This paper introduces a Relative Mapping Algorithm. This algorithm presents a new way of looking at the SLAM problem that does not use Probability, Iterative Closest Point, or Scan Matching techniques. A map of landmarks is generated by using the average relative location difference between landmarks. This means the algorithm does not use any known, estimated or predicted movement or position d...

We utilized molecular statics (MS) simulations to investigate the auxeticity of single layer black phosphorus (SLBP). Our simulation results show that the SLBP has a negative in-plane Poisson’s ratio in the zigzag direction when the applied strain along the armchair direction exceeds 0.018. We show that the interplay between bond stretching and bond rotating modes determines the in-plane Poisso...

The mechanical behavior of cold rolled sheets is significantly related to residual stresses that arise from bending and unbending processes. Measurement of residual stresses is mostly limited to surface measurement techniques. Experimental determination of stress variation through thickness is difficult and time-consuming. This paper presents a closed form solution for residual stresses, in whi...

The mechanical behavior of cold rolled sheets is significantly related to residual stresses that arise from bending and unbending processes. Measurement of residual stresses is mostly limited to surface measurement techniques. Experimental determination of stress variation through thickness is difficult and time-consuming. This paper presents a closed form solution for residual stresses, in whi...

We present some remarkable properties of the symmetry group for gravitational plane waves. Our main observation is that metrics with plane wave symmetry satisfy every system of generally covariant vacuum field equations except the Einstein equations. The proof uses the homothety admitted by metrics with plane wave symmetry and the scaling behavior of generally covariant field equations. We also...

The contribution of the propagating and the evanescent waves associated with freely propagating nonparaxial light fields whose transverse component is azimuthally polarized at some plane is investigated. Analytic expressions are derived for describing both the spatial shape and the relative weight of the propagating and the evanescent components integrated over the transverse plane. The analysi...

A digital plane is the set of integer points located between to parallel planes. We solve the following problem: how to compute the exact normal vector of a digital plane given only a predicate that answers the question “is a point x in the digital plane or not”. Our approach is iterative and “as local as possible”. We provide a worst-case complexity bound in O(ω logω) calls to the predicate, w...