Multiple Existence of the Multivortex Solutions of the Self-Dual Chern–Simons CP(1) Model on a Doubly Periodic Domain

In this Letter, we investigate multiple existence of the multivortex solutions of the self-dual Chern–Simons CP(1) model on a flat torus for each range of the symmetry breaking parameter. We also study asymptotics of solutions as the Chern–Simons coupling constant goes to zero.     

An Incompressible 2D Didactic Model with Singularity and Explicit Solutions of the 2D Boussinesq Equations

We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time for all time. In addition, we introduce a variant of the 2D Boussinesq equations which is perhaps a more faithful companion of the 3D axisymmetric Euler equations than the usual 2D Boussinesq equations.     

Permit allocation in emissions trading using the Boltzmann distribution

In emissions trading, the initial allocation of permits is an intractable issue because it needs to be essentially fair to the participating countries. There are many ways to distribute a given total amount of emissions permits among countries, but the existing distribution methods, such as auctioning and grandfathering, have been debated. In this paper we describe a new method for allocating permits in emissions trading using the Boltzmann distribution. We introduce the Boltzmann distribution to permit allocation by combining it with concepts in emissions trading. We then demonstrate through empirical data analysis how emissions permits can be allocated in practice among participating countries. The new allocation method using the Boltzmann distribution describes the most probable, natural, and unbiased distribution of emissions permits among multiple countries. Simple and versatile, this new method holds potential for many economic and environmental applications.     

Influences of ions and temperature on performance of carbon nano-particulates in supercapacitors with neutral aqueous electrolytes

A commercial product of carbon nano-particles,Cabot MONACH 1300 pigment black(CMPB),was studied for basic structural information and electrochemical performance in neutral aqueous electrolytes,aiming at applications in supercapacitors.As confirmed by SEM and HRTEM,the CMPB had a hierarchical structure,containing basic 10 nm nano-spheres which combined into ca.50 nm agglomerates which further aggregated into larger particles ofmicrometres.The capacitance of this commercial material was found to increase with decreasing the size of hydrous cation(Li~+→ Na~*→K~+),instead of the cation crystal radius(K~+→Na~+→Li~+) when coupled with the same anion(Cl~-).In electrolytes with the same cation concentration(K~+),changing the anion from the larger dianion(SO_4~(2-)) to the smaller monoanion(Cl~-) also increased the capacitance at high potential scan rates(50mV/s).Increasing electrolyte concentration produced expected effect,including raising the electrode capacitance,but lowering the equivalent series resistance(ESR).charge transfer resistance(CTR),and the diffusion resistance.At higher temperatures,the CMPB exhibited slightly higher capacitance,which does not agree with the Gouy-Chapman theory on electric double layer(EDL).A hypothesis is proposed to account for the capacitance increase with temperature as a result of the CMPB opening up some micro-pores for more ions to access in response to the temperature increase.     

Type-II Red Phosphorus: Wavy Packing of Twisted Pentagonal Tubes

Elemental phosphorus exhibits fascinating structural varieties and versatile properties. The unique nature of phosphorus bonds can lead to the formation of extremely complex structures, and detailed structural information on some phosphorus polymorphs is yet to be investigated. In this study, we investigated an unidentified crystalline phase of phosphorus, type-II red phosphorus (RP), by combining state-of-the-art structural characterization techniques. Electron diffraction tomography, atomic-resolution scanning transmission electron microscopy (STEM), powder X-ray diffraction, and Raman spectroscopy were concurrently used to elucidate the hidden structural motifs and their packing in type-II RP. Electron diffraction tomography, performed using individual crystalline nanowires, was used to identify a triclinic unit cell with volume of 5330 ų, which is the largest unit cell for elemental phosphorus crystals up to now and contains approximately 250 phosphorus atoms. Atomic-resolution STEM imaging, which was performed along different crystal-zone axes, confirmed that the twisted wavy tubular motif is the basic building block of type-II RP. Our study discovered and presented a new variation of building blocks in phosphorus, and it provides insights to clarify the complexities observed in phosphorus as well as other relevant systems.