundwater source behind a subsurface dam. Research on this subject has been mostly restricted to the use of a simplified sea boundary (e.g., static and no slope), ignoring sea level fluctuations driven by tides. In this study, the combined effect of tides and subsurface dams on nitrate pollution in upstream groundwater was examined through laboratory experiments and numerical simulations. The results revealed that the difference in the extent of nitrate contamination under various conditions (i.e., static, tidal, static with a dam, and tidal with a dam) was related to the temporal pollution behavior. In the early stage, nitrate contamination in upstream groundwater was essentially identical for different scenarios. Both tides and subsurface dams were found to increase nitrate contamination in upstream aquifers. The extent of nitrate contamination increased with higher tidal amplitudes, whereas the increment was more evident for a large tidal amplitude. The effects of tides and subsurface dams on nitrate contamination were also regulated by the locations and infiltration rates of the pollution source. Interestingly, under the joint action of tides and subsurface dams, the increment in the extent of nitrate pollution was greater than the sum of their individual effects. The increased pollutions caused by subsurface dams and tides were quantified as 9.47% and 37.22%, respectively, whereas the increased value caused by their joint action was measured as 51.10%. These findings suggest that tidal activity should not be overlooked when assessing nitrate contamination in upstream groundwater.

Asynchronous Boundary Stabilization of Stochastic Markov Jump Reaction-Diffusion Systems

Dissipativity-based asynchronous boundary stabilization problem is addressed for stochastic Markov jump reaction-diffusion systems (SMJRDSs). In practical engineering, nonsynchronous behavior between system modes and controller modes is inevitable, and the incomplete matrix information makes the problem analysis difficult, so this work considers the asynchronous stabilization. Different from the distributed control, we apply a simple boundary control strategy, which greatly reduces the cost of the control design. Note that three issues need to be addressed: 1) how to model the asynchronous behavior? 2) how to design the asynchronous boundary controller? and 3) how to process the incomplete matrix information? We deal with these problems one by one. Based on a general hidden Markov model (HMM), an asynchronous boundary feedback controller is considered. Via the Wirtinger-type inequality, Schur complement technique, and transition matrix properties, sufficient conditions ensuring exponentially mean square stability and strictly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(W, P, R)-\alpha $ </tex-math></inline-formula> dissipativity are established, which covers several special cases. Finally, a numerical example is presented to illustrate the proposed control strategies.

An inner boundary condition of moisture diffusion model for simulating transient nonlinear moisture transport in Chinese fir

This paper proposed an inner boundary condition of moisture diffusion model for simulating transient nonlinear moisture transport of Chinese fir (Cunninghamia lanceolata). The inner boundary condition is serviced for simulate the moisture diffusion of multi-layer boards and is mainly used for the boundary conditions inside component, which presents the diffusion of moisture between wood and its adjacent wood. Furthermore, the established simulation model contains fiber orientation information and is used to simulate the moisture diffusion under different boundary conditions, which considers the constrained boundary. Simulation of simple boundary condition models and the proposed inner boundary condition model under different boundary conditions for multilayer board specimen exposed to constant temperature and constant humidity with a known initial moisture content, and the model was then validated in a laboratory climate chamber. Different from the simple boundary condition model the direct error of the proposed inner boundary model was less than 2% (moisture content), which indicates the proposed inner boundary condition could improve the accuracy of moisture diffusion model. The results show that the inner boundary condition model can comprehensively analyze the transient nonlinear moisture transfer process in different fiber directions with high accuracy.

Articular contact vs. embedding: Effect of simplified boundary conditions on the stress distribution in the distal radius and volar plate implant loading

Boundary conditions (BCs) are often simplified in experimental and numerical models simulating distal radius fractures and their treatments. The aim of this study was to investigate the effects of simplified BCs at the radiocarpal joint: (1) on the stress distribution in the intact distal radius, and (2) on the loading of a volar locking plate (VLP) used for distal radius fracture treatment. Finite element models of the distal radius with contact between carpals and cartilage were created as reference models for an intact bone and a fractured bone with VLP treatment. Four models with simplified BCs were compared to these reference models: One with embedding material instead of carpals, one with carpals tied to the radius; each loaded either uniaxially or with statically equivalent loading to the reference model. Differences in distal bone stress distributions and mechanical parameters of the VLP (fracture gap movement, plate peak stresses, distal screw loads) were generally largest for the uniaxially loaded, embedded model (up to 250 % in individual screw loads) and smallest for the model with tied carpals and statically equivalent loads (<25 % for all parameters). Differences were greatly reduced if statically equivalent loads were applied, but subchondral stress peaks were absent without carpals. In conclusion, implementing realistic resultant forces and moments is more important than the exact articular load distribution, but carpal bones should be included if subchondral bone stresses are analyzed. In this case, a tie constraint may replace articular contact modelling with acceptable accuracy if statically equivalent loading is applied.

Natural vibration analysis of an embedded elastic metamaterial beam based on effective medium theory and Rayleigh–Ritz method

Elastic metamaterial (EM) beam is a kind of special composite structure with peculiar dynamic properties that are beneficial for relevant vibration isolating applications. The vibration properties and proper analysis methods of these special structures are the main concerns in practical designs and analyses. Existing analytic methods can only be applied to a few cases with simple geometric shapes and boundary conditions, hence more general analysis means are needed to be developed. In this paper, a general analysis method is proposed by combining the effective medium theory (EMT) and Rayleigh–Ritz method. Based on the method, the natural vibration properties of a typical EM beam are revealed clearly and correctly, such as absence of natural frequencies within bandgap, gathering of natural frequencies in the vicinity of band edges and particular modal correspondence before and behind bandgap. The effectiveness of the proposed method is validated by the analysis results, thus providing a feasible way for analyzing many complex cases where EM beams are included.

A novel algorithm to solve for an underwater line source sound field based on coupled modes and a spectral method

A high-precision numerical sound field is the basis of underwater target detection, positioning and communication. A line source in a plane is a common type of sound source in computational ocean acoustics. The exciting waveguide in a range-dependent ocean environment is often structurally complicated; however, traditional algorithms often assume that the waveguide has a simple seabed boundary and that the line source is located at a horizontal range of 0 m, although this ideal situation is rarely encountered in the actual ocean. In this paper, a novel algorithm is designed that can solve for the sound field excited by a line source at any position in a range-dependent ocean environment. The proposed algorithm uses the classic stepwise approximation approach to address the range dependence of the environment and uses the Chebyshev–Tau spectral method to solve for the horizontal wavenumbers and modes of approximately range-independent segments. Once the modal information of these flat segments has been obtained, a global matrix is constructed to solve for the coupling coefficients of all segments, and finally, the complete sound field is synthesized. Numerical experiments using a robust numerical program developed based on this algorithm verify the correctness and usability of our novel algorithm and software. Furthermore, a detailed analysis and test of the computational cost of this algorithm show that it is efficient.

A hexagon-based method for polygon generalization using morphological operators

Numerous methods based on square rasters have been proposed for polygon generalization. However, these methods ignore the inconsistent distance measurement among neighborhoods of squares, which may result in an imbalanced generalization in different directions. As an alternative raster, a hexagon has consistent connectivity and isotropic neighborhoods. This study proposed a hexagon-based method for polygon generalization using morphological operators. First, we defined three generalization operators: aggregation, elimination, and line simplification, based on hexagonal morphological operations. We then used corrective operations with selection, skeleton, and exaggeration to detect, classify, and correct the unreasonably reduced narrow parts of the polygons. To assess the effectiveness of the proposed method, we conducted experiments comparing the hexagonal raster to square raster and vector data. Unlike vector-based methods in which various algorithms simplified either areal objects or exterior boundaries, the hexagon-based method performed both simplifications simultaneously. Compared to the square-based method, the results of the hexagon-based method were more balanced in all neighborhood directions, matched better with the original polygons, and had smoother simplified boundaries. Moreover, it performed with shorter running time than the square-based method, where the minimal time difference was less than 1 min, and the maximal time difference reached more than 50 mins.

Simplified lateral free field boundary based on a lumped mass system

Simplified lateral free field boundary based on a lumped mass system

A pressure compensation method for lattice Boltzmann simulation of particle-laden flows in periodic geometries

A simple and efficient boundary treatment is proposed for periodic boundary conditions in a lattice Boltzmann method for simulating fully developed, pressure driven particle-laden flows in a complex geometry. The pressure driven effect is implemented by a simple pressure compensation method (PCM) using the pressure difference between the inlet and outlet boundaries. It eliminates the exchange of nonequilibrium distribution functions between inlet and outlet boundary nodes. It also eliminates the nonphysical oscillations of particle trajectory produced by a nonequilibrium extrapolation method when particles cross the periodic boundary. Simulation results show that the present PCM is equivalent to the body force method (BFM) for flow in a periodic straight channel with a uniform cross section. However, the BFM would significantly underestimate the fluid velocity for a flow and, hence, cannot accurately predict the particle trajectory in a periodic complex channel with a nonuniform cross section, especially at high Reynolds numbers.

Electromagnetic Modeling of Lossy Interconnects From DC to High Frequencies With a Potential-Based Boundary Element Formulation

The accurate electromagnetic modeling of both low- and high-frequency physics is crucial in the signal and power integrity analysis of electrical interconnects. The boundary element method (BEM) is appealing for lossy conductor modeling because it can capture the frequency-dependent variation of skin depth with only a surface-based discretization of the structure. Conventional BEM formulations rely on the mutual coupling of electric and magnetic fields, and can become inaccurate or unstable at low frequencies. We develop a new full-wave BEM formulation based on potentials which can accurately model lossy conductors from exactly DC to very high frequencies. A new set of simple boundary conditions is proposed along with a modified Lorenz gauge to ensure that the proposed formulation has a stable condition number down to DC. Moreover, coupling the potential-based integral equations to a circuit model allows the straightforward extraction of network parameters. Realistic numerical examples at both the chip and package level demonstrate the accuracy and stability of the proposed method from DC to high frequencies, beyond the capabilities of state-of-the-art BEM formulations based on fields.

Mechanics of micropillar confined thin film plasticity

Micropillar compression experiments probing size effects in confined plasticity of metal thin films, including the indirect imposition of ‘canonical’ simple shearing boundary conditions, show dramatically different responses in compression and shear of the film. The Mesoscale Field Dislocation Mechanics (MFDM) model is confronted with this set of experimental observations and shown to be capable of modeling such behavior, without any ad-hoc modification to the basic structure of the theory (including boundary conditions), or the use of extra fitting parameters. This is a required theoretical advance in the current state-of-the art of strain gradient plasticity models. It is also shown that significantly different inhomogeneous fields can display qualitatively similar size effect trends in overall agreement with the experimental results. The (plastic) Swift and (elastic) Poynting finite deformation effects are also demonstrated.

A realistic arteriovenous dialysis graft model for hemodynamic simulations.

ObjectiveThe hemodynamic benefit of novel arteriovenous graft (AVG) designs is typically assessed using computational models that assume highly idealized graft configurations and/or simplified boundary conditions representing the peripheral vasculature. The objective of this study is to evaluate whether idealized AVG models are suitable for hemodynamic evaluation of new graft designs, or whether more realistic models are required.MethodsAn idealized and a realistic, clinical imaging based, parametrized AVG geometry were created. Furthermore, two physiological boundary condition models were developed to represent the peripheral vasculature. We assessed how graft geometry (idealized or realistic) and applied boundary condition models of the peripheral vasculature (physiological or distal zero-flow) impacted hemodynamic metrics related to AVG dysfunction.ResultsAnastomotic regions exposed to high WSS (>7, ≤40 Pa), very high WSS (>40 Pa) and highly oscillatory WSS were larger in the simulations using the realistic AVG geometry. The magnitude of velocity perturbations in the venous segment was up to 1.7 times larger in the realistic AVG geometry compared to the idealized one. When applying a (non-physiological zero-flow) boundary condition that neglected blood flow to and from the peripheral vasculature, we observed large regions exposed to highly oscillatory WSS. These regions could not be observed when using either of the newly developed distal boundary condition models.ConclusionHemodynamic metrics related to AVG dysfunction are highly dependent on the geometry and the distal boundary condition model used. Consequently, the hemodynamic benefit of a novel graft design can be misrepresented when using idealized AVG modelling setups.

Electroelastic Coupled-Wave Scattering and Dynamic Stress Concentration of Piezoceramics Containing Regular N-Sided Holes

In this paper, the calculation method of dynamic stress concentration around piezoelectric ceramics containing regular n-sided holes under the action of electroelastic coupling wave was studied, and it was applied to promising barium calcium zirconate titanate material. First, electroelastic governing equations were decomposed by using the auxiliary function method, and the solution forms of the elastic wave field and electric field were obtained by using the wave function expansion method. Then, the triangular boundary was simplified to a circular boundary using the mapping function, and the corresponding modal coefficients were determined according to simplified boundary conditions. Finally, the dynamic stress-concentration factor was calculated to characterize the dynamic stress concentration. We performed numerical simulations with a correlation coefficient of (1 − x)[(Ba0.94Ca0.06) (Ti0.92Sn0.08)]-xSm2O3-0.06 mol% GeO2 (abbreviated as (1 − x)BCTS-xSm-0.06G). The numerical calculation results show that the incident wave number, piezoelectric properties, shape parameters of the hole, and deflection angle have a great influence on the dynamic stress around the defect, and some significant laws are summarized through analysis.

Analysis of 2-D Steady State Heat Conduction In A Slab Subjected With Different Types of Boundary Conditions Using Method of Lines

Many disciplines in science and engineering, heat transfer plays a vital role and the problems associated with heat transfer are of great importance. Generally, two-dimensional steady state conduction is governed and transformed into a second order partial differential equation (PDE). Satisfying the differential equation along with four boundary conditions is essential for a solution to be valid. There are analytical solutions available, but only for simple boundary conditions and these are not suitable for complex boundary conditions. A technique for solving partial differential equations is Method of Lines (MOL), in which one dimension is discretized. In this study an analytical approach to a two-dimensional slab with steady state heat conduction under different types of boundary conditions is considered. The complete description of heat flow through slab using MOL is presented and the obtained PDEs are solved. Temperature distribution profiles in the slab by using MOL were plotted and compared with the profiles of analytical solutions by using MATLAB. The steady state analysis of temperature distribution in a slab with specified Dirichlet boundary conditions and Neumann boundary conditions was developed by using Method of Lines. From the profiles it is observed that as the number of lines increases, the error between analytical and MOL (semi analytical) solutions decreases, and the profiles of analytical and MOL converged which indicates the preference of higher number of lines in order to obtain accurate values.

Rapid Model Development for GSFLOW With Python and pyGSFLOW

Following the advancement of high-performance computing and sensor technology and the increased availability of larger climate and land-use data sets, hydrologic models have become more sophisticated. Instead of simple boundary conditions, these data sets are incorporated with the aim of providing more accurate insights into hydrologic processes. Integrated surface-water and groundwater models are developed to represent the most important processes that affect the distribution of water in hydrologic systems. GSFLOW is an integrated hydrologic modeling software that couples surface-water processes from PRMS and groundwater processes from MODFLOW and simulates feedbacks between both components of the hydrologic system. Development of GSFLOW models has previously required multiple tools to separately create surface-water and groundwater input files. The use of these multiple tools, custom workflows, and manual processing complicates reproducibility and confidence in model results. Based on a need for rapid, reproduceable, and robust methods, we present two example problems that showcase the latest updates to pyGSFLOW. The software package, pyGSFLOW, is an end-to-end data processing tool made from open-source Python libraries that enables the user to edit, write input files, run models, and postprocess model output. The first example showcases pyGSFLOW’s capabilities by developing a streamflow network in the Russian River watershed with an area of 3,850 km2 located on the coast of northern California. A second example examines the effects of model discretization on hydrologic prediction for the Sagehen Creek watershed with an area of 28 km2, near Lake Tahoe, California, in the northern Sierra Nevada.

Experimental analysis and simulation of a centrifugal jet fan for impulse ventilation systems

Centrifugal jet fans are usually used to stir evenly, remove local airflow blind spots, and improve air quality. They are widely used in HAVC systems of garage buildings recently. However, there are few in-depth studies on its modeling methods, and even the experimental verification of the most basic centrifugal jet fan simulation model has not been fully demonstrated. This paper combines experimental verification with numerical simulation to investigate the appropriate modeling method and jet characteristics of centrifugal jet fans for impulse ventilation systems. Experimental data showed that the air volume of each nozzle of the centrifugal jet fan was different, and that even outlet velocity of a single nozzle was not uniform. Velocity decreased slightly in the jet core area and then decreased gradually until it approached the ambient velocity, while the amount of air entrained by the jet was approximately linear with respect to the jet range. In addition, the design key points and methods of impulse ventilation systems was summarized. CFD was used to simulate the flow field of centrifugal jet fans. Two modeling strategies, involving accurate boundary conditions based on experimental data, and simplified velocity boundary conditions, were used, and displayed differing characteristics. When designers focus on the coverage range of jet fans and the velocity distribution at the far-field, or the operation performance of jet fans in HAVC systems, the simplified velocity boundary conditions can be used. When the aim is to study and optimize nozzle, an accurate model and boundary conditions should be utilized.

Numerical simulation of axially impacted elastic bar

This numerical analysis considers a model of an elastic cylindrical bar impacted by rigid mass, where the accuracy of the model is benchmarked by a closed-form solution developed for this impact process. The analytical solution provides theoretical background and understanding, however, practical problem is not always restricted to a simple one-dimensional geometry and boundary conditions of a purely elastic material behaviour. Hence, the current work numerically simulates the impacted elastic bar, then explores parameters which are not considered in its theoretical model. A two-dimensional (2D) solid axisymmetric system is considered, in which rigid impactor is assigned with initial velocity corresponding to certain drop height and a 2D contact type is defined between interacting bodies. Both elastic and time-dependent viscoelastic material models are considered in this study. The simulation results reveal time intervals gradually increase in every sequential intervals, while relatively small discrepancies are recorded for peak load and pulse width outputs. The parameters of impactor’s mass, drop height and structural stiffness are varied; showing how these parameters individually affect the resulting force response at end struck. The models then evaluate time-dependent viscoelastic material model; showing stiffer response of the resulting force in comparison to models assigned with long-term elastic moduli. Derived elastic modulus-output variable relations show comparable mathematical forms to corresponding equations formulated analytically.

Research on modeling method of porous air bearing materials based on random particles

The porous air bearing materials enable the gas throttling effect through internal pore structures. The simulation modeling of the pore structure is the prerequisite for researching the gas flow state and the bearing air film stiffness parameters. Aiming to solve the distortion problems of a single pore structure and simplified boundary conditions in the current porous material modeling process, a filling model generated via random spherical particles was proposed. Based on the normal distribution of particle diameter as well as the random position distribution, the model was used to simulate the real pore structure of porous restrictor. Along with the composite modeling DIGIMAT software, the 3D model with micro-hardness simulation was generated using ABAQUS software. The feasibility of the random filling modeling method was verified by comparing the simulation results with those obtained through hardness experiments. Hence, a reference for the modeling of high-density porous materials was provided for studying the lubricating medium flow state and material cutting mechanism in porous materials.