Comment on "Why quantum mechanics cannot be formulated as a Markov process"

In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607, (1994)] claims that the theory of Markov stochastic processes cannot provide an adequate mathematical framework for quantum mechanics. In conjunction with the specific quantum dynamics considered there, we give a general analysis of the associated dichotomic jump processes. If we assume that Gillespie's "measurement probabilities" \it are \rm the transition probabilities of a stochastic process, then the process must have an invariant (time independent) probability measure. Alternatively, if we demand the probability measure of the process to follow the quantally implemented (via the Born statistical postulate) evolution, then we arrive at the jump process which \it can \rm be interpreted as a Markov process if restricted to a suitable duration time. However, there is no corresponding Markov process consistent with the $Z_2$ event space assumption, if we require its existence for all times $t\in R_+$.Comment: Latex file, resubm. to Phys. Rev.

Shell Model of Two-dimensional Turbulence in Polymer Solutions

We address the effect of polymer additives on two dimensional turbulence, an issue that was studied recently in experiments and direct numerical simulations. We show that the same simple shell model that reproduced drag reduction in three-dimensional turbulence reproduces all the reported effects in the two-dimensional case. The simplicity of the model offers a straightforward understanding of the all the major effects under consideration

Students' understanding of gravity using the rubber sheet analogy: an Italian experience

General Relativity (GR) represents the most recent theory of gravity, on which all modern astrophysics is based, including some of the most astonishing results of physics research. Nevertheless, its study is limited to university courses, while being ignored at high school level. To introduceGR in high school one of the approaches that can be used is the so-called rubber sheet analogy, i.e. comparing the space-time to a rubber sheet which deforms under a weight. In this paper we analyze the efficacy of an activity for high school students held at the Department of Mathematics and Physics of Roma Tre University that adopts the rubber sheet analogy to address several topics related to gravity. We present the results of the questionnaires we administered to investigate the understanding of the topics treated to over 150 Italian high school students who participated in this activity.Comment: 19 pages, 14 figure

Drag Reduction by Polymers in Turbulent Channel Flows: Energy Redistribution Between Invariant Empirical Modes

We address the phenomenon of drag reduction by dilute polymeric additive to turbulent flows, using Direct Numerical Simulations (DNS) of the FENE-P model of viscoelastic flows. It had been amply demonstrated that these model equations reproduce the phenomenon, but the results of DNS were not analyzed so far with the goal of interpreting the phenomenon. In order to construct a useful framework for the understanding of drag reduction we initiate in this paper an investigation of the most important modes that are sustained in the viscoelastic and Newtonian turbulent flows respectively. The modes are obtained empirically using the Karhunen-Loeve decomposition, allowing us to compare the most energetic modes in the viscoelastic and Newtonian flows. The main finding of the present study is that the spatial profile of the most energetic modes is hardly changed between the two flows. What changes is the energy associated with these modes, and their relative ordering in the decreasing order from the most energetic to the least. Modes that are highly excited in one flow can be strongly suppressed in the other, and vice versa. This dramatic energy redistribution is an important clue to the mechanism of drag reduction as is proposed in this paper. In particular there is an enhancement of the energy containing modes in the viscoelastic flow compared to the Newtonian one; drag reduction is seen in the energy containing modes rather than the dissipative modes as proposed in some previous theories.Comment: 11 pages, 13 figures, included, PRE, submitted, REVTeX

Towards automated loop-shaping in controller parameter space

This paper presents a data-based control design method for optimal tuning of the parameters of a fixed structure controller with respect to the given closed-loop (CL) performance specifications. The proposed approach is to translate the CL specifications into controller parameter space and to automate the parameter choice through optimization problems. The developed method ensures CL stability and close to optimal controller design for any user defined controller structure, given the frequency response data set of the uncertain plant

Saturation of Turbulent Drag Reduction in Dilute Polymer Solutions

Drag reduction by polymers in turbulent wall-bounded flows exhibits universal and non-universal aspects. The universal maximal mean velocity profile was explained in a recent theory. The saturation of this profile and the crossover back to the Newtonian plug are non-universal, depending on Reynolds number Re, concentration of polymer $c_p$ and the degree of polymerization $N_p$. We explain the mechanism of saturation stemming from the finiteness of extensibility of the polymers, predict its dependence on $c_p$ and $N$ in the limit of small $c_p$ and large Re, and present the excellent comparison of our predictions to experiments on drag reduction by DNA.Comment: 4 pages, 4 figs., included, PRL, submitte

Nonlinear graphene metamaterial

We demonstrate that the broadband nonlinear optical response of graphene can be resonantly enhanced by more than an order of magnitude through hybridization with a plasmonic metamaterial,while retaining an ultrafast nonlinear response time of ~1 ps. Transmission modulation close to ~1% is seen at a pump uence of ~0.03 mJ/cm^2 at the wavelength of ~1600 nm. This approach allows to engineer and enhance graphene's nonlinearity within a broad wavelength range enabling applications in optical switching, mode-locking and pulse shaping.Comment: The following article has been submitted to Applied Physics Letters. After it is published, it will be found at http://apl.aip.org

Phase-change chalcogenide glass metamaterial

Combining metamaterials with functional media brings a new dimension to their performance. Here we demonstrate substantial resonance frequency tuning in a photonic metamaterial hybridized with an electrically/optically switchable chalcogenide glass. The transition between amorphous and crystalline forms brings about a 10% shift in the near-infrared resonance wavelength of an asymmetric split-ring array, providing transmission modulation functionality with a contrast ratio of 4:1 in a device of sub-wavelength thickness.Comment: 3 pages, 3 figure

Haptics for the development of fundamental rhythm skills, including multi-limb coordination

This chapter considers the use of haptics for learning fundamental rhythm skills, including skills that depend on multi-limb coordination. Different sensory modalities have different strengths and weaknesses for the development of skills related to rhythm. For example, vision has low temporal resolution and performs poorly for tracking rhythms in real-time, whereas hearing is highly accurate. However, in the case of multi-limbed rhythms, neither hearing nor sight are particularly well suited to communicating exactly which limb does what and when, or how the limbs coordinate. By contrast, haptics can work especially well in this area, by applying haptic signals independently to each limb. We review relevant theories, including embodied interaction and biological entrainment. We present a range of applications of the Haptic Bracelets, which are computer-controlled wireless vibrotactile devices, one attached to each wrist and ankle. Haptic pulses are used to guide users in playing rhythmic patterns that require multi-limb coordination. One immediate aim of the system is to support the development of practical rhythm skills and multi-limb coordination. A longer-term goal is to aid the development of a wider range of fundamental rhythm skills including recognising, identifying, memorising, retaining, analysing, reproducing, coordinating, modifying and creating rhythms – particularly multi-stream (i.e. polyphonic) rhythmic sequences. Empirical results are presented. We reflect on related work, and discuss design issues for using haptics to support rhythm skills. Skills of this kind are essential not just to drummers and percussionists but also to keyboards players, and more generally to all musicians who need a firm grasp of rhythm