Integrable dispersionless KdV hierarchy with sources

An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived. Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated. Hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is obtained via hodograph transformation. Furthermore, the dispersionless Gelfand-Dickey hierarchy with sources (dGDHWS) is presented.Comment: 15 pages, to be published in J. Phys. A: Math. Ge

Single-particle subband structure of Quantum Cables

We proposed a model of Quantum Cable in analogy to the recently synthesized coaxial nanocable structure [Suenaga et al. Science, 278, 653 (1997); Zhang et al. ibid, 281, 973 (1998)], and studied its single-electron subband structure. Our results show that the subband spectrum of Quantum Cable is different from either double-quantum-wire (DQW) structure in two-dimensional electron gas (2DEG) or single quantum cylinder. Besides the double degeneracy of subbands arisen from the non-abelian mirrow reflection symmetry, interesting quasicrossings (accidental degeneracies), anticrossings and bundlings of Quantum Cable energy subbands are observed for some structure parameters. In the extreme limit (barrier width tends to infinity), the normal degeneracy of subbands different from the DQW structure is independent on the other structure parameters.Comment: 12 pages, 9 figure

Quantum Cable as transport spectroscopy of 1D DOS of cylindrical quantum wires

We considered the proposed Quantum Cable as a kind of transport spectroscopy of one-dimensional (1D) density of states (DOS) of cylindrical quantum wires. By simultaneously detecting the direct current through the cylindrical quantum wire and the leaked tunneling current into the neighboring wire at desired temperatures, one can obtain detailed information about 1D DOS and subband structure of cylindrical quantum wires.Comment: 7 pages, 4 figures, late

Ballistic electronic transport in Quantum Cables

We studied theoretically ballistic electronic transport in a proposed mesoscopic structure - Quantum Cable. Our results demonstrated that Qauntum Cable is a unique structure for the study of mesoscopic transport. As a function of Fermi energy, Ballistic conductance exhibits interesting stepwise features. Besides the steps of one or two quantum conductance units ($2e^2/h$), conductance plateaus of more than two quantum conductance units can also be expected due to the accidental degeneracies (crossings) of subbands. As structure parameters is varied, conductance width displays oscillatory properties arising from the inhomogeneous variation of energy difference betweeen adjoining transverse subbands. In the weak coupling limits, conductance steps of height $2e^2/h$ becomes the first and second plateaus for the Quantum Cable of two cylinder wires with the same width.Comment: 11 pages, 5 figure

On the Toda Lattice Equation with Self-Consistent Sources

The Toda lattice hierarchy with self-consistent sources and their Lax representation are derived. We construct a forward Darboux transformation (FDT) with arbitrary functions of time and a generalized forward Darboux transformation (GFDT) for Toda lattice with self-consistent sources (TLSCS), which can serve as a non-auto-Backlund transformation between TLSCS with different degrees of sources. With the help of such DT, we can construct many type of solutions to TLSCS, such as rational solution, solitons, positons, negetons, and soliton-positons, soliton-negatons, positon-negatons etc., and study properties and interactions of these solutions.Comment: 20 page

The Degasperis-Procesi equation with self-consistent sources

The Degasperis-Procesi equation with self-consistent sources(DPESCS) is derived. The Lax representation and the conservation laws for DPESCS are constructed. The peakon solution of DPESCS is obtained.Comment: 15 page

Multi-Agent-Based Modelling, Simulation and Heterogeneity Analysis of the Management Strategies for Enterprise Carbon Assets

Low carbon competitive patterns based upon low-carbon assets have developed in industries across the world. In the paper, three typical enterprises are used as examples to identify carbon assets from the perspective of enterprise business contexts, and to extract the interactive framework. This paper makes quantitative description of the value contribution principle of each carbon asset module and sets up the simulation strategies for relevant carbon assets. On the basis of these, an Agent-Based Modelling & Simulation (ABMS) system is created and built to simulate and analyse the difference in the evolution of carbon assets. The results demonstrate the emergent properties of enterprise carbon assets. The simulation study also shows remarkable heterogeneity of evolution paths with low-carbon technologies and low-carbon brands, which are the key factors leading to the evolution of other carbon assets and the adjustment of strategies. Finally, recommendations are made to improve the management of enterprises carbon assets