119 research outputs found
The Levi-Civita connections of Lorentzian manifolds with prescribed optical geometries
No full textWe explicitly derive the Christoffel symbols in terms of adapted frame fields for the Levi-Civita connection of a Lorentziann-manifold (M, g), equipped with a prescribed optical geometry of Kähler-Sasaki type. The formulas found in this paper have several important applications, such as determining the geometric invariants of Lorentzian manifolds with prescribed optical geometries or solving curvature con-straints
Lorentzian manifolds with shearfree congruences and Kähler-Sasaki geometry
No full textWe study Lorentzian manifolds (M,g) of dimension n≥4, equipped with a maximally twisting shearfree null vector field p, for which the leaf space S=M/{exptp} is a smooth manifold. If n=2k, the quotient S=M/{exptp} is naturally equipped with a subconformal structure of contact type and, in the most interesting cases, it is a regular Sasaki manifold projecting onto a quantisable Kähler manifold of real dimension 2k−2. Going backwards through this line of ideas, for any quantisable Kähler manifold with associated Sasaki manifold S, we give the local description of all Lorentzian metrics g on the total spaces M of A-bundles π:M→S, A=S1,R, such that the generator of the group action is a maximally twisting shearfree g-null vector field p. We also prove that on any such Lorentzian manifold (M,g) there exists a non-trivial generalised electromagnetic plane wave having p as propagating direction field, a result that can be considered as a generalisation of the classical 4-dimensional Robinson Theorem. We finally construct a 2-parametric family of Einstein metrics on a trivial bundle M=R×S for any prescribed value of the Einstein constant. If dimM=4, the Ricci flat metrics obtained in this way are the well-known Taub-NUT metrics
Application of nonlinear systems in nanomechanics and nanofluids : analytical methods and applications / Davood Domairry Ganji, Sayyid Habibollah Hashemi Kachapi.
No full textIncludes bibliographical references and index.xv, 395 pages :With Application of Nonlinear Systems in Nanomechanics and Nanofluids the reader gains a deep and practice-oriented understanding of nonlinear systems within areas of nanotechnology application as well as the necessary knowledge enabling the handling of such systems. The book helps readers understand relevant methods and techniques for solving nonlinear problems, and is an invaluable reference for researchers, professionals and PhD students interested in research areas and industries where nanofluidics and dynamic nano-mechanical systems are studied or applied. The book is useful in areas such as nanoelectronics and bionanotechnology, and the underlying framework can also be applied to other problems in various fields of engineering and applied sciences
Extended two-dimensional DTM and its application on nonlinear PDEs with proportional delay
No full textA criterion for local embeddability of three-dimensional CR structures
No full textWe introduce a CR-invariant class of Lorentzian metrics on a circle bundle over a three-dimensional CR structure, which we call FRT metrics. These metrics generalise the Fefferman metric, allowing for more control of the Ricci curvature, but are more special than the shearfree Lorentzian metrics introduced by Robinson and Trautman. Our main result is a criterion for embeddability of three-dimensional CR structures in terms of the Ricci curvature of the FRT metrics in the spirit of the results by Lewandowski et al. (Class Quantum Gravity 7(11):L241–L246, 1990) and also Hill et al. (Indiana Univ Math J 57(7):3131–3176, 2008. https://doi.org/10.1512/iumj.2008.57.3473)
Molecular gymnastics: Single-molecule investigations of protein jumping and dna dancing
No full textCasimir PhD series 2016-29BN/Cees Dekker La
Hydrogen purification performance of a nanoporous hexagonal boron nitride membrane: molecular dynamics and first-principle simulations
No full textDouble-layer models of porous h-BN monolayers, with pores differing in size and chemistry, were employed for efficient gas separation and purification. Performance was evaluated by DFT calculations and MD simulations.</p
Bayes estimation in a decapitated generalized negative binomial distribution and some of its applications
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