Search

Wormholes are considered both from the Wheeler deWitt equation, as well as from the field equations in the Euclidean background of Robertson Walker mini-superspace in R2 gravity. Quantum wormhole satisfies Hawking Page wormhole boundary condition in the Euclidean background of mini-superspace, however, in the Lorentzian background wave functional turns to the usual oscillatory function. The Euclidean field equations for κ = 0,±1 lead to the wormhole configuration, as well as oscillating universe in Euclidean time τ. The oscillating universe in Euclidean time τ transforms to an expanding universe only for κ = 1 in Lorentz time t under analytic continuation τ = it and asymptotically leads to an exponential solution. An Euclidean wormhole in the very early era evolves to an oscillating universe in τ, thereafter crossing deSitter radius transition to an inflationary era is evident at later epoch only for κ = 1. [ABSTRACT FROM AUTHOR]

AbstractWe study the plane strain problem associated with an elliptical thermoelectrically insulated and compressible liquid inclusion embedded in an infinite homogeneous and isotropic nonlinearly coupled thermoelectric matrix under uniform remote electric current density and energy flux. With the aid of conformal mapping and analytic continuation, an exact closed-form solution to the problem is derived. In particular, an elementary expression for the internal uniform hydrostatic tension within the compressible liquid inclusion is obtained. Our result shows that the internal uniform hydrostatic tension is unaffected by the remote energy flux and is proportional to the square of the two components of the remote electric current density vector. Also presented is the hoop stress distribution along the elliptical interface on the matrix side. [ABSTRACT FROM AUTHOR]

We use Muskhelishvili's complex variable formulation to study the interaction problem associated with a circular incompressible liquid inclusion embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation at an arbitrary position. A closed-form solution to the problem is derived largely with the aid of analytic continuation. We obtain, in explicit form, expressions for the internal uniform hydrostatic stresses, nonuniform strains and nonuniform rigid body rotation within the liquid inclusion; the hoop stress along the liquid-solid interface on the matrix side and the image force acting on the edge dislocation. We observe that (1) the internal strains and rigid body rotation within the liquid inclusion are independent of the elastic property of the matrix; (2) the internal hydrostatic stress field within the liquid inclusion is unaffected by Poisson's ratio of the matrix and is proportional to the shear modulus of the matrix; and (3) an unstable equilibrium position always exists for a climbing dislocation. [ABSTRACT FROM AUTHOR]

When considering initial stress field in geomaterial, nonzero resultant of shallow tunnel excavation exists, which produces logarithmic items in complex potentials, and would further lead to a unique displacement singularity at infinity to violate geo-engineering fact in real world. The mechanical and mathematical reasons of such a unique displacement singularity in the existing mechanical models are elaborated, and a new mechanical model is subsequently proposed to eliminate this singularity by constraining far-field ground surface displacement, and the original unbalanced resultant problem is converted into an equilibrium one with mixed boundary conditions. To solve stress and displacement in the new model, the analytic continuation is applied to transform the mixed boundary conditions into a homogenerous Riemann-Hilbert problem with extra constraints, which is then solved using an approximate and iterative method with good numerical stability. The Lanczos filtering is applied to the stress and displacement solution to reduce the Gibbs phenomena caused by abrupt change of the boundary conditions along ground surface. Several numerical cases are conducted to verify the proposed mechanical model and the results strongly validate that the proposed mechanical model successfully eliminates the displacement singularity caused by unbalanced resultant with good convergence and accuracy to obtain stress and displacement for shallow tunnel excavation. A parametric investigation is subsequently conducted to study the influence of tunnel depth, lateral coefficient, and free surface range on stress and displacement distribution in geomaterial. • A new mechanical model is proposed to obtain reasonable stress and displacement for shallow tunnel excavation. • The displacement singularity caused by unbalanced resultant of shallow tunnel excavation is eliminated. • Solution convergence is guaranteed using an approximate and iterative method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the representation and extension of the analytic functions of three variables by special families of functions, namely branched continued fractions. In particular, we establish new symmetric domains of the analytical continuation of Lauricella–Saran's hypergeometric function  F K  with certain conditions on real and complex parameters using their branched continued fraction representations. We use a technique that extends the convergence, which is already known for a small domain, to a larger domain to obtain domains of convergence of branched continued fractions and the PC method to prove that they are also domains of analytical continuation. In addition, we discuss some applicable special cases and vital remarks. [ABSTRACT FROM AUTHOR]

We first study the plane strain problem associated with an incompressible liquid inclusion having an n-fold axis of symmetry which is embedded in an infinite isotropic elastic matrix subjected to uniform remote hydrostatic stresses. A closed-form solution is derived using Muskhelishvili's complex variable formulation, a four-term conformal mapping function and the application of analytic continuation. The pair of analytic functions characterizing the elastic field in the matrix is completely determined in elementary closed-form. Explicit expressions are obtained and graphically illustrated for the internal uniform hydrostatic stresses within the liquid inclusion and the hoop stress along the liquid–solid interface on the matrix side. The closed-form solution for a linearly compressible liquid inclusion having an n-fold axis of symmetry is also obtained. [ABSTRACT FROM AUTHOR]

In this article, we investigate the problem of computing the $ * $ ∗ -product of domains in $ \mathbb {C}^N $ C N . Assuming that $ 0\in G\subset \mathbb {C}^N $ 0 ∈ G ⊂ C N is an arbitrary Runge domain and $ 0\in D\subset \mathbb {C}^N $ 0 ∈ D ⊂ C N is a bounded, smooth and linearly convex domain (or a non-decreasing union of such ones), we establish a geometric relation between $ D*G $ D ∗ G and another domain in $ \mathbb {C}^N $ C N which is 'extremal' (in an appropriate sense) with respect to a special coefficient multiplier dependent only on the dimension N. Next, for N = 2, we derive a characterization of the latter domain expressed in terms of planar geometry. These two results, when combined together, give a formula which allows to calculate $ D*G $ D ∗ G for two-dimensional domains D and G satisfying the outlined assumptions. [ABSTRACT FROM AUTHOR]

An analogue of Brylinski's knot beta function is defined for a compactly supported (Schwartz) distribution T on d -dimensional Euclidean space. This is a holomorphic function on a right half-plane. If T is a (uniform) double-layer on a compact smooth hypersurface, then the beta function has an analytic continuation to the complex plane as a meromorphic function, and the residues are integrals of invariants of the second fundamental form. The first few residues are computed when d = 2 and d = 3. [ABSTRACT FROM AUTHOR]

A new static equilibrium mechanical model on noncircular shallow tunnelling considering initial stress field is proposed in this paper by constraining far-field ground surface, and a mixed boundary value problem thus forms with elimination of displacement singularity at infinity. By applying analytic continuation, the mixed boundaries are transformed to a homogeneous Riemann–Hilbert problem, which is subsequently solved via an efficient and accurate iterative method with boundary conditions of static equilibrium, displacement single-valuedness, and traction along tunnel periphery. The Lanczos filtering technique is used in the final stress and displacement solution to reduce the Gibbs phenomena caused by the constrained far-field ground surface to obtain more reasonable results. Several numerical cases are conducted to intensively verify the proposed solution by examining the utilization of Lanczos filtering, the elimination of displacement singularity, and solution convergence of constraining arc and truncation number, and comparisons with existing solutions, and all the results are in good agreements. Finally, more numerical cases are conducted to investigate the stress and deformation distribution along ground surface and tunnel periphery considering different tunnel geometries, lateral coefficients, and tunnel depths. Further discussions on the defects of the proposed solution are also conducted for objectivity. [Display omitted] • A new mechanical model is proposed for noncircular shallow tunnelling. • Far-field ground surface is constrained to equilibrate unbalanced resultant due to tunnelling. • Displacement singularity at infinity caused by unbalanced resultant is eliminated. • The solution simultaneously gives correct stress and reasonable displacement. [ABSTRACT FROM AUTHOR]