Periodic String Research Articles

Observation of torsion on bowed strings

Research on bowed string motion focuses on transverse waves and not so much on torsional waves. These are believed to play only a minor role for stabilizing vibrations and no role for perception. Here, torsion is measured on both sides of the bow contact point for a variety of bridge-bow distances on a cello string. Electromagnetical and optical measurements correspond. Every periodic string release is preceded by a reverse torsional motion independent from bowing position or dynamics. Transverse and torsional motions are coupled and there are cases of stabilization, but also cases of perturbation or surrender. Structural and timing analyses of torsional waves suggest that the earlier concepts of differential slipping can be essentially confirmed. Other concepts cannot be confirmed, such as the Schelleng ripples, or are under question, such as the concept of subharmonics.

Experimental Investigation of the Vibration Control of Nonrotating Periodic Drill Strings

Abstract During the drilling process in oil and gas fields, slender drill strings often experience a multitude of complex and simultaneous vibrational phenomena. Drill string vibrations hinder the drilling process and can cause premature wear and damage to the drilling equipment. Here, the suppression of drill string vibrations during drilling operations is experimentally investigated using a novel drill string design, based on the use of innovative periodic inserts that control the vibration transmissibility in different directions. These inserts are equipped with viscoelastic rings that act as sources of local resonances, surrounding piezoelectric actuators that generate internal axial loading when electrically excited. An experimental prototype that combined all these details was constructed and tested to demonstrate the periodic drill string's feasibility and effectiveness in minimizing undesirable vibrations. The obtained results indicate that the periodic inserts’ careful design can effectively enhance the drill strings’ dynamic behavior and conveniently regulate its bandgap characteristics. Both radial and axial vibrations were controlled, and the vibrations’ amplitude was reduced significantly over a wide range of frequencies. The proposed approach appears to present a viable means for designing intelligent drill strings with tunable bandgap characteristics.

Periodic string complexes over string algebras

In this paper we develop combinatorial techniques for the case of string algebras with the aim to give a characterization of string complexes with infinite minimal projective resolution. These complexes will be called periodic string complexes. As a consequence of this characterization, we give two important applications. The first one, is a sufficient condition for a string algebra to have infinite global dimension. In the second one, we exhibit a class of indecomposable objects in the derived category for a special case of string algebras. Every construction, concept and consequence in this paper is followed by some illustrative examples.

CORENup: a combination of convolutional and recurrent deep neural networks for nucleosome positioning identification

BackgroundNucleosomes wrap the DNA into the nucleus of the Eukaryote cell and regulate its transcription phase. Several studies indicate that nucleosomes are determined by the combined effects of several factors, including DNA sequence organization. Interestingly, the identification of nucleosomes on a genomic scale has been successfully performed by computational methods using DNA sequence as input data.ResultsIn this work, we propose CORENup, a deep learning model for nucleosome identification. CORENup processes a DNA sequence as input using one-hot representation and combines in a parallel fashion a fully convolutional neural network and a recurrent layer. These two parallel levels are devoted to catching both non periodic and periodic DNA string features. A dense layer is devoted to their combination to give a final classification.ConclusionsResults computed on public data sets of different organisms show that CORENup is a state of the art methodology for nucleosome positioning identification based on a Deep Neural Network architecture. The comparisons have been carried out using two groups of datasets, currently adopted by the best performing methods, and CORENup has shown top performance both in terms of classification metrics and elapsed computation time.

Acoustic frequency spectrum characteristics in periodic drill string under tension

AbstractIt is a promising measure to transmit downhole information by acoustic wave through drill string. However, the transmission distance and quality of acoustic signals in field conditions are still not satisfied because the acoustic frequency spectrum in drill string is vulnerable to interference. This paper studied acoustic frequency spectrum characteristics in periodic drill string by experiments under different axial tensile forces. The multilevel method is established to evaluate frequency spectrum through drill string based on improved radar chart. The impact of axial tensile force on spectrum characteristics is analyzed by the proposed method. The results indicate that the axial tensile force has remarkable impact on the acoustic frequency spectrum and passband characteristics. The spectrum characteristics change with axial tensile force. These changes are reflected in the position, width, and attenuation of different passbands. And the extent of changes is distinct to different passbands. Both the evaluation indicators of each passband and spectrum are change with increasing axial tensile force. The spectrum quality is excellent in the range of 17‐134 MPa for axial tensile force in drill string. And when the force exceeds 152 MPa, methods such as adjusting the carrier frequency and relay installation location are necessary to improve the transmission quality of acoustic signals.

On the behaviour of infinite, periodic, mono-coupled waveguides using a transmission coefficient phase method

Abstract Wave propagation in a one dimensional, mono-coupled waveguide composed of an infinite wave-bearing structure supported by periodic discontinuities is analysed in terms of the transmission and reflection coefficients of a single discontinuity, expressions for which are often available in the literature. The general solution is presented and is applicable for arbitrary transmission and reflection coefficients. For conservative discontinuities, conservation of energy imposes relationships on the complex values of these coefficients and yields a simplified expression for the propagation constant, which is a function of the phase of the transmission coefficient, and a second phase angle which arises from the conditions of continuity and equilibrium at the discontinuity. Expressions for the bounding frequencies between pass and stop bands, the bandwidth of a stop band, and the upper bound of attenuation within a stop band are also given in terms of these phases. For some common systems, the phase of the transmission coefficient determines the behaviour of the entire system and thus provides a straightforward analysis. The proposed approach for mono-coupled waveguides can also be applied to some multi-coupled waveguides such as beams under the assumption that nearfield waves are negligible. The approach is then applied to an infinite periodic string on arbitrary supports, an Euler-Bernoulli beam on periodic arbitrary supports, and a system of thin beams that are hinged at periodic intervals with arbitrary supports.

Topological Phase Transition in a One-Dimensional Elastic String System

We show that topological interface mode can emerge in a one-dimensional elastic string system which consists of two periodic strings with different band topologies. To verify their topological features, Zak-phase of each band is calculated and reveals the condition of topological phase transition accordingly. Apart from that, the transmittance spectrum illustrates that topological interface mode arises when two topologically distinct structures are connected. The vibration profile further exhibits the non-trivial interface mode in the domain wall between two periodic string composites.

Further empirical data for torsion on bowed strings.

Research on bowed string motion focuses on transverse waves rather than on torsional waves. These are believed to play only a minor role for stabilizing vibrations and no role for perception. Here, torsion is measured on both sides of the bow contact point for a variety of bridge-bow distances on a cello string. Every periodic string release is preceeded by a reverse torsional motion independent from bowing position or dynamics. Transverse and torsional motions are coupled and there are cases of stabilization, but also cases of perturbation or surrender. Structural and timing analyses of torsional waves suggest that the earlier concepts of differential slipping can be essentially confirmed while the concept of Schelleng ripples cannot be confirmed and the concept of subharmonics is under question.

Band gap characteristics of periodic gyroscopic systems

The stop and pass bands (i.e. the band gaps) characteristics are determined for gyroscopic systems by developing an approach which is compatible with such class of systems which is based on the concept of Bloch wave propagation in periodic structures. In this approach, the dispersion curves of the periodic gyroscopic systems are determined for different rotational speeds. The obtained characteristics are compared with non-rotating systems in an attempt to quantify the effect of the gyroscopic forces on the “band gap” characteristics. The developed approach is illustrated by a new class of drill strings with passive periodic inserts. These inserts are utilized to filter out the vibration transmission along the drill string. Such mechanical filtering capabilities allow the vibrations to propagate along the periodic drill string only within specific frequency bands called the ‘pass bands’ and completely block it within other frequency bands called the ‘stop bands’. The inserts introduce impedance mismatch zones along the vibration transmission path to impede the propagation of vibration along the drill string. The design and the location of the inserts are selected to confine the dominant modes of vibration of the drill string within the stop bands generated by the periodic arrangement of the inserts in order to completely block the propagation of the vibrations.A finite element model (FEM) that simulates the operation of this new class of drill strings is developed to describe the complex nature of the vibration encountered during drilling operations. The FEM is used to extract the dispersion characteristics of the gyroscopic unit cell of the drill string in order to determine its stop and pass band characteristics. Experimental prototype of the passive periodic drill string is built and tested to demonstrate the feasibility and effectiveness of the concept of periodic drill string in mitigating undesirable vibrations. The experimental results are used to validate the developed theoretical model in order to develop a scalable design tool that can be used to predict the dynamical behavior of this new class of drill strings.

Diffraction and Smith-Purcell radiation on the hemispherical bulges in a metal plate

The radiation resulting from the uniform motion of a charged particle near a hemispheric bulge on a metal plane is considered. The description of the radiation process based on the method of images is developed for the case of non-relativistic particle and a perfectly conducting target. The spectral-angular and spectral densities of the diffraction radiation on the single bulge (as well as the Smith-Purcell radiation on the periodic string of bulges) are computed. The possibility of application of the developed approach to the case of relativistic incident particle is discussed.

Band Gap Characteristics of Nonrotating Passive Periodic Drill String

A new class of drill strings is investigated whereby strategically designed and placed periodic inserts are utilized to filter out the vibration transmission along the drill strings. Such mechanical filtering capabilities allow the vibrations to propagate along the periodic drill string only within specific frequency bands called the “pass bands” and completely block it within other frequency bands called the “stop bands.” The design and the location of the inserts are selected to confine the dominant modes of vibration of the drill string within the stop bands generated by the periodic arrangement of the inserts in order to completely block the propagation of the vibrations. A finite element model (FEM) that simulates the operation of this new class of drill strings is developed to describe the complex nature of the vibration encountered during drilling operations. Experimental prototype of the passive periodic drill string was built and tested to demonstrate the feasibility and effectiveness of the concept of periodic drill string in mitigating undesirable vibrations. The experimental results are used to validate the developed theoretical model and to develop a scalable design tool that can be used to predict the dynamical behavior of this new class of drill strings.

Radiation of non-relativistic particle on a conducting sphere and a string of spheres

The radiation resulting from the uniform motion of a charged particle by (or through) metal sphere is considered. The simple but rigorous description of the radiation process is developed for the case of non-relativistic particle and perfectly conducting sphere by the way of the method of images known from electrostatics. The spectral-angular and spectral densities of the diffraction and transition radiation on the single sphere are computed. The Smith–Purcell radiation caused by motion of the particle parallel to the periodic string of spheres is also considered.

Wave propagation in axially moving periodic strings

The paper deals with analytically studying transverse waves propagation in an axially moving string with periodically modulated cross section. The structure effectively models various relevant technological systems, e.g. belts, thread lines, band saws, etc., and, in particular, roller chain drives for diesel engines by capturing both their spatial periodicity and axial motion. The Method of Varying Amplitudes is employed in the analysis. It is shown that the compound wave traveling in the axially moving periodic string comprises many components with different frequencies and wavenumbers. This is in contrast to non-moving periodic structures, for which all components of the corresponding compound wave feature the same frequency. Due to this “multi-frequency” character of the wave motion, the conventional notion of frequency band-gaps appears to be not applicable for the moving periodic strings. Thus, for such structures, by frequency band-gaps it is proposed to understand frequency ranges in which the primary component of the compound wave attenuates. Such frequency band-gaps can be present for a moving periodic string, but only if its axial velocity is lower than the transverse wave speed, and, the higher the axial velocity, the narrower the frequency band-gaps. The revealed effects could be of potential importance for applications, e.g. they indicate that due to spatial inhomogeneity, oscillations of axially moving periodic chains always involve a multitude of frequencies.

Where is the beat?

The ability to find the beat in a sequence of auditory events may be linked to the ability to learn vocal communication, raising the question of how beat structure in speech events relates to that in other event sequences. We conducted a series of entrainment experiments designed to compare spoken syllable repetition with tapping. Producing taps to a periodic string of auditorily-presented spoken /pa/ syllables resulted in the tap falling between the release burst for the /p/ and the onset of voicing for the vowel. This is consistent with participants intending to align their taps with the vowel onsets but exhibiting the well-documented Negative Mean Asynchrony (NMA) effect, such that the taps precede their “target.” The finding of alignment with the voicing onset is reminiscent of a large body of work on the P-center in repeated spoken syllables. In contrast, producing repeated utterances of the syllable /pa/ to an auditorily-presented click train resulted in coincident occurrence of the release burst with the click, putting the voicing onset after the stimulus (inconsistent with a voicing-onset target with associated NMA). These findings indicate that the location of the beat may differ across tasks involving speech perception and various types of speech production.

Lattice fractional Laplacian and its continuum limit kernel on the finite cyclic chain

The aim of this paper is to deduce a discrete version of the fractional Laplacian in matrix form defined on the 1D periodic (cyclically closed) linear chain of finite length. We obtain explicit expressions for this fractional Laplacian matrix and deduce also its periodic continuum limit kernel. The continuum limit kernel gives an exact expression for the fractional Laplacian (Riesz fractional derivative) on the finite periodic string. In this approach we introduce two material parameters, the particle mass μ and a frequency Ωα. The requirement of finiteness of the the total mass and total elastic energy in the continuum limit (lattice constant h → 0) leads to scaling relations for the two parameters, namely μ ∼ h and Ωα2∼h−α. The present approach can be generalized to define lattice fractional calculus on periodic lattices in full analogy to the usual ‘continuous’ fractional calculus.

Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit

We deduce explicit representations for the 1D discrete lattice counterpart of fractional Laplacian on the finite periodic linear chain. The continuum limit of the fractional lattice Laplacian operator yields the periodic Riesz fractional derivative on the finite periodic string. In the limiting case of infinite lattices known representations are recovered. The fractional finite-lattice Laplacian operator is of importance for the description and analysis of a wide range of problems of certain kinds of anomalous phenomena such as Lévy flights and problems of fractional quantum mechanics.

Approximate periodicity

Finding an approximate period in a given string S of length n is defined as follows. Let S′ be a periodic string closest to S under some distance metric, find the smallest period of S′. This period is called an approximate period of S under the given metric. Let the distance between the input string S and a closest periodic string under the Hamming distance S′ be k. We develop algorithms that construct an approximate period of S under the Hamming distance in time O(nklog⁡log⁡n) and under the swap distance in time O(n2). Finally, we show an O(nlog⁡n) algorithm for finite alphabets, and an O(nlog3⁡n) algorithm for infinite alphabets, that approximate the minimum number of mismatches between the input string and a closest periodic string under the Hamming distance.

Propagation properties of acoustic waves inside periodic pipelines

This paper presents a new method to model and to simulate the propagation properties of the acoustic wave in periodic pipelines. First, an ideal model of pipeline and its dispersion equations of acoustic waves are constructed and described in detail in order to implement this method. Subsequently, the classical finite difference method is applied to determine the boundary conditions of the pipelines. In addition, the transfer matrix method is used to simulate the propagation process of the acoustic waves inside the pipelines. Finally, by conducting length-limited periodic drill string experiments, it is shown that this model and algorithm can be used to obtain the acoustic-wave spectrum distribution and impulse response characteristics inside periodic pipelines under operational conditions. This method provides a theoretical basis for the fault diagnosis of acoustic-wave transmission systems for oil industry applications.

Long-wave asymptotic theories: The connection between functionally graded waveguides and periodic media

This article explores the deep connections that exist between the mathematical representations of dynamic phenomena in functionally graded waveguides and those in periodic media. These connections are at their most obvious for low-frequency and long-wave asymptotics where well established theories hold. However, there is also a complementary limit of high-frequency long-wave asymptotics corresponding to various features that arise near cut-off frequencies in waveguides, including trapped modes. Simultaneously, periodic media exhibit standing wave frequencies, and the long-wave asymptotics near these frequencies characterise localised defect modes along with other high-frequency phenomena. The physics associated with waveguides and periodic media are, at first sight, apparently quite different, however the final equations that distill the essential physics are virtually identical. The connection is illustrated by the comparative study of a periodic string and a functionally graded acoustic waveguide.

Wilson loops T-dual to short strings

We show that closed string solutions in the bulk of AdS space are related by T-duality to solutions representing an open string ending at the boundary of AdS. By combining the limit in which a closed string becomes small with a large boost, we find that the near-flat space short string in the bulk maps to a periodic open string world surface ending on a wavy line at the boundary. This open string solution was previously found by Mikhailov and corresponds to a time-like near-BPS Wilson loop differing by small fluctuations from a straight line. A simple relation is found between the shape of the Wilson loop and the shape of the closed string at the moment when it crosses the horizon of the Poincaré patch. As a result, the energy and spin of the closed string are encoded in properties of the Wilson loop. This suggests that closed string amplitudes with one of the closed strings falling into the Poincaré horizon should be dual to gauge theory correlators involving local operators and a Wilson loop of the T-dual (“momentum”) theory.