Search

We introduce the compactness locus of a geometric functor between rigidly‐compactly generated tensor‐triangulated categories, and describe it for several examples arising in equivariant homotopy theory and algebraic geometry. It is a subset of the tensor‐triangular spectrum of the target category which, crudely speaking, measures the failure of the functor to satisfy Grothendieck–Neeman duality (or equivalently, to admit a left adjoint). We prove that any geometric functor — even one which does not admit a left adjoint — gives rise to a Wirthmüller isomorphism once one passes to a colocalization of the target category determined by the compactness locus. When applied to the inflation functor in equivariant stable homotopy theory, this produces the Adams isomorphism. [ABSTRACT FROM AUTHOR]

Abstract: In this article, an integral equation satisfied by the second moment function M2(t) of a geometric process is obtained. The numerical method based on the trapezoidal integration rule proposed by Tang and Lam for the geometric function M(t) is adapted to solve this integral equation. To illustrate the numerical method, the first interarrival time is assumed to be one of four common lifetime distributions, namely, exponential, gamma, Weibull, and lognormal. In addition to this method, a power series expansion is derived using the integral equation for the second moment function M2(t), when the first interarrival time has an exponential distribution. [ABSTRACT FROM AUTHOR]

Random phase approximation (RPA) electron correlation methods have gained in popularity in the recent years. A number of RPA correlation energy variants emerged in the Kohn-Sham DFT framework and in the theory of strongly orthogonal geminals. Foundations of most RPA approaches trace back to an exact expression for two-electron reduced density matrix written in terms of one-electron density matrix and dynamic one-electron response functions, originally presented in the seminal paper of McLachlan and Ball ( Rev. Mod. Phys. 1964, 36, 844). The aim of this article is to give a pedagogical introduction to possible approaches for describing electron correlation energy based on the McLachlan and Ball formula. The focus of the presentation is to formulate electron-interaction energy expressions as functions of reduced density matrices. On one hand, it provides a common umbrella for RPA approximations proposed for uncorrelated (Hartree-Fock or Kohn-Sham) as well as partially correlated (strongly orthogonal geminals) references. On the other hand, such presentation may stimulate new developments in density matrix functional theory. [ABSTRACT FROM AUTHOR]

Continuous conformal maps are typically approximated numerically using a triangle mesh which discretizes the plane. Computing a conformal map subject to user-provided constraints then reduces to a sparse linear system, minimizing a quadratic 'conformal energy'. We address the more general case of non-triangular elements, and provide a complete analysis of the case where the plane is discretized using a mesh of regular polygons, e.g. equilateral triangles, squares and hexagons, whose interiors are mapped using barycentric coordinate functions. We demonstrate experimentally that faster convergence to continuous conformal maps may be obtained this way. We provide a formulation of the problem and its solution using complex number algebra, significantly simplifying the notation. We examine a number of common barycentric coordinate functions and demonstrate that superior approximation to harmonic coordinates of a polygon are achieved by the Moving Least Squares coordinates. We also provide a simple iterative algorithm to invert barycentric maps of regular polygon meshes, allowing to apply them in practical applications, e.g. for texture mapping. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the simultaneous distribution of the fractional parts of [ABSTRACT FROM AUTHOR]

A significant number of real-time control applications include computational activities where the results have to be delivered at precise instants, rather than within a deadline. The performance of such systems significantly degrades if outputs are generated before or after the desired target time. This work presents a general methodology that can be used to design and analyze target-sensitive applications in which the timing parameters of the computational activities are tightly coupled with the physical characteristics of the system to be controlled. For the sake of clarity, the proposed methodology is illustrated through a sample case study used to show how to derive and verify real-time constraints from the mission requirements. Software implementation issues necessary to map the computational activities into tasks running on a real-time kernel are also discussed to identify the kernel mechanisms necessary to enforce timing constraints and analyze the feasibility of the application. A set of experiments are finally presented with the purpose of validating the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

When an underwater tunnel is excavated, the groundwater may flow into the tunnel. The seepage forces consequently induced can have important effects on the effective stresses around the tunnel. Moreover, the influences of the free surface of a shallow underwater tunnel should also be considered. In this research, an analytical solution is presented to calculate the seepage-induced effective stresses around a shallow underwater tunnel in an elastic half plane. The solution uses the complex variable method and consists of conformally mapping the half plane with a hole onto a transformed circular ring. The coefficients of the various terms in the Laurent series expansions of the stress functions in the transformed region can be obtained from the boundary conditions. The total stress distribution around a shallow underwater tunnel can be calculated by the potentials in the half plane. The effective stress can be obtained by subtracting the pore pressure from the total stress. The analytical solution is validated by numerical simulations and can be used to perform both the short-term and long-term analyses. By using the proposed solution, it is found that the circumferential effective stresses around the tunnel increase greatly because of seepage, and they increase with the increase of water depth in both the undrained and drained conditions. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Using the Schwartz-Christoffel conformal mapping method together with the complex variable techniques, we derive steady state analytical solutions for pumping in a rectangular aquifer with four different combinations of impermeable and constant-head boundaries. These four scenarios include: (1) one constant-head boundary and three impermeable boundaries, (2) two pairs of orthogonal impermeable and constant-head boundaries, (3) three constant-head boundaries and one impermeable boundary, and (4) four constant-head boundaries. For these scenarios, the impermeable and constant-head boundaries can be combined after applying the mapping functions, and hence only three image wells exist in the transformed plane, despite an infinite number of image wells in the real plane. The closed-form solutions reflect the advantage of the conformal mapping method, though the method is applicable for the aspect ratio of the rectangle between 1/10.9 and 10.9/1 due to the limitation in the numerical computation of the conformal transformation from a half plane onto an elongated region (i.e., so-called "crowding" phenomenon). By contrast, for an additional scenario with two parallel constant-head boundaries and two parallel impermeable boundaries, an infinite series of image wells is necessary to express the solution, since it is impossible to combine these two kinds of boundaries through the conformal transformation. The usefulness of the results derived is demonstrated by an application to pumping in a finite coastal aquifer. [ABSTRACT FROM AUTHOR]

ABSTRACT Long bones respond to mechanical loading through functional adaptation in a suite of morphological characteristics that together ensure structural competence to in vivo loading. As such, adult bone structure is often used to make inferences about past behavior from archaeological remains. However, such biomechanical approaches often investigate change in just one aspect of morphology, typically cross-sectional morphology or trabecular structure. The relationship between longitudinal bone curvature and mobility patterns is less well understood, particularly in the tibia, and it is unknown how tibial curvature and diaphyseal cross-sectional geometry interact to meet the structural requirements of loading. This study examines tibial curvature and its relationship with diaphyseal cross-sectional geometry (CSG) and body size in preindustrial Central Europeans spanning ∼6150 years following the introduction of agriculture in the region. Anteroposterior centroid displacement from the proximo-distal longitudinal axis was quantified at nine diaphyseal section locations (collectively representative of diaphyseal curvature) in 216 tibial three-dimensional laser scans. Results documented significant and corresponding temporal declines in midshaft centroid displacement and CSG properties. Significant correlations were found between mid-diaphyseal centroid displacement and all mobility-related CSG properties, while the relationship weakened toward the diaphyseal ends. No significant relationship was found between centroid displacement and body size variables with the exception of the most distal section location. Results support a relationship between tibial curvature and cross-sectional geometry among prehistoric Central European agricultural populations, and suggest that changes in mechanical loading may have influenced a suite of morphological features related to bone adaptation in the lower limb. Am J Phys Anthropol 157:260-275, 2015. © 2015 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Some boundary value problems are solved for time-harmonic electromagnetic fields on fractal domains, in the framework of exploiting hypercomplex function theory. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a mode-I crack problem is address for a piezoelectric plate cut along two-equal-collinear semi-permeable cracks. The plate being subjected to combined in-plane mechanical and electric displacement loads, respectively. Problem is formulated using Stroh formalism and solved using complex variable technique. Closed form expressions are derived for crack opening displacement, crack opening potential drop, field intensity factors, mechanical and total energy release rates. Theoretical derivations are validated by exact solutions existing in literature. Numerical examples considered for poled ceramics PZT-4, PZT-5H, and PZT-7A show the effect of applied mechanical and electrical displacement loadings on field intensity factors, mechanical and total energy release rates. Moreover, the effect of inter-crack distance as well as different types of crack-face electric boundary conditions on field intensity factors, mechanical and total energy release rates are presented graphically, discussed, and concluded. [ABSTRACT FROM AUTHOR]