Loop-tree duality from vertices and edges

The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This representation is found to manifest compact expressions for multi-loop topologies that have the same number of vertices. Interestingly, integrands considered in former studies, with up-to six vertices and L internal lines, display the same structure of up-to four-loop ones. The former is an insight that there should be a correspondence between vertices and the collection of internal lines, edges, that characterise a multi-loop topology. By virtue of this relation, in this paper, we embrace an approach to properly classify multi-loop topologies according to vertices and edges. Differently from former studies, we consider the most general topologies, by connecting vertices and edges in all possible ways. Likewise, we provide a procedure to generate causal representation of multi-loop topologies by considering the structure of causal propagators. Explicit causal representations of loop topologies with up-to nine vertices are provided.

Importance of small loops within PIM-1 topology on gas separation selectivity in thin film composite membranes

Studies of blends of topologically distinct samples of the polymer of intrinsic microporosity PIM-1 provide, for the CO2/N2 gas pair, insight into the optimum loop topology required for high selectivity and permeance of thin film composite (TFC) membranes.

High-Efficiency Crossed-Loop 4G LTE Antenna for All Display Metal-Rimmed Smartphones

A symmetrically crossed-loop antenna featuring very high radiation efficiency across the entire LTE frequency bands for metal-rimmed smartphones with only 2 mm ground clearance is proposed, analyzed, and verified. The employment of even and odd modes is utilized to achieve wide bandwidth across 698–960 MHz (low-frequency spectrum), 1710–2170 MHz (middle-frequency spectrum), and 2300–2690 MHz (high-frequency spectrum). Empirical analysis confirms the crossed-loop topology results in a 180° phase shift of the electric current distribution on the ground plane, resulting in enhancement of the radiation resistance. As a result, the devised LTE antenna exhibits more than 48% to 75% total system efficiency across the entire band of interest, which is the highest efficiency reported in literature for metal-rimmed smartphones with extremely small ground clearance.

Steady State Analysis of Non-Isolated Single-Input Multi-Output SEPIC Converter for Stand-alone Applications

<p>This paper proposes a non-isolated three port SEPIC converter for stand-alone photovoltaic applications. The proposed topology uses the Single Input Multi Output (SIMO) structure. This topology consists of a single photovoltaic source as input and it is a unidirectional power converter. Mathematical analysis for the proposed system is performed and simulations are carried out using MATLAB/Simulink. The design parameters of capacitors and inductors are calculated from small ripple analysis. The simulation analysis for the proposed open loop topology is verified using a real time hardware setup.The entire process is carried out in Continuous Current Mode (CCM) of operation. The experimental results for hardware are verified with simulations and compared.</p>