Meaningful Boundary Research Articles

Numerical analysis and visualization of fine structures of the fields of two-dimensional attached internal waves

In the linear approximation, we compute the patterns of two-dimensional perturbations formed in a viscous exponentially stratified fluid in the process of motion of a plate at an arbitrary angle to the horizon. The exact solution of the problem obtained in quadratures and satisfying the physically meaningful boundary conditions is numerically analyzed. The properties of the fields are computed and described in broad ranges of all parameters of the problem, including the length and velocity of motion of the plate, the characteristics of stratification and viscosity of the medium, and the slope of the path. In the picture of currents, we distinguish two groups of waves and compact nonwave singularities near the edges of a source of generation. The results of comparison with the available data of independently performed calculations and experiments reveal the existing agreement between the computed and observed pictures of the currents.

Image‐based modeling of lung structure and function

The current state-of-the-art in image-based modeling allows derivation of patient-specific models of the lung, lobes, airways, and pulmonary vascular trees. The application of traditional engineering analyses of fluid and structural mechanics to image-based subject-specific models has the potential to provide new insight into structure-function relationships in the individual via functional interpretation that complements imaging and experimental studies. Three major issues that are encountered in studies of airflow through the bronchial airways are the representation of airway geometry, the imposition of physiological boundary conditions, and the treatment of turbulence. Here we review some efforts to resolve each of these issues, with particular focus on image-based models that have been developed to simulate airflow from the mouth to the terminal bronchiole, and subjected to physiologically meaningful boundary conditions via image registration and soft-tissue mechanics models.

On the propagation of localization in the plasticity collapse of hardening–softening beams

This paper is focused on the propagation of localization in hardening–softening plasticity media. Using a piecewise linear plasticity hardening–softening constitutive law, we look at the 1D propagation of plastic strains along a bending beam. Such simplified models can be useful for the understanding of plastic buckling of tubes in bending, the bending response of thin-walled members experiencing softening induced by the local buckling phenomenon, or the bending of composite structures at the ultimate state (reinforced concrete members, timber beams, composite members, etc.). The cantilever beam is considered as a structural paradigm associated to generalized stress gradient. An integral-based non-local plasticity model is developed, in order to overcome Wood’s paradox when softening prevails. This plasticity model is derived from a variational principle, leading to meaningful boundary conditions. The need to introduce some non-locality in the hardening regime is also discussed. We show that the non-local plastic variable during the softening process has to be strictly defined within the localized softening domain. The propagation of localization is theoretically highlighted, and the softening region grows during the softening process until a finite length region. The pre-hardening response has no influence on the propagation law of localization in the softening regime. It is also shown that the “material” time derivative and the “partial” time derivative have to be explicitly distinguished, especially for moving elastoplastic boundaries. It is recommended to use the “material” time derivative in the rate-format of the boundary value problem.

Electromagnetic Boundary Conditions Defined in Terms of Normal Field Components

A set of four scalar conditions involving normal components of the fields <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</b> and <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</b> and their normal derivatives at a planar surface is introduced, among which different pairs can be chosen to represent possible boundary conditions for the electromagnetic fields. Four such pairs turn out to yield meaningful boundary conditions and their responses for an incident plane wave at a planar boundary are studied. The theory is subsequently generalized to more general boundary surfaces defined by a coordinate function. It is found that two of the pairs correspond to the PEC and PMC conditions while the other two correspond to a mixture of PEC and PMC conditions for fields polarized TE or TM with respect to the coordinate defining the surface.

Shell theory equations consistent with boundary conditions at face surfaces

Shell theory equations consistent with physically meaningful boundary conditions at face surfaces are obtained from the three-dimensional deformable-body mechanics equations related to the reference and actual configurations.

Generation of Gevrey class semigroup by non-selfadjoint Euler–Bernoulli beam model

Asymptotic and spectral properties of a non-selfadjoint operator that is a dynamics generator for the Euler–Bernoulli beam model of a finite length are studied in this paper. The hyperbolic equation, which governs the vibrations of the Euler–Bernoulli beam model, is supplied with a one-parameter family of physically meaningful boundary conditions containing damping terms. The initial boundary-value problem is equivalent to the evolution equation that generates a strongly continuous semigroup in the state space of the system. It is found that the semigroup, being non-analytic, belongs to Gevrey class semigroups. This means that the differentiability of such semigroup is slightly weaker than that of an analytic semigroup. In the forthcoming works, the results of the present paper will be applied (a) to the solution of the exact controllability problem for Euler–Bernoulli beam and (b) to spectral analysis of a planar network of serially connected Euler–Bernoulli beams modelling ‘flying wing configurations’ in aeronautic engineering. Copyright © 2006 John Wiley & Sons, Ltd.

Evaluation of seismic site factors in the Mississippi Embayment. II. Probabilistic seismic hazard analysis with nonlinear site effects

An integrated probabilistic seismic hazard analysis procedure that incorporates nonlinear site effects, PSHA-NL, is developed and used to characterize the influence of thick deposits of the upper Mississippi Embayment (ME) on seismic site coefficients. PSHA-NL follows the methodology of the 2002 USGS hazard maps and generates a compatible set of ground motion records. The motions are propagated using nonlinear and equivalent linear site response analyses and ME properties developed in a companion paper and used to derive surface uniform hazard response spectra. A set of generic site coefficients are derived and summarized in a format similar to NEHRP site coefficients, with an added dimension of ME deposits thickness to the Paleozoic rock, a physically meaningful impedance boundary. These coefficients compare well with NEHRP site coefficients for 30 m profiles. For thicker soil profiles, developed site coefficients are lower at short periods and higher at long periods than NEHRP site coefficients.

A NUMERICAL METHOD FOR WAVE SCATTERING IN POROELASTIC MEDIA

Wave scattering in the Biot's poroelastic media is investigated using a numerical method based on the boundary integral formulation. The formulation adopts the fundamental solution derived with a direct manner and traction operators for physically meaningful boundary conditions. Some numerical examples for wave incidence on a spherical scatterer is presented. In the examples, coupling effects of solid and fluid are parameterized with coupling parameters and the boundary conditions. The results show that scattered fields, especially pore pressure, are highly influenced by the coupling effects with the conversion of the fast longitudinal wave to the slow one.

A symmetric nonlocal damage theory

The paper presents a thermodynamically consistent formulation for nonlocal damage models. Nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening. The main features of the presented formulation are: (i) relations derived by the free energy potential fully complying with nonlocal thermodynamic principles; (ii) nonlocal integral operator which is self-adjoint at every point of the solid, including zones near to the solid’s boundary; (iii) capacity of regularizing the softening ill-posed continuum problem, restoring a meaningful nonlocal boundary value problem. In the present approach the nonlocal integral operator is applied consistently to the damage variable and to its thermodynamic conjugate force, i.e. nonlocality is restricted to internal variables only. The present model, when associative nonlocal damage flow rules are assumed, allows the derivation of the continuum tangent moduli tensor and the consistent tangent stiffness matrix which are symmetric. The formulation has been compared with other available nonlocal damage theories. Finally, the theory has been implemented in a finite element program and the numerical results obtained for 1-D and 2-D problems show its capability to reproduce in every circumstance a physical meaningful solution and fully mesh independent results.

Electrostatic potentials and covalent radii.

We begin with a brief overview of the electrostatic potential V(r) as a fundamental determinant of the properties of systems of electrons and nuclei. The minimum of V(r) along the internuclear axis between two bonded atoms is a natural and physically meaningful boundary point, at which the electrostatic forces of the two nuclei upon an element of charge exactly cancel. We propose that the distances from nuclei to V(r) bond minima provide the basis for a well-defined set of covalent radii. Density functional calculations at the B3PW91/6-311+G** level were carried out for 59 molecules to locate the V(r) minima in 95 bonds and use these as the basis for determining single- and multiple-bond covalent radii for eight first- and second-row atoms plus hydrogen. It was found to be unrealistic to assign a single covalent radius to each atom; different values are needed for bonds to first- and second-row atoms, as well as to hydrogen. Using these results, we are able to predict the bond lengths of 33 single and multiple bonds with average errors of less than 0.04 A relative to experimental data.

Statistical Methods in Assessing Agreement

Measurements of agreement are needed to assess the acceptability of a new or generic process, methodology, and formulation in areas of laboratory performance, instrument or assay validation, method comparisons, statistical process control, goodness of fit, and individual bioequivalence. In all of these areas, one needs measurements that capture a large proportion of data that are within a meaningful boundary from target values. Target values can be considered random (measured with error) or fixed (known), depending on the situation. Various meaningful measures to cope with such diverse and complex situations have become available only in the last decade. These measures often assume that the target values are random. This article reviews the literature and presents methodologies in terms of “coverage probability.” In addition, analytical expressions are introduced for all of the aforementioned measurements when the target values are fixed and when the error structure is homogenous or heterogeneous (proportional to target values). This article compares the asymptotic power of accepting the agreement across all competing methods and discusses the pros and cons of each. Data when the target values are random or fixed are used for illustration. A SAS macro program to compute all of the proposed methods is available for download at http://www.uic.edu/~hedayat/.

Completely Regularized Integral Representations and Integral Equations for Anisotropic Bodies with Initial Strains

The present paper is devoted to the boundary formulation for anisotropic bodies subjected to a distribution of initial strains. Concerning both interior and exterior problems, the results are featured by the complete regularization of all the derived expressions: the integral representation of the displacement gradients and the stresses as well as the ordinary or derivative integral equations. The formulation also includes the case of piecewise regular boundary with edges or corners. Furthermore, explicit expressions in terms of physical meaningful boundary quantities such as the stresses related to the normal vector and the tangent derivatives of the displacements are given, which is particularly useful for further numerical implementations.

Does Latin America Exist? (And is There a Confucian Culture?): A Global Analysis of Cross-Cultural Differences

Does Latin America exist?Latin American studies centers (like African, or Middle Eastern or West European studies centers) are based on the assumption that Latin America (and Africa, the Middle East, etc.) are more than arbitary geographic expressions: they define coherent cultural regions, having people with distinctive values and worldviews that make them think differently and behave differently from people of other cultures.The most powerful challenge to this view currently comes from the rational choice school, whose practitioners occasionally mention the importance of cultural differences but whose models almost always ignore them, implicitly assuming that in a given situation all people will make the same “rational” choices regardless of cultural perspectives. But if major differences exist between the worldviews and motivations of people in different cultural zones, a rational choice model that applies to the United States may not accurately describe the behavior of people in other cultures.The existence of meaningful cultural areas has been challenged on other grounds as well. Modernization theory focuses on the differences between “traditional” and “modern” societies, each of which are characterized by distinctive economic, political, social, and cultural institutions. This perspective tends to attribute any differences between Latin American and highly industrialized societies to differences in their levels of economic development: with economic development, these differences will tend to disappear. Differences between various “traditional” cultures tend to be ignored.The usefulness of “Latin America” as a meaningful cultural boundary could also be disputed on various other grounds.

Does Latin America Exist? (And is There a Confucian Culture?): A Global Analysis of Cross-Cultural Differences

Does Latin America exist?Latin American studies centers (like African, or Middle Eastern or West European studies centers) are based on the assumption that Latin America (and Africa, the Middle East, etc.) are more than arbitary geographic expressions: they define coherent cultural regions, having people with distinctive values and worldviews that make them think differently and behave differently from people of other cultures.The most powerful challenge to this view currently comes from the rational choice school, whose practitioners occasionally mention the importance of cultural differences but whose models almost always ignore them, implicitly assuming that in a given situation all people will make the same “rational” choices regardless of cultural perspectives. But if major differences exist between the worldviews and motivations of people in different cultural zones, a rational choice model that applies to the United States may not accurately describe the behavior of people in other cultures.The existence of meaningful cultural areas has been challenged on other grounds as well. Modernization theory focuses on the differences between “traditional” and “modern” societies, each of which are characterized by distinctive economic, political, social, and cultural institutions. This perspective tends to attribute any differences between Latin American and highly industrialized societies to differences in their levels of economic development: with economic development, these differences will tend to disappear. Differences between various “traditional” cultures tend to be ignored.The usefulness of “Latin America” as a meaningful cultural boundary could also be disputed on various other grounds.

PDE boundary conditions from minimum reduction of the PDE

Convection-diffusion partial differential equations (PDEs) are second order in the direction of flow, and therefore require two boundary conditions with respect to the spatial independent variable in that direction. The entering or “inflow” boundary condition is usually obvious. The exiting or “outflow” boundary condition is not so obvious. We propose reducing the PDE by one order in the direction of flow to produce the outflow boundary condition. This procedure is illustrated with a dynamic version of the classical Graetz problem in heat transfer. The proposed procedure has the advantages of physically meaningful boundary conditions which produce numerical solutions of good accuracy, and ease of implementation in a method of lines code.

Finite element implementation of boundary conditions for the pressure Poisson equation of incompressible flow

AbstractIn this paper we address the problem of the implementation of boundary conditions for the derived pressure Poisson equation of incompressible flow. It is shown that the direct Galerkin finite element formulation of the pressure Poisson equation automatically satisfies the inhomogeneous Neumann boundary conditions, thus avoiding the difficulty in specifying boundary conditions for pressure. This ensures that only physically meaningful pressure boundary conditions consistent with the Navier‐Stokes equations are imposed. Since second derivatives appear in this formulation, the conforming finite element method requires C1 continuity. However, for many problems of practical interest (i.e. high Reynolds numbers) the second derivatives need not be included, thus allowing the use of more conventional C0 elements. Numerical results using this approach for a wall‐driven contained flow within a square cavity verify the validity of the approach. Although the results were obtained for a two‐dimensional problem using the p‐version of the finite element method, the approach presented here is general and remains valid for the conventional h‐version as well as three‐dimensional problems.

Nodal-based finite-element modeling of Maxwell's equations

Weak forms are derived for Maxwell's equations which are suitable for implementation on conventional C/sup 0/ elements with scalar bases. The governing equations are expressed in terms of general vector and scalar potentials for the electric field intensity vector. Gauge theory is invoked to close the system and dictates the continuity requirements for the potentials at material interfaces as well as the blend of boundary conditions at exterior boundaries. Two specific gauges are presented, both of which lead to Helmholtz weak forms which are parasite-free and enjoy simple, physically meaningful boundary conditions. A general and numerically efficient procedure for enforcing the jump discontinuities on the normal components of vector fields at dielectric interfaces and boundary conditions on curved surfaces is also given. >

Continuity requirements for density functions in the boundary integral equation method

Two methods of forming regular or hypersingular boundary integral equations starting from an interior integral representations are discussed. One method involves direct treatment of the singularities such as Cauchy principal value and/or finite-part interpretation of the integrals and the other does not. By either approach, theory places the same restrictions on the smoothness of the density function for the integrals to exist, assuming sufficient smoothness of the geometrical boundary itself. Specifically, necessary conditions on the smoothness of the density function for meaningful boundary integral formulas to exist as required for the collocation procedure are established here. Cases for which such conditions may not be sufficient are also mentioned and it is understood that with Galerkin techniques, weaker smoothness requirements may pertain. Finally, the bearing of these issues on the choice of boundary elements, to numerically solve a hypersingular boundary integral equation, is explored and numerical examples in 2D are presented.

Non‐linear boundary value problems for the annular membrane: New results on existence of positive solutions

AbstractThe Föppl‐Hencky theory of small finite deflections has been applied to the study of axisymmetric deformations of annular membranes by various authors. The mathematical problem of uniqueness of tensile solutions for the corresponding non‐linear boundary value problems in the full range of physically meaningful boundary data was solved only recently.3, 4 In this paper, a new integral equation technique of solution is developed which yields the existence of tensile solutions for a parameter range of the boundary data where previous investigations on this matter had not been successful. It is shown that tensile solutions no longer exist, when sufficiently large positive radial displacements are prescribed at the inner edge of the annulus.

The dependence of bacterial sulfate reduction on sulfate concentration in marine sediments

The effect of dissolved sulfate concentration on the rate of bacterial sulfate reduction in marine sediment from Long Island Sound was examined using a radio-sulfur technique. The experimental results show that the rate is independent of the dissolved sulfate concentration until low levels are reached (<3 mM), and that, when interpreted using a Monod-type rate law, a saturation constant, K s , of 1.62 ± 0.16 M results. This weak dependence implies that the dissolved sulfate exerts only a limited influence on the rate of sulfate reduction in marine sediments. Given such a weak dependence, dissolved sulfate profiles in marine sediments must resemble profiles generated by models with sulfate independent kinetics. Initially, this would suggest that currently used sulfate-independent diagenetic models are appropriate in modelling sulfate profiles. However, comparison of these models with those containing weak sulfate-dependent kinetic terms shows that there exists considerable disagreement between these models when the parameter grouping (D sk) 1 2 /w is larger than ~0.2 and smaller than ~3.0. (Here D s is the SO ; 4 diffusion coefficient, k the organic matter decay constant and w the sediment burial velocity.) When the currently used models are corrected by employing physically meaningful boundary conditions, this divergence disappears. The modelling results, therefore, confirm the conclusion that any sulfate dependence inherent to the reduction kinetics does not appreciably affect sulfate pore water profiles, and that previous diagenetic studies using strong sulfate dependent models are erroneous.