Dynamic Control of Local Field Emission Current from Carbon Nanowalls

We report on a systematic study of modulation of the field emission current from carbon nanowalls using a sharp probe as the anode in an ultrahigh vacuum system. Modulation of the local emission current was achieved by either varying the anode-cathode distance (d) with the aid of an AC magnetic field or superimposing a small AC bias on a DC bias during the field emission measurement. Current modulation ratio of over two orders of magnitude was achieved with the modulation becoming more efficient at a smaller d. The experimental results are discussed using the Fowler-Nordheim theory in combination with a simple cantilever model to account for the modulation effect. The experimental results demonstrated good static stability and dynamic controllability of local field emission current from the carbon nanowalls

Note on Soft Graviton theorem by KLT Relation

Recently, new soft graviton theorem proposed by Cachazo and Strominger has inspired a lot of works. In this note, we use the KLT-formula to investigate the theorem. We have shown how the soft behavior of color ordered Yang-Mills amplitudes can be combined with KLT relation to give the soft behavior of gravity amplitudes. As a byproduct, we find two nontrivial identities of the KLT momentum kernel must hold.Comment: 25 page

Numerical algorithm based on Adomian decomposition for fractional differential equations

AbstractIn this paper, a novel algorithm based on Adomian decomposition for fractional differential equations is proposed. Comparing the present method with the fractional Adams method, we use this derived computational method to find a smaller “efficient dimension” such that the fractional Lorenz equation is chaotic. We also apply this new method to the time-fractional Burgers equation with initial and boundary value conditions. Numerical results and computer graphics show that the constructed numerical is efficient

Building Momentum Kernel from Shapovalov Form

These notes are an extended version of the talks given by the authors at the XIV International Workshop on Lie Theory and Its Applications in Physics, Sofia, Bulgaria, 20-26 June 2021. The concise version published in the proceedings of the workshop contains additional discussions for the q-deformed scenario: https://link.springer.com/chapter/10.1007/978-981-19-4751-3_23 In these notes we identify KLT kernel with the Shapovalov form on Verma module with its highest/lowest weight given by the reference momentum and rest of the momenta as roots. We then take a step forward and show how the Feynman diagrams emerge naturally as the Shapovalov duals of the Verma module basis vectors. We show such algebraic construct offers a compact expression for the BCJ numerators. Explicit examples are shown for nonlinear sigma model and HEFT pre-numerators.Comment: 18 pages, 2 figures, Published in: Springer Proc.Math.Stat. 396 (2022) 287-29