Infinite Boundary Conditions Research Articles

The Effect of Wind-Soil-Structure Interaction on the Longitudinal Response of High-Rise Buildings

In this work, the modelling of the wind impact on the standard tall building of CAARC (Commonwealth Advisory Aeronautical Council), which is placed on a surface spread footing, is done numerically utilizing the ABAQUS program. The wind is demonstrated as an exponential way in the boundary layer of the atmosphere. Then, stream turbulence is modeled by the ILES technique and a cosimulation is accepted to exchange non-uniform loads from fluid to structural nodes. Damping of the structure is controlled by the Rayleigh strategy. Mechanical reaction of the footing-soil framework is modeled utilizing direct strategy. Infinite boundary conditions have been added to the numerical model for the simulation of free boundaries, and reasonable contact elements for sliding and separating between subsurface components are considered. Finally, fluid solutions and structural reactions are compared with the mean and root mean squares of experimental estimations on an extensive range of reduced speeds. Numerical results for the framework of soil-structure systems were compared with base conditions without association of soil-structure interaction. It is concluded that dynamic properties and reactions of the building influence soil-structure interaction and accordingly the planners should consider these parameters keeping in mind to guarantee the practical designing.

Forced convection of Al2O3–water nanofluid flow over a porous plate under the variable magnetic field effect

In this paper, the effect of variable magnetic field on the forced-convection boundary-layer of MHD Al2O3–water nanofluid flow over a porous nonlinearly stretching flat plate is investigated using Optimal Collocation Method (OCM) and fourth order Runge–Kutta numerical method. This is the first time that CM method is developed for the problems with coupled equations which have infinite boundary condition. Comparison between OCM and numerical method shows that OCM is an exact and high efficient method for solving these kinds of problems. The influence of the nanofluid volume fraction (φ) and magnetic parameter (Mn) on non-dimensional temperature and velocity profiles are investigated. As an important outcome, by increasing Mn number, thermal boundary layer thickness significantly increased but increasing the nanofluid volume fraction hasn’t very sensible effect on it. Also it is understandable that the temperature of the fluid decreases by increasing suction parameter.

The effects of foundation size on the seismic performance of buildings considering the soil-foundation-structure interaction

Shallow footings are one of the most common types of foundations used to support mid-rise buildings in high risk seismic zones. Recent findings have revealed that the dynamic interaction between the soil, foundation, and the superstructure can influence the seismic response of the building during earthquakes. Accordingly, the properties of a foundation can alter the dynamic characteristics (natural frequency and damping) of the soil-foundation-structure system. In this paper the influence that shallow foundations have on the seismic response of a mid-rise moment resisting building is investigated. For this purpose, a fifteen storey moment resisting frame sitting on shallow footings with different sizes was simulated numerically using ABAQUS software. By adopting a direct calculation method, the numerical model can perform a fully nonlinear time history dynamic analysis to realistically simulate the dynamic behaviour of soil, foundation, and structure under seismic excitations. This three-dimensional numerical model accounts for the nonlinear behaviour of the soil medium and structural elements. Infinite boundary conditions were assigned to the numerical model to simulate free field boundaries, and appropriate contact elements capable of modelling sliding and separation between the foundation and soil elements are also considered. The influence of foundation size on the natural frequency of the system and structural response spectrum was also studied. The numerical results for cases of soil-foundation-structure systems with different sized foundations and fixed base conditions (excluding soil-foundation-structure interaction) in terms of lateral deformations, inter-storey drifts, rocking, and shear force distribution of the structure were then compared. Due to natural period lengthening, there was a significant reduction in the base shears when the size of the foundation was reduced. It was concluded that the size of a shallow foundation influences the dynamic characteristics and the seismic response of the building due to interaction between the soil, foundation, and structure, and therefore design engineer should carefully consider these parameters in order to ensure a safe and cost effective seismic design.

A differential quadrature procedure for linear and nonlinear steady state vibrations of infinite beams traversed by a moving point load

A differential quadrature procedure is proposed to study the steady state linear and nonlinear vibrations of an infinite beam resting on an elastic Winkler foundation and subjected to a moving point load. The governing nonlinear partial differential equation of motion of the beam is first expressed with respect to a moving coordinate system. This step reduces the governing nonlinear partial differential equation of motion of the beam to an ordinary nonlinear differential equation. This equation is then converted to a set of nonlinear algebraic equations by application of the differential quadrature method. The Newton–Raphson method is used to solve the resultant system of nonlinear algebraic equations. Issues related to implementation of infinite boundary conditions and modeling the point load are addressed. To accurately predict the dynamic behavior of the beam at high speeds of the moving point load, an efficient and robust absorbing boundary condition is also introduced. The fast rate of convergence of the method is demonstrated and to verify its accuracy, comparison study with available analytical solutions in the literature is performed. Numerical results reveal that the proposed procedure can be used as an effective tool for handling nonlinear moving load problems on infinite domains.

Analytical solutions for flow of horizontal well in compressible, three-dimensional unconsolidated formations

A novel mathematical model for single-phase fluid flow from unconsolidated formations to a horizontal well with the consideration of stress-sensitive permeability is presented. The model assumes the formation permeability is an exponential function of the pore pressure. Using a perturbation technique, the model is solved for either constant pressure or constant flux or infinite lateral boundary conditions with closed top and bottom boundaries. Through Laplace transformation, finite Fourier transformation and numerical inversion methods, the solutions are obtained and the pressure response curves are analyzed. The agreement between the analytical solutions in this paper and the numerical results from commercial software (Saphir) is excellent, which manifests the accuracy of the results derived in this paper.

A New Method and Applications of the Boundary Value Problem of Differential Equation

The similar structure of solution for the boundary value problem of second order linear homogeneous differential equation has been studied. Based on the analysis of the relationship between similar structure of solution, its kernel function, the equation and boundary conditions, similar constructive method (shortened as SCM) of solution is obtained. According to the SCM, the similar structure of solution and its kernel function are constructed for the mathematical model of homogeneous reservoir which considers the influence of bottom-hole storage and skin effect under the infinite outer boundary condition. The SCM is a new and innovative way to solve boundary value problem of differential equation and seepage flow theory, which is especially used in Petroleum Engineering.

Geometry and edge effects on the energy levels of graphene quantum rings: A comparison between tight-binding and simplified Dirac models

We present a systematic study of the energy spectra of graphene quantum rings having different geometries and edge types in the presence of a perpendicular magnetic field. Results are obtained within the tight-binding (TB) and Dirac models and we discuss which features of the former can be recovered by using the approximations imposed by the latter. Energy levels of graphene quantum rings obtained by diagonalizing the TB Hamiltonian are demonstrated to be strongly dependent on the rings geometry and the microscopical structure of the edges. This makes it difficult to recover those spectra by the existing theories that are based on the continuum (Dirac) model. Nevertheless, our results show that both approaches (i.e., TB and Dirac model) may provide similar results, but only for very specific combinations of ring geometry and edge types. The results obtained by a simplified model describing an infinitely thin circular Dirac ring show good agreement with those obtained for hexagonal and rhombus armchair graphene rings within the TB model. Moreover, we show that the energy levels of a circular quantum ring with an infinite mass boundary condition obtained within the Dirac model agree with those for a ring defined by a ring-shaped staggered potential obtained within the TB model.

Influence of the geomembrane on time-lapse ERT measurements for leachate injection monitoring

Leachate recirculation is a key process in the operation of municipal waste landfills as bioreactors. To quantify the water content and to evaluate the leachate injection system, in situ methods are required to obtain spatially distributed information, usually electrical resistivity tomography (ERT). However, this method can present false variations in the observations due to several parameters. This study investigates the impact of the geomembrane on ERT measurements. Indeed, the geomembrane tends to be ignored in the inversion process in most previously conducted studies. The presence of the geomembrane can change the boundary conditions of the inversion models, which have classically infinite boundary conditions. Using a numerical modelling approach, the authors demonstrate that a minimum distance is required between the electrode line and the geomembrane to satisfy the good conditions of use of the classical inversion tools. This distance is a function of the electrode line length (i.e. of the unit electrode spacing) used, the array type and the orientation of the electrode line. Moreover, this study shows that if this criterion on the minimum distance is not satisfied, it is possible to significantly improve the inversion process by introducing the complex geometry and the geomembrane location into the inversion tools. These results are finally validated on a field data set gathered on a small municipal solid waste landfill cell where this minimum distance criterion cannot be satisfied.

Three-dimensional dynamic analyses of track-embankment-ground system subjected to high speed train loads.

A three-dimensional finite element model was developed to investigate dynamic response of track-embankment-ground system subjected to moving loads caused by high speed trains. The track-embankment-ground systems such as the sleepers, the ballast, the embankment, and the ground are represented by 8-noded solid elements. The infinite elements are used to represent the infinite boundary condition to absorb vibration waves induced by the passing of train load at the boundary. The loads were applied on the rails directly to simulate the real moving loads of trains. The effects of train speed on dynamic response of the system are considered. The effect of material parameters, especially the modulus changes of ballast and embankment, is taken into account to demonstrate the effectiveness of strengthening the ballast, embankment, and ground for mitigating system vibration in detail. The numerical results show that the model is reliable for predicting the amplitude of vibrations produced in the track-embankment-ground system by high-speed trains. Stiffening of fill under the embankment can reduce the vibration level, on the other hand, it can be realized by installing a concrete slab under the embankment. The influence of axle load on the vibration of the system is obviously lower than that of train speed.

Kinematic dynamo action in square and hexagonal patterns

We consider kinematic dynamo action in rapidly rotating Boussinesq convection just above onset. The velocity is constrained to have either a square or a hexagonal pattern. For the square pattern, large-scale dynamo action is observed at onset, with most of the magnetic energy being contained in the horizontally averaged component. As the magnetic Reynolds number increases, small-scale dynamo action becomes possible, reducing the overall growth rate of the dynamo. For the hexagonal pattern, the breaking of symmetry between up and down flows results in an effective pumping velocity. For intermediate rotation rates, this additional effect can prevent the growth of any mean-field dynamo, so that only a small-scale dynamo is eventually possible at large enough magnetic Reynolds number. For very large rotation rates, this pumping term becomes negligible, and the dynamo properties of square and hexagonal patterns are qualitatively similar. These results hold for both perfectly conducting and infinite magnetic permeability boundary conditions.

Dynamical windows for real-time evolution with matrix product states

We propose the use of a dynamical window to investigate the real-time evolution of quantum many-body systems in a one-dimensional lattice. In a recent paper [Phien et al., Phys. Rev. B 86, 245107 (2012)], we introduced infinite boundary conditions in order to investigate real-time evolution of an infinite system under a local perturbation. This was accomplished by restricting the update of the tensors in the matrix product state to a finite region known as a window, with left and right boundaries held at fixed positions. Here we consider instead the use of a dynamical window, where the positions of left and right boundaries are allowed to change in time. In this way, all computational efforts can be devoted to the space-time region of interest, which leads to a remarkable reduction in simulation costs. For illustrative purposes, we consider two applications in the context of the spin-1 antiferromagnetic Heisenberg model in an infinite spin chain: one is an expanding window, with boundaries that are adjusted to capture the expansion in time of a local perturbation of the system; the other is a moving window of fixed size, where the position of the window follows the front of a propagating wave.

An algebraic approach to the problem of specification description by means of one-point subsystems

In the paper [5] necessary and sufficient conditions (consistency conditions) under which the system of one-point probability distributions indexed by infinite boundary conditions is a subsystem of some specification were found. In this note we give an algebraic interpretation of the above consistency conditions, as well as present their physical interpretation introduced by Dachian and Nahapetian.

A New Mathematical Model for Predicting CO2 Injectivity

This paper presents a new mathematical model for the estimation of CO2 injectivity in saline formations. The model is derived for pressure build-up at a fully penetrating vertical well located in a homogeneous and horizontal formation. Solutions are presented for infinite acting, closed and constant pressure formation boundary conditions. The model includes the effects of relative permeability and CO2 dissolution into formation brine and the formation of a drying-out zone around the well. To calculate the parameters required for the model, the best methods and correlations available in the literature are used. The new model is validated with numerical simulation. Using the superposition technique, the new model is extended to estimate the multi-well injectivity of CO2 in an infinite-acting saline formation.

Infinite boundary conditions for matrix product state calculations

We propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with infinite boundary conditions (IBC) where both finite size effects and boundary effects have been eliminated. For one-dimensional systems, infinite boundary conditions are obtained by attaching two boundary sites to a finite system, where each of these two sites effectively represents a semi-infinite extension of the system. One can then use standard finite-size matrix product state techniques to study a region of the system while avoiding many of the complications normally associated with finite-size calculations such as boundary Friedel oscillations. We illustrate the technique with an example of time evolution of a local perturbation applied to an infinite (translationally invariant) ground state, and use this to calculate the spectral function of the S=1 Heisenberg spin chain. This approach is more efficient and more accurate than conventional simulations based on finite-size matrix product state and density-matrix renormalization-group approaches.

Three-dimensional earthquake analysis of roller-compacted concrete dams

Abstract. Ground motion effect on a roller-compacted concrete (RCC) dams in the earthquake zone should be taken into account for the most critical conditions. This study presents three-dimensional earthquake response of a RCC dam considering geometrical non-linearity. Besides, material and connection non-linearity are also taken into consideration in the time-history analyses. Bilinear and multilinear kinematic hardening material models are utilized in the materially non-linear analyses for concrete and foundation rock respectively. The contraction joints inside the dam blocks and dam–foundation–reservoir interaction are modeled by the contact elements. The hydrostatic and hydrodynamic pressures of the reservoir water are modeled with the fluid finite elements based on the Lagrangian approach. The gravity and hydrostatic pressure effects are employed as initial condition before the strong ground motion. In the earthquake analyses, viscous dampers are defined in the finite element model to represent infinite boundary conditions. According to numerical solutions, horizontal displacements increase under hydrodynamic pressure. Besides, those also increase in the materially non-linear analyses of the dam. In addition, while the principle stress components by the hydrodynamic pressure effect the reservoir water, those decrease in the materially non-linear time-history analyses.

AN ALGEBRAIC QUANTUM DYNAMICS INVESTIGATION OF PARTICLE TRANSPORT IN A QUANTUM RING

The quantum dynamics of a driven single-band tight-binding model with infinite and Dirichlet boundary conditions is considered. The polynomial algebra for the above model but with periodic boundary conditions (quantum ring) is constructed. Based on analyzing the algebraic structures of Hamiltonian, the solution of the time-dependent Schrödinger equation is also obtained exactly.

Floquet Spectrum and Transport through an Irradiated Graphene Ribbon

Graphene subject to a spatially uniform, circularly polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator. The transport properties of this system, however, are complicated by the nonequilibrium occupations of the Floquet states. We address this by considering transport in a two-terminal ribbon geometry for which the leads have well-defined chemical potentials, with an irradiated central scattering region. We demonstrate the presence of edge states, which for infinite mass boundary conditions may be associated with only one of the two valleys. At low frequencies, the bulk dc conductivity near zero energy is shown to be dominated by a series of states with very narrow anticrossings, leading to superdiffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates.

Transmission through biased graphene strip

We solve the 2D Dirac equation describing graphene in the presence of a linear vector potential. The discretization of the transverse momentum due to the infinite mass boundary condition reduced our 2D Dirac equation to an effective massive 1D Dirac equation with an effective mass equal to the quantized transverse momentum. We use both a numerical Poincaré map approach, based on space discretization of the original Dirac equation, and a direct analytical method. These two approaches have been used to study tunneling phenomena through a biased graphene strip. The numerical results generated by the Poincaré map are in complete agreement with the analytical results.

Electronic states and optical transitions in a graphene quantum dot in a normal magnetic field

An analytical approach using the Dirac-Weyl equation is implemented to obtain the energy spectrum and optical absorption of a circular graphene quantum dot in the presence of an external magnetic field. The results are obtained for the infinite-mass and zigzag boundary conditions. We found that the energy spectra of a dot with zigzag boundary condition exhibit a zero energy band regardless of the value of the magnetic field, while for the infinite mass boundary conditions, the zero energy states appear only for high magnetic fields.

Roles of Conformational Restrictions of a Bismalonate in the Interactions with a Carbon Nanotube

We found strong site-selectivity of double cyclopropanations of the armchair (10,10) nanotube by a bismalonate with 2,3-butanediol tether. We compare this site selectivity with double cyclopropanations by CH2 and with those of the C60 fullerene. We employed density functional theory PW91 calculations based on a finite-length system as well as infinite periodic boundary condition calculations. In the double cyclopropanations by CH2, the two CH2 molecules preferentially bind to bonds orthogonal with respect to the tube axis, but several configurations remain energetically competitive. However, after the first cyclopropanation of an orthogonal bond of the tube by the bismalonate, a specific orthogonal bond is selected for the second substituent position. The key finding is that some sites display enhanced site selectivity in the double cyclopropanation partially due to geometrical strains of the bismalonate. Further essential factors include the weakening of selected bonds in the tube and the effect of the orientations of two COOH groups attached to the C atoms binding to the tube. The two factors strongly depend on the location and type of a CC bond at the attachment. The presented selectivity may aid the design of reagents for the external patterning of carbon nanotubes.