On Classification of Modular Tensor Categories

We classify all unitary modular tensor categories (UMTCs) of rank ≤ 4. There are a total of 35 UMTCs of rank ≤ 4 up to ribbon tensor equivalence. Since the distinction between the modular S-matrix S and −S has both topological and physical significance, so in our convention there are a total of 70 UMTCs of rank ≤ 4. In particular, there are two trivial UMTCs with S = (±1). Each such UMTC can be obtained from 10 non-trivial prime UMTCs by direct product, and some symmetry operations. Explicit data of the 10 non-trivial prime UMTCs are given in Sect. 5. Relevance of UMTCs to topological quantum computation and various conjectures are given in Sect. 6.     

Non-quadratic defect energy: A comparison of gradient plasticity simulations to discrete dislocation dynamics results

A small-deformation strain gradient plasticity (GP) model for single-crystals has been proposed in [1], including a grain boundary (GB) yield condition without hardening. It has been extended by a hardening term for the GBs after a comparison to discrete dislocation dynamics (DDD) results in [2]. Differences between the strain gradients of the GP results and the DDD results motivate the consideration of a non-quadratic defect energy [3] in the GP model. It is shown that the gradients in the GP model can be improved using an exponent different from two. Remaining discrepancies in the strain profiles, compared to the DDD results, are attributed to the neglect of the individual gradients of plastic slip and due to the lack of a mechanism for the misorientation-dependent elastic interactions of dislocations across GBs [4] in the GP model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variable Charge-Densities in Hydrophilic Weak-Base Ion-Exchange Membranes. V. Equilibrium Properties with Pure 1-1 Electrolytes. Swelling and Ion-Exclusion

Abstract

The equilibrium distribution of chloride or nitrate counter-ions of K or NH₄ co-ions and of water is determined experimentally at different degrees of ionization X[xbar] of hydrophylic weak-base aminated polyvinyl-alcohol membranes. These data are analyzed and explained in terms of thermodynamics interrelating the molality of fixed-charge densities and of counter-ions to that of the amount of water and of diffused salt in the membrane.

Three domains have to be considered: the polyelectrolyte domain with small external concentration compared to the internal net fixed charge concentration (notion of “net-charge” densities), the domain of homogeneous interstitial liquid of the concentrated electrolyte type with sufficiently concentrated salt solution, and the intermediate domain.     

Stability constants of metal complexes of macrocyclic ligands with pendant donor groups

Abstract

In our studies of the stability constants of metal complexes, we have investigated a number of macrocyclic ligands with pendant donor groups. The ligands are characterized by the fact that they have nitrogen donors in the macrocyclic ring and oxygen or sulfur donors in the pendant arms. These ligands represent seven different macrocycles, and by varying the pendant donor groups, ten different ligands are indicated. The affinities of these ligands for fifteen metal ions will be described. The Fe(III) complex of triazanonane with o-hydroxypyridyl or o-hydroxybenzyl pendant donor groups are the most stable ferric complexes ever reported. The In(III) complex of triazacyclononane with pendant mercaptoethyl donor groups, is exceptionally stable. Also, the Ca(II) complex of DOTA probably has the highest stability of any calcium(II) complex. These, and other comparisons will be made on the basis of the thermodynamic stability constant data for the ligands described.     

Graphene screen‐printed radio‐frequency identification devices on flexible substrates

Despite the great promise of printed flexible electronics from 2D crystals, and especially graphene, few scalable applications have been reported so far that can be termed roll‐to‐roll compatible. Here we combine screen printed graphene with photonic annealing to realize radio‐frequency identification devices with a reading range of up to 4 meters. Most notably our approach leads to fatigue resistant devices showing less than 1% deterioration of electrical properties after 1000 bending cycles. The bending fatigue resistance demonstrated on a variety of technologically relevant plastic and paper substrates renders the material highly suitable for various printable wearable devices, where repeatable dynamic bending stress is expected during usage. All applied printing and post‐processing methods are compatible with roll‐to‐roll manufacturing and temperature sensitive flexible substrates providing a platform for the scalable manufacturing of mechanically stable and environmentally friendly graphene printed electronics.

     

Fiber-optic beam shaper based on multimode interference

A new method of fiber-optic based beam shaping is investigated both numerically and experimentally. A cylindrically symmetric method of lines (MoLs) is developed to simulate the device. The device is fabricated by fusion splicing a predetermined length of multimode fiber (MMF) to a single-mode fiber. The multimode interference (MMI) effects create ring-shaped field profiles at certain positions inside the MMF. The shaped beam can be used in medical applications requiring particular irradiation patterns.     

Ultrafast Photoswitching in a Copper‐Nitroxide‐Based Molecular Magnet

Molecular compounds with photoswitchable magnetic properties have been intensively investigated over the last decades due to their prospective applications in nanoelectronics, sensing and magnetic data storage. The family of copper‐nitroxide‐based molecular magnets represents a new promising type of photoswitchable compounds. We report the first study of these appealing systems using femtosecond optical spectroscopy. We unveil the mechanism of ultrafast (<50 fs) spin state photoswitching and establish its principal differences compared to other photoswitchable magnets. On this basis, we propose potential advantages of copper‐nitroxide‐based molecular magnets for the future design of ultrafast magnetic materials.