Rate of convergence for periodic homogenization of convex Hamilton-Jacobi equations in one dimension

Let $u^\varepsilon$ and $u$ be viscosity solutions of the oscillatory Hamilton-Jacobi equation and its corresponding effective equation. Given bounded, Lipschitz initial data, we present a simple proof to obtain the optimal rate of convergence $\mathcal{O}(\varepsilon)$ of $u^\varepsilon \rightarrow u$ as $\varepsilon \rightarrow 0^+$ for a large class of convex Hamiltonians $H(x,y,p)$ in one dimension. This class includes the Hamiltonians from classical mechanics with separable potential. The proof makes use of optimal control theory and a quantitative version of the ergodic theorem for periodic functions in dimension $n = 1$.Comment: 22 pages, typos corrected, references added, final accepted versio

Analysis of thin-film structures with nuclear backscattering and x-ray diffraction

Backscattering of MeV ^(4)He ions and Seemann-Bohlin x-ray diffraction techniques have been used to study silicide formation on Si and SiO_2 covered with evaporated metal films. Backscattering techniques provide information on the composition of thin-film structures as a function of depth. The glancing-angle x-ray technique provides identification of phases and structural information. Examples are given of V on Si and on SiO_2 to illustrate the major features of these analysis techniques. We also give a general review of recent studies of silicide formation

Influence of bandwidth restriction on the signal-to-noise performance of a modulated PCM/NRZ signal, part 2

Analyzing effects of bandlimiting on performance of digital transmission corrupted by additive white Gaussian noise by averaging and series expansio

Surface morphological evolutions on single crystal films by strong anisotropic drift-diffusion under the capillary and electromigration forces

The morphological evolution of voids at the unpassivated surfaces and the sidewalls of the single crystal metallic films are investigated via computer simulations by using the novel mathematical model developed by Ogurtani relying on the fundamental postulates of irreversible thermodynamics. The effects of the drift-diffusion anisotropy on the development of the surface morphological scenarios are fully explored under the action of the electromigration (EM) and capillary forces (CF), utilizing numerous combination of the surface textures and the directions of the applied electric field. The interconnect failure time due to the EM induced wedge shape internal voids and the incubation time of the oscillatory surface waves, under the severe instability regimes, are deduced by the novel renormalization procedures applied on the outputs of the computer simulation experiments.Comment: 41 pages, 18 figures. related simulation movies utilizing numerous combination of the surface texture, see http://www.csl.mete.metu.edu.tr/aytac/thesis/movies/index.ht

Projected entangled-pair states can describe chiral topological states

We show that Projected Entangled-Pair States (PEPS) in two spatial dimensions can describe chiral topological states by explicitly constructing a family of such states with a non-trivial Chern number. They are ground states of two different kinds of free-fermion Hamiltonians: (i) local and gapless; (ii) gapped, but with hopping amplitudes that decay according to a power law. We derive general conditions on topological free fermionic PEPS which show that they cannot correspond to exact ground states of gapped, local parent Hamiltonians, and provide numerical evidence demonstrating that they can nevertheless approximate well the physical properties of topological insulators with local Hamiltonians at arbitrary temperatures.Comment: v2: minor changes, references added. v3: accepted version, Journal-Ref adde

Analysis of rolling bearing power loss models for twin screw oil injected compressor

The mechanical losses inside a screw compressor limit the performance of the compressor in terms of efficiency. These losses arise due to relative motion between elements inside the screw compressor. The estimation of mechanical losses predicted in the literature is around 10-15% of the total shaft power. One of the elements which contribute significantly to these losses is rolling element bearings. There are numerous mathematical models available which predict power losses in the rolling bearings. The objective of this paper is to study different models to predict power loss for rolling bearings and to predict the power losses for the bearings used for oil injected, twin screw compressor. A comparison between different power loss models for different operating conditions of compressor is also presented in this paper and results of analysis are compared with available experimental observations. The analysis helps to determine suitable power loss model for different operating conditions and more realistic predictions of the power losses. This allows designers for more accurate estimation of the performance of screw compressors

Search for new phenomena in events containing a same-flavour opposite-sign dilepton pair, jets, and large missing transverse momentum in √s=13 TeV pp collisions with the ATLAS detector

published_or_final_versio