640 Gbits/s photonic logic gates

We demonstrate 640 Gbits/s all-optical A AND B, and ā AND B logic functions using pump depletion in a periodically poled lithium niobate waveguide. Bit-error-rate measurements show the effectiveness of the scheme, with a penalty of <2 dB.     

Near-surface turbulence in the atmospheric boundary layer

Measurements of the near-surface turbulence in the atmospheric boundary layer have been made using hot-wire probes above the salt flats of northwestern Utah, where the momentum thickness Reynolds number, R_θ, is O(10⁶), and the surface is smooth and nearly devoid of flow obstructions. The measurements were made with arrays of up to 24 parallel straight sensors and with a modular 12-sensor probe capable of measuring all of the components of the instantaneous velocity vector and velocity gradient tensor. Measurements were also made in a laboratory wind tunnel at R_θ=1730 using 22 straight sensors. The data analysis focuses on the effects of the Reynolds number on turbulence properties and on the physics of the dissipation rate of turbulent kinetic energy.Some properties are found to be dependent on the Reynolds number when normalized with inner variables, while others are not. Among those that show the significant Reynolds number dependence are the rms and the skewness factor of the streamwise velocity fluctuations.Significant differences in flow structure, particularly those related to high rates of dissipation, are implied by the data. The joint PDF and covariance integrand of streamwise and wall normal vorticity fluctuations show less preferred orientation of the vorticity vector in the buffer layer at R_θ of O(10⁶) than at R_θ=1070. The largest contribution to the dissipation rate, at O(10⁶) is by the ∂w/∂z velocity gradient, while this term makes a quite small contribution to the dissipation rate at low R_θ. Here w and z are the spanwise velocity fluctuations and direction, respectively. Conditional analysis in the streamwise-wall normal (x−y) plane based on high instantaneous dissipation rate shows that the typical high dissipation rate events are generally similar at high and low Reynolds numbers, but display some significant differences.     

Extended Antipodal Theorems

In infinite-dimensional Hilbert spaces, we prove that the iterative sequence generated by the extragradient method for solving pseudo-monotone variational inequalities converges weakly to a solution. A class of pseudo-monotone variational inequalities is considered to illustrate the convergent behavior. The result obtained in this note extends some recent results in the literature; especially, it gives a positive answer to a question raised in Khanh (Acta Math Vietnam 41:251–263, 2016).     

Speeding up IP-based algorithms for constrained quadratic 0–1 optimization

In many practical applications, the task is to optimize a non-linear objective function over the vertices of a well-studied polytope as, e.g., the matching polytope or the travelling salesman polytope (TSP). Prominent examples are the quadratic assignment problem and the quadratic knapsack problem; further applications occur in various areas such as production planning or automatic graph drawing. In order to apply branch-and-cut methods for the exact solution of such problems, the objective function has to be linearized. However, the standard linearization usually leads to very weak relaxations. On the other hand, problem-specific polyhedral studies are often time-consuming. Our goal is the design of general separation routines that can replace detailed polyhedral studies of the resulting polytope and that can be used as a black box. As unconstrained binary quadratic optimization is equivalent to the maximum-cut problem, knowledge about cut polytopes can be used in our setting. Other separation routines are inspired by the local cuts that have been developed by Applegate, Bixby, Chvátal and Cook for faster solution of large-scale traveling salesman instances. Finally, we apply quadratic reformulations of the linear constraints as proposed by Helmberg, Rendl and Weismantel for the quadratic knapsack problem. By extensive experiments, we show that a suitable combination of these methods leads to a drastic speedup in the solution of constrained quadratic 0–1 problems. We also discuss possible generalizations of these methods to arbitrary non-linear objective functions.     

Real-variables characterization of generalized Stieltjes functions

We obtain a characterization of generalized Stieltjes functions of any order λ>0$\lambda >0$ in terms of inequalities for their derivatives on (0,∞)$(0,\infty )$. When λ=1$\lambda =1$, this provides a new and simple proof of a characterization of Stieltjes functions first obtained by Widder in 1938.     

Liquid structure of the ionic liquid 1,3-dimethylimidazolium bis[(trifluoromethyl)sulfonyl]amide

Neutron diffraction has been used to determine the liquid structure of 1,3-dimethylimidazolium bis[(trifluoromethyl)sulfonyl]amide ([dmim][NTf2]). Significantly smaller charge ordering is found in this liquid compared with analogous chloride and hexafluorophosphate salts due to the diffuse charge density and size of the [NTf2]- anion. This is manifested in a much larger cation-cation and cation-anion separation and an overlap of the cation-cation and cation-anion shells. Comparison of the liquid structure with the crystal structure reported by Holbrey et al. (Dalton Trans. 2004, 2267) indicates little correlation, for example, the [NTf2]- anion adopts a trans orientation predominantly in the liquid whereas a cis orientation is found in the solid phase.     

Synthesis and characterization of long perylenediimide polymer fibers: from bulk to the single-molecule level

The synthesis and characterization of perylenediimide polyisocyanides is reported. In addition to short oligomers, our synthetic approach results in the formation of extremely long, well-defined, and rigid perylenediimide polymers. Ordering and close-packing of the chromophores in these long polymers is guaranteed by attachment to a polyisocyanide backbone with amino acid side chains. Hydrogen bonding interactions between those groups stabilize and rigidify the helical polymer structure. The rodlike nature of the synthesized long perylenediimide pendant polyisocyanides as well as the helical arrangement of the chromophores is demonstrated by means of atomic force microscopy. Remarkably, polymer fibers up to 1 mum in length have been visualized, containing several thousands of perylenediimide molecules. Circular dichroism spectroscopy reveals the chiral organization of the chromophore units in the polymer, whereas absorption and emission measurements prove the occurrence of excited-state interactions between those moieties due to the close packing of the chromophore groups. However, an intricate optical behavior is encountered in bulk as a result of the coexistence of short oligomers and long polymers of perylenediimide, a situation subsequently uncovered by means of single-molecule experiments. Individual long helical perylenediimide polyisocyanides exhibit a typical red-shifted fluorescence spectrum, which, together with depolarized emission continuously decreasing in time, demonstrate that fluorescence arises from multiple excimer-like species in the polymer. Upon continuous irradiation of these long polymers, a fast decay in fluorescence lifetime is observed, a situation explained by photoinduced creation of quenching sites. Radical/ion formation by intramolecular electron transfer between close-by perylenediimide moieties is the most probable mechanism for this process. Appropriate control of the electron-transfer process might open the possibility of applying these polymers as perylenediimide-based supramolecular nanowires.