The amplituhedron from momentum twistor diagrams

We propose a new diagrammatic formulation of the all-loop scattering amplitudes/Wilson loops in planar N=4 SYM, dubbed the "momentum-twistor diagrams". These are on-shell-diagrams obtained by gluing trivalent black and white vertices defined in momentum twistor space, which, in the reduced diagram case, are known to be related to diagrams in the original twistor space. The new diagrams are manifestly Yangian invariant, and they naturally represent factorization and forward-limit contributions in the all-loop BCFW recursion relations in momentum twistor space, in a fashion that is completely different from those in momentum space. We show how to construct and evaluate momentum-twistor diagrams, and how to use them to obtain tree-level amplitudes and loop-level integrands; in particular for the latter we identify an isolated bubble-structure for each loop variable, arising from a forward limit, or entangled removal of particles. From a given diagram one can directly read off the C, D matrices via a generalized "boundary measurement"; this in turn determines a cell in the amplituhedron associated with the amplitude, and our diagrammatic representations of the amplitude can provide triangulations of the amplituhedron with generally very intricate geometries. To demonstrate the computational power of the formalism, we give explicit results for general two-loop integrands, and the cells of the complete amplituhedron for two-loop MHV amplitudes.Comment: 39 pages, 34 figure

Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet

The search for a theory of the S-Matrix has revealed surprising geometric structures underlying amplitudes ranging from the worldsheet to the amplituhedron, but these are all geometries in auxiliary spaces as opposed to kinematic space where amplitudes live. In this paper, we propose a novel geometric understanding of amplitudes for a large class of theories. The key is to think of amplitudes as differential forms directly on kinematic space. We explore this picture for a wide range of massless theories in general spacetime dimensions. For the bi-adjoint cubic scalar, we establish a direct connection between its "scattering form" and a classic polytope--the associahedron--known to mathematicians since the 1960's. We find an associahedron living naturally in kinematic space, and the tree amplitude is simply the "canonical form" associated with this "positive geometry". Basic physical properties such as locality, unitarity and novel "soft" limits are fully determined by the geometry. Furthermore, the moduli space for the open string worldsheet has also long been recognized as an associahedron. We show that the scattering equations act as a diffeomorphism between this old "worldsheet associahedron" and the new "kinematic associahedron", providing a geometric interpretation and novel derivation of the bi-adjoint CHY formula. We also find "scattering forms" on kinematic space for Yang-Mills and the Non-linear Sigma Model, which are dual to the color-dressed amplitudes despite having no explicit color factors. This is possible due to a remarkable fact--"Color is Kinematics"--whereby kinematic wedge products in the scattering forms satisfy the same Jacobi relations as color factors. Finally, our scattering forms are well-defined on the projectivized kinematic space, a property that provides a geometric origin for color-kinematics duality.Comment: 77 pages, 25 figures; v2, corrected discussion of worldsheet associahedron canonical for

Influence of air supply velocity on temperature field in the self heating process of coal

The air supply velocity is an important factor affecting the spontaneous combustion of coal. The appropriate air velocity can not only provide the oxygen required for the oxidation reaction, but maintains the good heat storage environment. Therefore, it is necessary to study the influence of the actual air velocity in the pore space on the self-heating process of coal particles. This paper focuses on studying the real space piled up by spherical particles. CFD simulation software is used to establish the numerical model from pore scale. Good fitness of the simulation results with the existing results verifies the feasibility of the calculation method. Later, the calculation conditions are changed to calculate and analyze the velocity field and the temperature field for self-heating of some particles (the surface of the particles is at a certain temperature) and expound the effect of different air supply velocities on gathering and dissipating the heat

Stability Analysis of ITER Side Correction Coils

AbstractThe stability of the Side Correction Coils (SCC) cable-in-conduit conductors (CICC) for the International Thermonuclear Experimental Reactor (ITER) has been analyzed by the formulas and the code Gandalf. This paper describes the 1-dimensional mathematical code Gandalf, uses the code to simulate the quench and the recovery status of ITER SCC CICC, discusses the dependence of the stability margin on various operating parameters including operating current, operating temperature and mass flow rate, and analyzes the differences between the simulated values and the calculated values. The ITER SCC's quenching is also simulated to investigate its temperature distribution and temperature margin. Dependence of temperature margin on magnetic fields and operating temperature has been researched. The studies of ITER SCC provide a basis for the stable operation and optimization design of SCC CICC

Mastering Autonomous Assembly in Fusion Application with Learning-by-doing: a Peg-in-hole Study

Robotic peg-in-hole assembly is an essential task in robotic automation research. Reinforcement learning (RL) combined with deep neural networks (DNNs) lead to extraordinary achievements in this area. However, current RL-based approaches could hardly perform well under the unique environmental and mission requirements of fusion applications. Therefore, we have proposed a new designed RL-based method. Furthermore, unlike other approaches, we focus on innovations in the structure of DNNs instead of the RL model. Data from the RGB camera and force/torque (F/T) sensor as the input are fed into a multi-input branch network, and the best action in the current state is output by the network. All training and experiments are carried out in a realistic environment, and from the experiment result, this multi-sensor fusion approach has been shown to work well in rigid peg-in-hole assembly tasks with 0.1mm precision in uncertain and unstable environments

A comparative study on the effect of carbon fillers on electrical and thermal conductivity of a cyanate ester resin

Carbon fillers including multi-walled carbon nanotubes (MWCNTs), carbon black (CB) and graphite were introduced in a cyanate ester (CE) resin, respectively. The effects of the fillers on the electrical and thermal conductivity of the resin were measured and analyzed based on the microscopic observations. MWCNTs, CB and graphite exhibited percolation threshold at 0.1 wt%, 0.5 wt% and 10 wt%, respectively. The maximal electrical conductivity of the composites was 1.08 S/cm, 9.94 × 10−3 S/cm and 1.70 × 10−5 S/cm. MWCNTs showed the best enhancement on the electrical conductivity. The thermal behavior of the composites was analyzed by calorimetry method. Incorporation of MWCNTs, CB and graphite increased the thermal conductivity of CE resin by 90%, 15% and 92%, respectively. Theoretical models were introduced to correlate the thermal conductivity of the CE/MWCNTs composite. The interfacial thermal resistance between CE resin and MWCNTs was 8 × 10−8 m2K/W and the straightness ratio was 0.2. The MWCNTs were seriously entangled and agglomerated. Simulation results revealed that thermal conductivity of the CE/MWCNTs composites can be substantially elevated by increasing the straightness ratio and/or filler content of MWCNTs