Weak turbulence for a vibrating plate: can one hear a Kolmogorov spectrum?

We study the long-time evolution of waves of a thin elastic plate in the limit of small deformation so that modes of oscillations interact weakly. According to the theory of weak turbulence (successfully applied in the past to plasma, optics, and hydrodynamic waves), this nonlinear wave system evolves at long times with a slow transfer of energy from one mode to another. We derive a kinetic equation for the spectral transfer in terms of the second order moment. We show that such a theory describes the approach to an equilibrium wave spectrum and represents also an energy cascade, often called the Kolmogorov-Zakharov spectrum. We perform numerical simulations that confirm this scenario.     

Can one hear the dimension of a fractal?

We consider the spectrum of the Laplacian in a bounded open domain of ⁿ with a rough boundary (i.e. with possibly non-integer dimension) and we discuss a conjecture by M. V. Berry generalizing Weyl's conjecture. Then using ideas Mark Kac developed in his famous study of the drum, we give upper and lower bounds for the second term of the expansion of the partition function. The main thesis of the paper is to show that the relevant measure of the roughness of the boundary should be based on Minkowski dimensions and on Minkowski measures rather than on Haussdorff ones.Dedicated to the memory of Mark Kac     

Can’t one really hear the shape of a drum?

In this paper we study the wave and the Klein-Gordon equations in frontiers with the same set of eigen values using a computational algorithm based on the finite difference method and the discrete Fourier transform. Doing this we found that although the set of eigen values in the two shapes are equal, the intensities in the spectrum are different, which means that the question, can one hear the shape of a drum? is still open.     

How fast can cracks propagate?

We have performed atomic simulations of crack propagation along a weak interface joining two harmonic crystals. The simulations show that a mode II shear dominated crack can accelerate to the Rayleigh wave speed and then nucleate an intersonic daughter that travels at the longitudinal wave speed. This contradicts the general belief that a crack can travel no faster than the Rayleigh speed.     

Can listeners hear who is singing? A comparison of three-note and six-note discrimination tasks

Timbre is typically investigated as a perceptual attribute that differentiates a sound source at one pitch and loudness. Yet the perceptual usefulness of timbre is that it allows the listener to recognize one sound source at different pitches. This paper investigated the ability of listeners to identify which pitch in an ascending or descending sequence of three or six stimuli was sung by a different singer. For three-note sequences, the task was extremely difficult, and with rare exceptions, listeners chose the most dissimilarly pitched stimulus as coming from the oddball singer. For six-note sequences, the detection of the oddball singer was much improved in spite of the added complexity of the task. These results support the idea that timbre should be understood as a transformation that connects the different sounds of one source and that a "rich" set of sounds is necessary to discover the trajectory.     

How narrow can a meniscus be?

A water meniscus naturally forms in air between an atomic force microscope (AFM) tip and a substrate. This nanoscale meniscus produces a capillary force on the AFM, and also serves as a molecular transport channel in dip-pen nanolithography (DPN). A stable meniscus is a necessary condition for DPN and for the validity of the Kelvin equation commonly applied to AFM experiments. Lattice gas Monte Carlo simulations show that, due to thermal fluctuation, a stable meniscus has a lower limit in width. We find a minimum width of 5 molecular diameters (1.9 nm) when the tip becomes atomically sharp (terminated by a single atom).     

Can one hear the shape of an electrode? II. Theoretical study of the Laplacian transfer

The flux across resistive irregular interfaces driven by a force deriving from a Laplacian potential is computed on a rigorous basis. The theory permits one to relate the size of the active zone to the derivative of the spectroscopic impedance with respect to the surface resistivity r through: . It is shown that the macroscopic transfer properties through a system of arbitrary shape are determined by the characteristics of a first-passage interface-interface random walk operator . More precisely, it is the distribution of the harmonic measure (or normalized primary current) on the eigenmodes of this linear operator that controls the transfer. In addition, it is also shown that, whatever the dimension, the impedance of a weakly polarizable electrode for any irregular geometry scales under a homothety transformation as L^d-1, L being the size of the system and d its topological dimension. In this new formalism, the question addressed in the title is transformed in a open mathematical question: “Knowing the distribution of the harmonic measure on the eigenmodes of the self-transport operator, can one retrieve the shape of the interface?” Received 3 November 1998     

What we can learn from γγ→ππ,K \bar K in the resonance region

The two photon couplings of hadronic states are believed to be key pointers to their parton constitutents. With the aim of studying these, we present a method of analysing data on γγ→ππ (andK \(\bar K\) ), which embodies the constraints of unitarity and analyticity while respecting the QED low energy theorem required by gauge invariance. We apply this analysis to presently available data on ππ production and find that within the existing uncertainties few definitive conclusions can yet be drawn in the resonance region. For instance, even the claim that thef-resonance has a largely helicity two coupling is shown not to be established. We illustrate the importance of the angular dependence of the data to reach almost all conclusions not only on the helicity structure off-production but also on the couplings of the scalar states to this vital channel. In the near threshold region, however, we confirm the overwhelming dominance of the QED Born amplitude modified by final state interactions in contradiction with several recent datasets on the π⁺π^? channel. We show how the new Crystal Ball experiment on π⁺0⁰ production not only confirms this conclusion on the near threshold cross-section but angular analysis of their data with its better statistics using the method we present should shed light on the nature of the scalar mesons in the 1 GeV region.     

Photons can hide where they have been

Recently,the nested Mach–Zehnder interferometer[Phys.Rev.Lett.111,240402(2013)]was modified by adding Dove prisms in a paper[Quantum Stud.:Math.Found.2,255(2015)],and an interesting result is that,after the Dove prisms were inserted,a signal at the first mirror of the nested interferometer was obtained.But,according to the former original paper,the photons have never been present near that mirror.In this work,we interpret this result naturally by resorting to the three-path interference method.Moreover,we find that even though the photons have been somewhere,they can hide the trace of being there.     

What can a chemist learn from nature’s macrocycles? – A brief, conceptual view

Macrocyclic natural products often display remarkable biological activities, and many of these compounds (or their derivatives) are used as drugs. The chemical diversity of these compounds is immense and may provide inspiration for innovative drug design. Therefore, a database of naturally occurring macrocycles was analyzed for ring size, molecular weight distribution, and the frequency of some common substructural motifs. The underlying principles of the chemical diversity are reviewed in terms of biosynthetic origin and natures strategies for diversity and complexity generation in relation to the structural diversity and similarities found in the macrocycle database. Finally, it is suggested that synthetic chemists should use not only natures molecules, but also natures strategies as a source of inspiration. To illustrate this, the biosynthesis of macrocycles by non-ribosomal peptide synthetases and terpene and polyketide cyclases, as well as recent advances of these strategies in an integrated synthesis/biotechnology approach are briefly reviewed.     

Observations of deterministic chaos in financial time series by recurrence plots, can one control chaotic economy?

Several economical time series such as exchange rates US$/British Pound, USA Treasure Bonds rates and Warsaw Stock Index WIG have been investigated using the method of recurrence plots. The percentage of recurrence REC and the percentage of determinism DET have been calculated for the original and for shuffled data. We have found that in some cases the values of REC and DET parameters are about 20% lower for the surrogate data which indicates the presence of unstable periodical orbits in the considered data. A similar result has been obtained for the chaotic Lorenz model contaminated by noise. Our investigations suggest that real economical dynamics is a mixture of deterministic and stochastic chaos. We show how a simple chaotic economic model can be controlled by appropriate influence of time-delayed feedback. Received 13 October 2000     

How complex a dynamical network can be?

Positive Lyapunov exponents measure the asymptotic exponential divergence of nearby trajectories of a dynamical system. Not only they quantify how chaotic a dynamical system is, but since their sum is an upper bound for the rate of information production, they also provide a convenient way to quantify the complexity of a dynamical network. We conjecture based on numerical evidences that for a large class of dynamical networks composed by equal nodes, the sum of the positive Lyapunov exponents is bounded by the sum of all the positive Lyapunov exponents of both the synchronization manifold and its transversal directions, the last quantity being in principle easier to compute than the latter. As applications of our conjecture we: (i) show that a dynamical network composed of equal nodes and whose nodes are fully linearly connected produces more information than similar networks but whose nodes are connected with any other possible connecting topology; (ii) show how one can calculate upper bounds for the information production of realistic networks whose nodes have parameter mismatches, randomly chosen; (iii) discuss how to predict the behavior of a large dynamical network by knowing the information provided by a system composed of only two coupled nodes.     

Desktop supercomputer: what can it do?

The paper addresses the issues of solving complex problems that require using supercomputers or multiprocessor clusters available for most researchers nowadays. Efficient distribution of high performance computing resources according to actual application needs has been a major research topic since high-performance computing (HPC) technologies became widely introduced. At the same time, comfortable and transparent access to these resources was a key user requirement. In this paper we discuss approaches to build a virtual private supercomputer available at user’s desktop: a virtual computing environment tailored specifically for a target user with a particular target application. We describe and evaluate possibilities to create the virtual supercomputer based on light-weight virtualization technologies, and analyze the efficiency of our approach compared to traditional methods of HPC resource management.     

How far can one send a photon?

The answer to the question How far can one send a photon? depends heavily on what one means by a photon and on what one intends to do with that photon. For direct quantum communication, the limit is approximately 500 km. For terrestrial quantum communication, near-future technologies based on quantum teleportation and quantum memories will soon enable quantum repeaters that will turn the development of a world-wide-quantum-web (WWQW) into a highly non-trivial engineering problem. For Device-Independent Quantum Information Processing, near-future qubit amplifiers (i.e., probabilistic heralded amplification of the probability amplitude of the presence of photonic qubits) will soon allow demonstrations over a few tens of kilometers.     

How we can interpret the T1 dispersion of MC, HPMC and HPC polymers above glass temperature?

The chain dynamics in methyl cellulose (MC), hydroxypropylmethyl cellulose (HPMC) and hydroxypropyl cellulose (HPC) were studied with the aid of field-cycling NMR relaxometry technique in the temperature range from 300 to 480 K that is above the glass transition, but below thermal degradation. The frequency dependence of proton spin-lattice relaxation time was determined between 24 kHz and 40 MHz for selected temperatures. The experimental spin-lattice relaxation dispersion data were fitted with the power law relations of T(1) proportional variant omega(gamma) predicted by the tube/reptation model. The exponent's values found from the fitting procedure for MC, HPMC and HPC almost exactly match the ones predicted in tube/reptation model for limit II (gamma=0.75) and in MC also for limit III (gamma=0.50). Remarkably, this finding concerns the polymers in networks formed of the same polymer species.