We derive reciprocal integral relations between phases and amplitude moduli for a class of wave functions that are cyclically varying in time. The relations imply that changes of a certain kind (e.g. not arising from the dynamic phase) obligate changes in the other. Numerical results indicate the approximate validity of the relationships for arbitrarily (non-cyclically) varying states in the ad...

Passive gradient motion found in nature is becoming a point of interest for heat exchange and green energy technologies. Surfaces with topographical could potentially enhance exchanger performance, promote dropwise vs filmwise condensation, or delay icing on wind turbines by assisting the removal condensed impacted droplets. Coating-free surface tension gradients can be fabricated via various m...

We derive the exact equation of motion for a vortex in twoand three-dimensional nonrelativistic systems governed by the Ginzburg-Landau equation with complex coefficients. The velocity is given in terms of local gradients of the magnitude and phase of the complex field and is exact also for arbitrarily small intervortex distances. The results for vortices in a superfluid or a superconductor are...

Chemical gradient surfaces are described as surfaces with a gradually varying composition along their length. Continuous chemical gradients have recently been proposed as an alternative to discrete microarrays for the high-throughput screening of the effects of ligand concentration in cells. Here, we review some of the most recent examples in which gradients have been used to evaluate the effec...

In this paper, the relation between synchronization and control of chaotic nodes connected through a time–varying network is discussed. In particular, the effects of pinning control on a set of moving chaotic agents are investigated showing that the role of system parameters, like agent density, is critical in order to reach the synchronous behavior and also to control the whole network by pinn...

In this work we characterize the rate-distortion function of a Wyner-Ziv source, depending on an arbitrarily varying state, known non-causally at the encoder. We then consider the problem of joint source-channel coding of this source transmitted over an arbitrarily varying Gel’fand-Pinsker channel, where we assume that one jammer controls both, the source state sequence and the channel state se...

We consider compound as well as arbitrarily varying classical-quantum channel models. For classical-quantum compound channels, we give an elementary proof of the direct part of the coding theorem. A weak converse under average error criterion to this statement is also established. We use this result together with the robustification and elimination technique developed by Ahlswede in order to gi...

Orbital angular momentum (OAM) of photons, as a new fundamental degree of freedom, has excited a great diversity of interest, because of a variety of emerging applications. Arbitrarily tunable OAM has gained much attention, but its creation remains still a tremendous challenge. We demonstrate the realization of well-controlled arbitrarily tunable OAM in both theory and experiment. We present th...

The relationship between biodiversity and ecosystem functioning is a central issue in ecology, but how this relationship is affected by nutrient stress is still unknown. In this study, we analyzed the phytoplankton diversity effects on community biomass and stability along nutrient gradients in an artificial eutrophic lake. Four nutrient gradients, varying from slightly eutrophic to highly eutr...