Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices

Coherent states and their generalizations, displaced Fock states, are of fundamental importance to quantum optics. Here we present a direct observation of a classical analogue for the emergence of these states from the eigenstates of the harmonic oscillator. To this end, the light propagation in a Glauber-Fock waveguide lattice serves as equivalent for the displacement of Fock states in phase space. Theoretical calculations and analogue classical experiments show that the square-root distribution of the coupling parameter in such lattices supports a new family of intriguing quantum correlations not encountered in uniform arrays. Because of the broken shift invariance of the lattice, these correlations strongly depend on the transverse position. Consequently, quantum random walks with this extra degree of freedom may be realized in Glauber-Fock lattices.     

Structure effects on the energetics of the electrochemical reduction of CO2 by copper surfaces

Polycrystalline copper electrocatalysts have been experimentally shown to be capable of reducing CO₂ into CH₄ and C₂H₄ with relatively high selectivity, and a mechanism has recently been proposed for this reduction on the fcc(211) surface of copper, which was assumed to be the most active facet. In the current work, we use computational methods to explore the effects of the nanostructure of the copper surface and compare the effects of the fcc(111), fcc(100) and fcc(211) facets of copper on the energetics of the electroreduction of CO₂. The calculations performed in this study generally show that the intermediates in CO₂ reduction are most stabilized by the (211) facet, followed by the (100) facet, with the (111) surface binding the adsorbates most weakly. This leads to the prediction that the (211) facet is the most active surface among the three in producing CH₄ from CO₂, as well as the by-products H₂ and CO. HCOOH production may be mildly enhanced on the more close-packed surfaces ((111) and (100)) as compared to the (211) facet, due to a change in mechanism from a carboxyl intermediate to a formate intermediate. The results are compared to published experimental data on these same surfaces; the predicted trends in voltage requirements are consistent between the experimental and computational data.     

Properties of the Time-Optimal Feedback Control for a Pendulum-Like System

A time-optimal control problem for a pendulum-like system is considered. The system describes the dynamics of an inertial object under the action of a bounded control force and an external force which is periodic in coordinate. The terminal set consists of points on the abscissa axis of the phase plane, and the distance between two neighboring points is equal to the period of the external force. In the general case, the solution can be obtained only numerically. An estimate is found for the amplitude of the control for which the time-optimal feedback control has the simplest structure: the number of switchings is not greater than one for any initial conditions. For the estimated interval of the control constraints, we analyze the feedback control pattern.     

A Biologically Inspired Optimization Algorithm for Solving Fuzzy Shortest Path Problems with Mixed Fuzzy Arc Lengths

The shortest path problem is among fundamental problems of network optimization. Majority of the optimization algorithms assume that weights of data graph’s edges are pre-determined real numbers. However, in real-world situations, the parameters (costs, capacities, demands, time) are not well defined. The fuzzy set has been widely used as it is very flexible and cost less time when compared with the stochastic approaches. We design a bio-inspired algorithm for computing a shortest path in a network with various types of fuzzy arc lengths by defining a distance function for fuzzy edge weights using \(\alpha \) cuts. We illustrate effectiveness and adaptability of the proposed method with numerical examples, and compare our algorithm with existing approaches.     

PotLLL: a polynomial time version of LLL with deep insertions

Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with provable output quality. One early improvement of the LLL algorithm was LLL with deep insertions (DeepLLL). The output of this version of LLL has higher quality in practice but the running time seems to explode. Weaker variants of DeepLLL, where the insertions are restricted to blocks, behave nicely in practice concerning the running time. However no proof of polynomial running time is known. In this paper PotLLL, a new variant of DeepLLL with provably polynomial running time, is presented. We compare the practical behavior of the new algorithm to classical LLL, BKZ as well as blockwise variants of DeepLLL regarding both the output quality and running time.     

Lubrication approximation with prescribed nonzero contact anggle

We prove long existence for a weak solutions ss(t,x)≥0 of the lubrication approximation ?_t+?_x(s?s)=0 in{s>0> with prescribed contact anglo of, say,(?_xs)²=1 on ?{s>0}     

An amphibious vibration-driven microrobot with a piezoelectric actuator

This article concerns microrobots for solid and liquid environments. A short overview of microrobotics, suitable actuators and energy systems is given. The principles of terrestrial and aquatic locomotion are discussed and illustrated with examples from the literature on robotics. The state of the art with a focus on piezo microrobots for solid and liquid environments is presented. Furthermore, we report an amphibious prototype, which can move on flat solid ground and on the free surface of water. The design, characteristic parameters and experiments on locomotion are described. The robot is characterized by a light and simple design and can perform twodimensional locomotion in different environments with a speed up to 30 mm/s. An analytical model to predict the maximum carrying capacity of the robot on water is solved numerically.     

Foliations of asymptotically flat manifolds by surfaces of Willmore type

The goal of this paper is to establish the existence of a foliation of the asymptotic region of an asymptotically flat manifold with positive mass by surfaces which are critical points of the Willmore functional subject to an area constraint. Equivalently these surfaces are critical points of the Geroch–Hawking mass. Thus our result has applications in the theory of general relativity.     

The second volume moment of the typical cell and higher moments of edge lengths of the spatial Poisson–Voronoi tessellation

This paper presents analytical results for higher moments of characteristics of a Voronoi tessellation generated by a homogeneous Poisson point process in the three-dimensional Euclidean space. The second moment of the volume of the typical cell as well as higher moments for the edge length distribution and the linear contact distribution are given. These characteristics are calculated analytically and presented in a unified form.