We discuss Einstein’s field equations in the presence of signature change using variational methods, obtaining a generalization of the Lanczos equation relating the distributional term in the stress tensor to the discontinuity of the extrinsic curvature. In particular, there is no distributional term in the stress tensor, and hence no surface layer, precisely when the extrinsic curvature is con...

We present a phase-imaging method with an axial range that can in principle be arbitrarily large compared to the wavelength and does not involve the usual phase unwrapping by detection of phase discontinuity. The method consists of the generation and combination of two phase maps in a digital holography system by use of two separate wavelengths. For example, we reconstructed the surface of a sp...

Strong local minimizers with surfaces of gradient discontinuity appear in variational problems when the energy density function is not rank-one convex. In this paper we show that stability of such surfaces is related to stability outside the surface via a single jump relation that can be regarded as interchange stability condition. Although this relation appears in the setting of equilibrium el...

The ability of human visual system to interpolate surfaces when the structure of the objects was defined through motion was investigated in a series of experiments. The type of the surface, the position of an area devoid of dots (the gap) and the type of gap edges was varied. The local orientation of the interpolated surfaces was estimated by a method of adjustment. The results show that the in...

Scattering of electromagnetic radiation by an object of arbitrary shape or a structured surface, infinite in extent, is considered. When radiation is incident on an interface separating vacuum from a material medium, a current density is induced in the bulk and a surface current density may appear on the boundary surface. The electromagnetic field is then the sum of the incident field and the f...

Normal mapping uses normal perturbations stored in a texture to give objects a more geometrically complex appearance without increasing the number of geometric primitives. Standard biand trilinear interpolation of normal maps works well if the normal field is continuous, but may result in visible artifacts in the areas where the field is discontinuous, which is common for surfaces with creases ...

Chandra and XMM-Newton observations of many clusters reveal sharp discontinuities in the surface brightness, which, unlike shocks, have lower gas temperature on the X-ray brighter side of the discontinuity. For that reason these features are called “cold fronts”. It is believed that some cold fronts are formed when a subcluster merges with another cluster and the ram pressure of gas flowing out...

We consider the approximate solution of the initial value problem du du , .. . . _ = _ „(*,0) = »(*), by a dissipative Galerkin method. When v is taken to have a jump discontinuity at zero, that discontinuity will propagate along x + t = 0, in the true solution u. Estimates in L^ and Lx of the pollution effects of the discontinuity are found. These estimates show those effects to decay exponent...

The electrostatic image method was applied to investigate the conformation of peptides characterized by different hydrophobicities in a water]membrane interface model. The interface was represented by a surface of discontinuity between two media with different dielectric constants, taking into account the difference between the polarizabilities of the aqueous medium and the hydrocarbon one. The...