In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

In this work, we study the possibility of finite-time future cosmological singularities appearing in $f(R,T)$ gravity, where $R$ is Ricci scalar and $T$ trace stress-energy tensor. We present theory both geometrical dynamically equivalent scalar-tensor representation obtain respective equations motion. a background Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) universe with an arbitrary curvat...

The Isogeometric Analysis (IA) is utilized for structural topology optimization  considering minimization of weight and local stress constraints. For this purpose, material density of the structure  is  assumed  as  a  continuous  function  throughout  the  design  domain  and approximated using the Non-Uniform Rational B-Spline (NURBS) basis functions. Control points of the density surface are...

First-order semiclassical perturbations to the Schwarzschild black hole geometry are studied within the black hole interior. The source of the perturbations is taken to be the vacuum stress-energy of quantized scalar, spinor, and vector fields, evaluated using analytic approximations developed by Page and others (for massless fields) and the DeWitt-Schwinger approximation (for massive fields). ...

Entrainment in wetting and dewetting flows often occurs through the formation of a corner with a very sharp tip. This corner singularity comes on top of the divergence of viscous stress near the contact line, which is only regularized at molecular scales. We investigate the fine structure of corners appearing at the rear of sliding drops. Experiments reveal a sudden decrease of tip radius, down...

curvature at the horizon away from the Hawking temperature O. B. Zaslavskii Department of Physics, Kharkov State University, Svobody Sq.4, Kharkov 310077, Ukraine E-mail: [email protected] It is shown that static solutions with a finite curvature at the horizon may exist in dilaton gravity at temperatures T 6= TH (including T = 0) where TH is the Hawking one. Hawking radiation is absent and the s...

We consider branes N in a Schwarzschild-AdS(n+2) bulk, where the stress energy tensor is dominated by the energy density of a scalar fields map φ : N → S with potential V , where S is a semiRiemannian moduli space. By transforming the field equation appropriately, we get an equivalent field equation that is smooth across the singularity r = 0, and which has smooth and uniquely determined soluti...

A concurrent multigrid method is devised for the direct estimation of stress intensity factors (SIF) and higher order coefficients of the elastic crack tip asymptotic field. The proposed method bridges three characteristic length scales that can be present in fracture mechanics: the structure, the crack and the singularity at the crack tip. For each of them, a relevant model is proposed. First,...

We review the paradoxes of the problem of a moving gas–liquid–solid contact line, and the ways to eliminate them by modifying both hydrodynamic equations at mesoscopic distances and boundary conditions at the solid surface. Two kinds of applicable models are represented by the Stokes equation amended by intermolecular forces and a diffuse interface model where the fluid density enters as an add...

Firstand second-order asymptotic solutions are given for the problem of a Mode I crack rapidly propagating in an elastic}viscoplastic solid. Results are obtained for the order of the crack-tip singularity, the angular position at which unloading occurs, and the angular variations of stresses and velocities. It is shown that the eigenvalue, which determines the order of stress singularity, relat...