New Type Of Boundary Condition Research Articles

One-Shot Omnidirectional Pressure Integration Through Matrix Inversion

In this work, we present a method to perform 2D and 3D omnidirectional pressure integration from velocity measurements with a single-iteration matrix inversion approach. This work builds upon our previous work, where the rotating parallel ray approach was extended to the limit of infinite rays by taking continuous projection integrals of the ray paths and recasting the problem as an iterative matrix inversion problem. This iterative matrix equation is now ``fast-forwarded'' to the ``infinity'' iteration, leading to a different matrix equation that can be solved in a single iteration, thereby presenting the same computational complexity as the Poisson equation. We observe computational speedups of $\sim10^6$ when compared to brute-force omnidirectional integration methods, enabling the treatment of grids of $\sim 10^9$ points and potentially even larger in a desktop setup at the time of publication. Further examination of the boundary conditions of our one-shot method shows that omnidirectional pressure integration implements a new type of boundary condition, which treats the boundary points as interior points to the extent that information is available.

GPU-based molecular dynamics of fluid flows: Reaching for turbulence

Fluid dynamics is a ubiquitous problem that arises in different branches of science and industry. It is usually tackled by numerically solving continuum Navier-Stokes type equations. Molecular dynamics has been not a feasible tool to approach fluid dynamics until very recently due to its disproportional computational complexity for relevant system sizes. In this paper, we propose a new type of boundary conditions for molecular dynamics simulations of stationary fluid flows and present its possible GPU-based implementations in OpenMM and LAMMPS. We examine the performance and scalability of the proposed implementations. The benchmarking results show promising performance that makes it possible to reach turbulence in atomistic models of stationary fluid flows using modern supercomputers.

2D Linear CA with Mixing Boundary Conditions and Reversibility

In this paper, we consider two-dimensional cellular automata (CA) with the von Neumann neighborhood. We study the characterization of 2D linear cellular automata defined by the von Neumann neighborhood with new type of boundary conditions over the field [Formula: see text]. Furthermore, we investigate the rule matrices of 2D von Neumann CA by applying the group of permutations [Formula: see text]. Moreover, the algorithm for computing the rank of rule matrices is given. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for considered two-dimensional cellular automata are obtained.

A class of short-term models for the oil industry that accounts for speculative oil storage

We propose a plausible mechanism for the short-term dynamics of the oil market based on the interaction of a cartel, a fringe of competitive producers, and a crowd of capacity-constrained physical arbitrageurs that store the resource. The model leads to a system of two coupled nonlinear partial differential equations, with a new type of boundary conditions that play a key role and translate the fact that when storage is either full or empty, the cartel has enhanced strategic power. We propose a finite difference scheme and report numerical simulations. The latter result in apparently surprising facts: 1) the optimal control of the cartel (i.e., its level of production) is a discontinuous function of the state variables; 2) the optimal trajectories (in the state variables) are cycles which take place around the discontinuity line. These patterns help explain remarkable price swings in oil prices in 2015 and 2020.

On a new type of boundary condition

On a new type of boundary condition

Heat flux during boiling of superfluid helium inside a porous body based on a two-fluid model

The calculation of the recovery heat flux density is considered for superfluid helium boiling on the cylindrical heater inside porous structure. System of equations is based on the methods of continuum mechanics and molecular kinetic theory. The new type of boundary condition on the vapor-liquid interface based on the two-fluid model is formulated. Heat transfer in a free liquid is described by the Gorter-Mellink semi-empirical theory. Inside the porous structure the processes is discussed by the two-fluid model and filtration equation. Experimental data on the boiling of superfluid helium inside the porous structure are interpreted based on the formulated mathematical model. The qualitative and in some cases quantitative agreement between the calculated and experimental values of the recovery heat flux were obtained in the considered range of parameters

Methods of the wall interference reduction at low supersonic velocities in wind tunnels

The paper describes the research aimed at reducing wall interference in wind tunnels at low supersonic velocities. The results of such wind tunnel tests are often affected by wave perturbations generated by the model and reflected from the test section walls. This research describes the methods that can effectively reduce the wave reflection from the wall. A numerical investigation is presented that includes a novel boundary condition that eliminates disadvantages of previously considered methods. The numerical study was conducted in the frame of electronic wind tunnel concept and ANSYS CFX software. The numerical investigation showed that the effect of shock wave reflection could be reduced using a new type of boundary condition that is a combination of perforated walls and a controlled boundary layer.

Nonlinear Fractionalq-Difference Equation with Fractional Hadamard and Quantum Integral Nonlocal Conditions

In this paper, we establish existence and uniqueness results for a boundary value problem consisting by a nonlinear fractionalq-difference equation subject to a new type of boundary condition, combining the fractional Hadamard and quantum integrals. Our analysis is based on Banach’s fixed point theorem, a fixed point theorem for nonlinear contractions, Krasnosel’skii˘’s fixed point theorem, and Leray-Schauder nonlinear alternative. Examples are given to illustrate our results.

Thermal Casimir interactions for higher derivative field Lagrangians: generalized Brazovskii models

We examine the Casimir effect for free statistical field theories which have Hamiltonians with second order derivative terms. Examples of such Hamiltonians arise from models of non-local electrostatics, membranes with non-zero bending rigidities and field theories of the Brazovskii type that arise for polymer systems. The presence of a second derivative term means that new types of boundary conditions can be imposed, leading to a richer phenomenology of interaction phenomena. In addition zero modes can be generated that are not present in standard first derivative models, and it is these zero modes which give rise to long range Casimir forces. Two physically distinct cases are considered: (i) unconfined fields, usually considered for finite size embedded inclusions in an infinite fluctuating medium, here in a two plate geometry the fluctuating field exists both inside and outside the plates, (ii) confined fields, where the field is absent outside the slab confined between the two plates. We show how these two physically distinct cases are mathematically related and discuss a wide range of commonly applied boundary conditions. We concentrate our analysis to the critical region where the underlying bulk Hamiltonian has zero modes and show that very exotic Casimir forces can arise, characterised by very long range effects and oscillatory behavior that can lead to strong metastability in the system.

Energy conversion and deposition behaviour in gravitational collapse of granular columns

The high-density gravitational collapse of granular columns is very similar to the movements of large collapsing columns in nature. Based on the development of dangerous columnar rock mass in fields, granular column collapse boundary condition in the physical experiments of this study is a new type of boundary conditions with a single free face and a three-dimensional deposit. Physical experiments have shown that the mobility of small particles during the collapse of granular columns was greater than that of large particles. For example, when particle size was increased from 5 to 15 mm, deposit runout was decreased by about 16.4%. When a column consisted of two particle types with different sizes, these particles could mix in the vicinity of layer interfaces and small particles might increase the mobility of large particles. In the process of collapse, potential and kinetic energy conversion rate is fluctuated. By increasing initial aspect ratio a, the ratio of the initial height of column to its length along flow direction, potential and kinetic energy conversion rate is decreased. For example, as a was increased from 0.5 to 4, the ratio of maximum kinetic energy obtained and total potential energy loss was decreased from 47.6% to 7.4%. After movement stopped, an almost trapezoidal body remained in the column and a fanlike or fan-shaped accumulation was formed on the periphery of column. Using multiple exponential functions of the aspect ratio a, the planar morphology of the collapse deposit of granular columns could be quantitatively characterized. The movement of pillar dangerous rock masses with collapse failure mode could be evaluated using this granular column experimental results.

Convergence of a [formula omitted]-[formula omitted] based finite element method for MHD models on Lipschitz domains

We discuss a class of magnetic–electric fields based finite element schemes for stationary magnetohydrodynamics (MHD) systems with two types of boundary conditions. We establish a key L3 estimate for divergence-free finite element functions for a new type of boundary conditions. With this estimate and a similar one in Hu and Xu (2018), we rigorously prove the convergence of Picard iterations and the finite element schemes with weak regularity assumptions. These results demonstrate the convergence of the finite element methods for singular solutions.

Variational formulations, model comparisons and numerical methods for Euler–Bernoulli micro- and nano-beam models

As a first step, variational formulations and governing equations with boundary conditions are derived for a pair of Euler–Bernoulli beam bending models following a simplified version of Mindlin’s strain gradient elasticity theory of form II. For both models, this leads to sixth-order boundary value problems with new types of boundary conditions that are given additional attributes singly and doubly, referring to a physically relevant distinguishing feature between free and prescribed curvature, respectively. Second, the variational formulations are analyzed with rigorous mathematical tools: the existence and uniqueness of weak solutions are established by proving continuity and ellipticity of the associated symmetric bilinear forms. This guarantees optimal convergence for conforming Galerkin discretization methods. Third, the variational analysis is extended to cover two other generalized beam models: another modification of the strain gradient elasticity theory and a modified version of the couple stress theory. A model comparison reveals essential differences and similarities in the physicality of these four closely related beam models: they demonstrate essentially two different kinds of parameter-dependent stiffening behavior, where one of these kinds (possessed by three models out of four) provides results in a very good agreement with the size effects of experimental tests. Finally, numerical results for isogeometric Galerkin discretizations with B-splines confirm the theoretical stability and convergence results. Influences of the gradient and thickness parameters connected to size effects, boundary layers and dispersion relations are studied thoroughly with a series of benchmark problems for statics and free vibrations. The size-dependency of the effective Young’s modulus is demonstrated for an auxetic cellular metamaterial ruled by bending-dominated deformation of cell struts.

A seepage outlet boundary condition in hemodynamics modeling.

In computational fluid dynamics (CFD) models for hemodynamics applications, boundary conditions remain one of the major issues in obtaining accurate fluid flow predictions. As an important part of the arterial circulation, microcirculation plays important roles in many aspects, such as substance exchange, interstitial fluid generation and inverse flow. It is necessary to consider microcirculation in hemodynamics modeling. This is a methodological paper to test and validate a new type of boundary condition never applied to microcirculation before. In order to address this issue, we introduce microcirculation as a seepage outlet boundary condition in computational hemodynamics. Microcirculation is treated as a porous medium in this paper. Numerical comparisons of the seepage and traditional boundary conditions are made. The results show that the seepage boundary condition has significant impacts on numerical simulation. Under the seepage boundary condition, the fluctuation range of the pressures progressively rises in the artery zone. The results obtained from the traditional boundary condition show that the pressure fluctuation range gradually falls. In addition, the wall shear stresses under the traditional outlet boundary condition are much higher than those under the seepage outlet boundary condition. The proposed boundary condition is more suitable in hemodynamics modeling.

Parallelized 3D CSEM modeling using edge-based finite element with total field formulation and unstructured mesh

We solve the 3D controlled-source electromagnetic (CSEM) problem using the edge-based finite element method. The modeling domain is discretized using unstructured tetrahedral mesh. We adopt the total field formulation for the quasi-static variant of Maxwell's equation and the computation cost to calculate the primary field can be saved. We adopt a new boundary condition which approximate the total field on the boundary by the primary field corresponding to the layered earth approximation of the complicated conductivity model. The primary field on the modeling boundary is calculated using fast Hankel transform. By using this new type of boundary condition, the computation cost can be reduced significantly and the modeling accuracy can be improved. We consider that the conductivity can be anisotropic. We solve the finite element system of equations using a parallelized multifrontal solver which works efficiently for multiple source and large scale electromagnetic modeling.

Variational formulations and general boundary conditions for sixth-order boundary value problems of gradient-elastic Kirchhoff plates

Abstract Sixth-order boundary value problems for gradient-elastic Kirchhoff plate bending models are formulated in a variational form within an H 3 Sobolev space setting. Existence and uniqueness of the weak solutions are then established by proving the continuity and coercivity of the associated symmetric bilinear forms. Complete sets of boundary conditions, including both the essential and the natural conditions, are derived accordingly. In particular, the gradient-elastic Kirchhoff plate models feature two different types of clamped and simply supported boundary conditions in contrast to the classical Kirchhoff plate model. These new types of boundary conditions are given additional attributes singly and doubly ; referring to free and prescribed normal curvature, respectively. The formulations and results of the analyzed strain gradient plate models are compared to two other generalized Kirchhoff plate models which follow a modified strain gradient elasticity theory and a modified couple stress theory. It is clarified that the results are extendable to these model variants as well. Finally, the relationship of the natural boundary conditions to external loadings is analyzed.

Boundary conditions for Maxwell fields in Kerr-AdS spacetimes

Perturbative methods are useful to study the interaction between black holes and test fields. The equation for a perturbation itself, however, is not complete to study such a composed system if we do not assign physically relevant boundary conditions. Recently we have proposed a new type of boundary conditions for Maxwell fields in Kerr-anti-de Sitter (Kerr-AdS) spacetimes, from the viewpoint that the AdS boundary may be regarded as a perfectly reflecting mirror, in the sense that energy flux vanishes asymptotically. In this paper, we prove explicitly that a vanishing energy flux leads to a vanishing angular momentum flux. Thus, these boundary conditions may be dubbed as vanishing flux boundary conditions.

Variational formulation and isogeometric analysis for fourth-order boundary value problems of gradient-elastic bar and plane strain/stress problems

The fourth-order boundary value problems of one parameter gradient-elastic bar and plane strain/stress models are formulated in a variational form within an H2 Sobolev space setting. For both problems, the existence and uniqueness of the solution is established by proving the continuity and coercivity of the associated symmetric bilinear form. For completeness, the full sets of boundary conditions of the problems are derived and, in particular, the new types of boundary conditions featured by the gradient-elastic models are given the additional attributes singly and doubly. By utilizing the continuity and coercivity of the continuous problems, corresponding error estimates are formulated for conforming Galerkin formulations. Finally, numerical results, with isogeometric Cp−1-continuous discretizations for NURBS basis functions of order p≥2, confirm the theoretical results and illustrate the essentials of both static and vibration problems.

Development of a new analytic function expansion nodal code, HexDANM, for solving the neutron diffusion equation in hexagonal-Z geometry

Abstract In this paper, we developed a new approach of analytic function expansion nodal (AFEN) method to solve the multi-group and multi-dimensional neutron diffusion equation in reactor cores with hexagonal fuel assembly. This method represents a multidimensional intra nodal flux distribution in terms of analytic basis functions at any points in the node. New types of boundary conditions have been considered that constrain the intranodal flux distributions in the hexagonal-z node, which include twelve radial surface-averaged partial currents and two axial surface-averaged partial currents. We utilized the coarse group rebalancing (CGR) method to increase the speed of code calculations. The computer code takes a few-groups cross sections produced by a lattice code and calculates the effective multiplication factor (keff ), flux in multi-group energy, reactivity, and the relative power density at each fuel assembly. Finally, the solution accuracy is tested for two well-known benchmark problems. The numerical results demonstrate that the new AFEN method is an accurate method for calculating keff and power density distribution in hexagonal-z geometries.

Plane elasticity solutions for beams with fixed ends

The plane stress problem of beams is a typical one in elasticity theory. In this paper a new set of boundary conditions for the fixed end is proposed to improve the accuracy of the plane elasticity solution for beams with fixed end(s). Plane elasticity solutions are then derived for the cantilever beam, propped cantilever beam, and fixed-fixed beam. The new set of boundary conditions is constructed by combining two conventional ones with a parameter. The parameters for different kinds of beams are determined by minimizing the square sum of the longitudinal displacements through the thickness of the fixed end. Comparison with the results obtained by the finite element method (FEM) shows the efficiency of the new type of boundary conditions. When the beam is a deep one, it is found that different boundary conditions yield different errors, and the elasticity solution obtained by the new boundary conditions best approaches the FEM results.

Analysis of the propagation characteristics of circular step-index fibre with new sheath helix boundary condition

A circular step-index fibre with a helical winding on the core-cladding boundary is proposed and investigated analytically with a new type of boundary condition. Using cylindrical coordinate system (r, ϕ, z), new boundary conditions are imposed and longitudinal field components are obtained. The equation involves Bessel and modified Bessel functions. Numerical computations are made. Dispersion curves are obtained for different pitch angles. The main effect of the helical winding on the characteristics is to introduce band gaps.