Segments Of Finite Length Research Articles

Initiation and suppression of Taconis oscillations in tubes with junctions and variable-diameter tube segments

Taconis oscillations represent spontaneous, usually unwanted excitations of acoustic modes in narrow pipes going from warm ambient environment into cold cryogenic space. These oscillations can drastically magnify heat leak and create vibrations undesirable for measurement instruments. In this study, modifications of a classical constant-diameter-tube Taconis setup are investigated. Specifically, variable-diameter tubes were found to strongly affect excitation, with wider tube segments in the warm environment encouraging oscillations, while additions of properly chosen pipe network configurations can supress the oscillations. The low-amplitude thermoacoustic theory, previously developed for thermoacoustic engines and refrigerators, was adapted for modelling Taconis phenomena, accounting for finite-length segments with temperature evolution where thermal-to-acoustic energy conversion takes place. Experiments were conducted using primarily hydrogen as a working fluid to validate theoretical predictions. With the rapid development of various hydrogen storage and transfer systems, it is expected that Taconis oscillations may become an issue, and this study provides an initial modelling framework to assess this phenomenon in hydrogen systems.

Periodic necking of misfit hyperelastic filaments embedded in a soft matrix

The necking instability is a precursor to tensile failure and rupture of materials. A quasistatically loaded free-standing uniaxial specimen typically exhibits necking at a single location, thus corresponding to a long wavelength bifurcation mode. If confined to a substrate or embedded in a matrix the same filament can exhibit periodic necking and fragmentation thus creating segments of finite length. While such periodic instabilities have been extensively studied in ductile metal filaments and thin sheets, less is known about necking in hyperelastic materials. Nonetheless, in recent years, there has been a renewed interest in the role of necking in novel materials, for the advancement of fabrication processes and to explain fragmentation phenomena observed in 3D printed active biological matter. In both cases materials are not well described by the existing frameworks that employ J2 deformation theory of plasticity, and existing studies do not account for the significant role of misfit stretches that may emerge in these systems through chemical, or biological contraction. To address these limitations, in this paper we begin by experimentally demonstrating the role of the surrounding matrix on the necking and fragmentation of a compliant filament embedded in a tunable rubber matrix. Using a generalized hyperelastic model with strain softening, our analytical bifurcation analysis explains the experimental observations and is shown to agree with numerical predictions. The analysis reveals three distinct bifurcation modes: the long wavelength necking, thus recovering the Considère criterion; the periodic necking observed in our experiments; and a short wavelength mode that is characterized by localization along the center cord of the filament and is independent of the film-to-matrix stiffness ratio. We find that the softening coefficient and the filament misfit stretch can significantly influence the stability threshold and observed wavelength, respectively. Our results can guide the design and fabrication of novel composite materials and can explain the fragmentation processes observed in active biological materials.

Characteristic Analysis of the Dynamics of Shock Wave Propagation in a Medium with a Nonuniform Density Distribution

This paper is devoted to the numerical study of shock wave (SW) propagation in a medium with a nonuniform density distribution. The mathematical model is based on the Euler equations, which are solved in the shock-attached frame. This approach makes it possible to carry out an accurate characteristic analysis of the problem. First, the problems of SW propagation in a medium with finite-length segments with linearly increasing and decreasing density are considered. The obtained results are compared with the known analytical solutions. Then the case of a continuous change in the density of the medium in front of the SW according to the sinusoidal law is considered. The resulting flow is described and explained using the results for the case of a linear density gradient.

Fast virtual coiling algorithm for intracranial aneurysms using pre-shape path planning

To aid in predicting and improving treatment outcome of endovascular coiling of intracranial aneurysms, simulation of patient-specific coil deployment should be both accurate and fast. We developed a fast virtual coiling algorithm called Pre-shape Path Planning (P3). It captures the mechanical propensity of a released coil to restore its pre-shape for bending energy minimization, producing coils without unrealistic kinks and bends. A coil is discretized into finite-length segments and extruded from the delivery catheter segment-by-segment following a generic coil pre-shape. With the release of each segment, coil-wall and coil-coil collisions are detected and resolved. Modeling of each case took seconds to minutes. To test the algorithm, we evaluated its output against the literature, experiments, and patient angiograms. The periphery-to-core ratio of coils deployed by P3 decreased with increasing coil packing density, consistent with observations in the literature. Coils deployed by P3 compared well with in vitro experiments, free from unphysical kinks and loops that arose from previous virtual coiling algorithms. Simulations of coiling in four patient-specific aneurysms agreed well with the patient angiograms. To test the influence of coil pre-shape on P3, we performed hemodynamic simulations in aneurysms with coils deployed by P3 using the generic pre-shape, P3 using a coil-specific pre-shape, and full finite-element-method simulation. We found that the generic pre-shape was sufficient to produce results comparable to virtual coiling by finite element modeling. Based on these findings, P3 can rapidly simulate coiling in patient-specific aneurysms with good accuracy and is thus a potential candidate for clinical treatment planning.

Superadiabatic small-scale combustor with counter-flow heat exchange: Flame structure and limits to narrow-channel approximation

Small-scale superadiabatic combustors with counter-flow heat exchange segments of finite length are studied using irreversible Arrhenius kinetics. First, the complete two-dimensional conservation equations for the gas phase and the solid walls separating the channels are investigated numerically. Next, a simplified one-dimensional model, also known as the narrow-channel approximation, is derived asymptotically and the results are compared with those of the complete model. The main aim of the study is to assess the applicability limits of the simplified model. The analysis shows that this approximation provides valid results beyond its strict limits of validity.

On a remarkable example of F. Almgren and H. Federer in the global theory of minimizing geodesics

We present an exposition of a remarkable example attributed to Frederick Almgren Jr. in \cite[Section 5.11]{Federer74} to illustrate the need of certain definitions in the calculus of variations. The Almgren-Federer example, besides its intended goal of illustrating subtle aspects of geometric measure theory, is also a problem in the theory of geodesics. Hence, we wrote an exposition of the beautiful ideas of Almgren and Federer from the point of view of geodesics. In the language of geodesics, Almgren-Federer example constructs metrics in $\mathbb{S}^1\times \mathbb{S}^2$, with the property that none of the Tonelli geodesics (geodesics which minimize the length in a homotopy class) are Class-A minimizers in the sense of Morse (any finite length segment in the universal cover minimizes the length between the end points; this is also sometimes given other names). In other words, even if a curve is a minimizer of length among all the curves homotopic to it, by repeating it enough times, we get a closed curve which does not minimize in its homotopy class. In that respect, the example is more dramatic than a better known example due to Hedlund of a metric in $\mathbb{T}^3$ for which only 3 Tonelli minimizers (and their multiples) are Class-A minimizers. For dynamics, the example also illustrates different definitions of `integrable' and clarifies the relation between minimization and hyperbolicity and its interaction with topology.

Identification of underwater vehicles using surface wave pattern

The surface waves are generated due to motion of underwater vehicles near the free surface. The characteristics of such waves depend on the fluid, vehicle and motion properties. Using the characteristics of the generated waves by underwater vehicles moving near the free surface of water, an algorithm is developed to identify overall dimensions, velocity and submergence depth of the vehicles. The pressure distribution around the body is divided into several segments of finite length. It is assumed that each segment creates its own cosine wave on the free surface. The length of the body is obtained by using these waves’ amplitudes distribution. The speed of the vehicle is obtained based on the far-field wave length. The submergence depth is estimated by using a developed non-dimensional diagram which shows the variation of non-dimensional depth as a function of non-dimensional amplitude and Froude number. The diameter of the body is calculated approximately by the near field Kelvin wake or the Bernoulli hump. The algorithm is applied to several bodies with various dimensions at different submergence depth moving at various speeds. The algorithm gives a good estimation of the desired parameters.

State switching kinetics for quasi-one-dimensional nanosystems: Effects of Finite length and irradiation

The state switching in an extended quasi-one-dimensional material is modeled by the stochastic formation of local new-state nuclei and their subsequent growth along the system axis. An analytical approach is developed to describe the influence of defects, dividing a sample into an ensemble of finite-length segments, on its state switching kinetics. As applied to magnetic systems, the method makes it possible to calculate magnetization curves for different defect concentrations and parameters of material.

Conductance of a proximitized nanowire in the Coulomb blockade regime

We identify the leading processes of electron transport across finite-length segments of proximitized nanowires and build a quantitative theory of their two-terminal conductance. In the presence of spin-orbit interaction, a nanowire can be tuned across the topological transition point by an applied magnetic field. Due to a finite segment length, electron transport is controlled by the Coulomb blockade. Upon increasing of the field, the shape and magnitude of the Coulomb blockade peaks in the linear conductance is defined, respectively, by Andreev reflection, single-electron tunneling, and resonant tunneling through the Majorana modes emerging after the topological transition. Our theory provides the framework for the analysis of experiments with proximitized nanowires, such as reported in Albrecht et al., Nature 531, 206-209 (2016), and identifies the signatures of the topological transition in the two-terminal conductance.

Conductance dips and spin precession in a nonuniform waveguide with spin–orbit coupling

An infinite waveguide with a nonuniformity, a segment of finite length with spin–orbit coupling, is considered in the case when the Rashba and Dresselhaus parameters are identical. Analytical expressions have been derived in the single-mode approximation for the conductance of the system for an arbitrary initial spin state. Based on numerical calculations with several size quantization modes, we have detected and described the conductance dips arising when the waves are localized in the nonuniformity due to the formation of an effective potential well in it. We show that allowance for the evanescent modes under carrier spin precession in an effective magnetic field does not lead to a change in the direction of the average spin vector at the output of the system.

Flexible fiber transport by a fluid flow in fractures with smooth and rough walls

The transport of flexible fibers by a flowing fluid has been studied experimentally in transparent model fractures. Both finite length segments (20mm ≤ l ≤ 150 mm) and continuous fibers penetrating freely into the model were used; their motion is monitored by means of a digital camera and of an image thresholding technique and is induced by the flow of water or of a polymer solution at a mean velocity U (50 ≤ U ≤ 400 mm.s−1). In a model with plane smooth parallel walls, the influence of the friction with the walls is small: fiber segments reach quickly a constant velocity as their distance xm to the inlet increases, the velocity of continuous fibers increases slower with distance before reaching a constant value. The second model fracture has two complementary rough self-affine walls with a relative lateral shift; it displays, in addition, a gradient of the aperture in the direction transverse to the mean flow. For this model, the transport of the fibers by flowing water is only possible in the region of largest aperture and is of a "stop and go" type at low velocities. If water is replaced by the shear thinning polymer solution, the fibers move faster and continuously in high aperture regions; fiber transport also becomes possible in narrower regions.

Distance Bounds for an Ensemble of LDPC Convolutional Codes

An ensemble of <emphasis xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"><tex>$(J,K)$</tex> </formula></emphasis> -regular low-density parity- check (LDPC) convolutional codes is introduced and existence-type lower bounds on the minimum distance <emphasis xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"><tex>$d _ {\rm L}$</tex></formula></emphasis> of code segments of finite length <emphasis xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"><tex>$L$</tex> </formula></emphasis> and on the free distance <emphasis xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"> <tex>$d _{\rm free}$</tex></formula></emphasis> are derived. For sufficiently large constraint lengths <emphasis xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"><tex>$\nu$</tex> </formula></emphasis> , the distances are shown to grow linearly with <emphasis xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"><tex>$\nu$</tex></formula></emphasis> and the ratio <emphasis xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"><tex>$d_ {\rm L}/\nu$</tex></formula></emphasis> approaches the ratio <emphasis xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"><tex>$d _{ {\rm free}}/\nu$</tex> </formula></emphasis> for large <emphasis xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><formula formulatype="inline"><tex>$L$</tex> </formula></emphasis> . Moreover, the ratio of free distance to constraint length is several times larger than the ratio of minimum distance to block length for Gallager's ensemble of (J,K)-regular LDPC block codes.

Stabilization of a laminar boundary layer by an active surface-localized action

A method for rapidly damping instability waves is proposed as a means of actively controlling a perturbed gas boundary layer flow. The method is based on the use of an active body surface segment which reacts to an instantaneous local pressure variation by producing a proportional local wall displacement normal to the surface with a constant time lag calculated to result in the optimal suppression of unstable disturbances. It is shown that in the one-frequency case the wave number spectrum of the optimal control law contains multiple eigenvalues. The effectiveness of the method is demonstrated over a wide range of variation of the instability wave frequencies and directions. The propagation of an instability wave over an active segment of finite length is calculated using an integral-equation method based on solving the problem of boundary layer flow receptivity to surface vibration. Explicit formulas describing the process of scattering of the instability wave into stable modes at the junction point of the rigid and active surfaces are obtained using the Fourier method and the integral Cauchy theorem.

Evidence for one-dimensional electron propagation onSi(111)−(2×1)from Coulomb blockade

Scanning tunneling spectroscopy is used to study the electronic properties of the $\mathrm{Si}(111)\text{\ensuremath{-}}2\ifmmode\times\else\texttimes\fi{}1$ surface at $8\phantom{\rule{0.3em}{0ex}}\mathrm{\text{K}}$. Wave-function mapping reveals highly anisotropic scattering of electrons with one-dimensional (1D) confinement on the $\ensuremath{\pi}$-bonded chains. The differential tunneling conductance is strongly reduced at the Fermi energy ${E}_{F}$ and exhibits a Coulomb gap. The gap width $W$ scales with the inverse length $L$ of the chain segments defined by the distance between two adjacent scatterers such as surface steps or dopant atoms within a given chain. A model of electronic transport through 1D chain segments of finite length describes the observed behavior.

Improvement of frequency extraction accuracy of linear predictive analysis by a combination of autocorrelation and integral procedure for noise wave shape

AbstractThe accurate and rapid identification or detection of the electrical noise sources causing noise malfunctions in communication equipment is an important issue in determining corrective measures. In this paper, we explain an improvement in the frequency extraction accuracy of linear predictive analysis for noise waveforms in order to identify the noise sources from noise waveforms such as the audible noise generated by communication equipment like telephones and noise currents penetrating into the communication equipment. In this study, we propose an improvement of the frequency extraction accuracy of linear predictive analysis by using correlation and integration. This method preserves specific frequency components of the original noise waveforms although correlation and integration are performed. In this paper, we divide the noise waveform into finite‐length segments, correlate and integrate the time series data within a given segment, and formulate dynamic frequency analysis (time–frequency analysis) based on linear predictive analysis for the time series data in the postprocessing. We also verify the effectiveness of the proposed method by using known noise waveforms. The result of applying the proposed method to a noise waveform that convolved white noise with sine wave signals having known frequencies was clearly the ability to extract the frequencies of the sine waves included in the noise waveform even for a signal‐to‐noise ratio (SNR) of 0 dB with an error range of about 10 to 15%. This assumes that the frequencies of the sine waves included in the noise can be extracted even under the worst case SNR due to the suppression of white noise by the correlation and the emphasis of the low‐frequency components by the integration. Thus, we show that the characteristic frequencies in the noise waveform can be accurately extracted by using linear predictive analysis combining correlation and integration, and present the remaining issues. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 88(1): 1–11, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.20153

Experimental and theoretical evidence for the existence of photonic bandgaps and selective transmissions in serial loop structures

We have investigated the electromagnetic band structure, transmission, and phase time through a one-dimensional structure made of loops pasted together with segments of finite length. In this serial loop structure, the loops and segments are constituted of dielectric monomode materials. Analytic expressions are reported for the band structure for a large number N of loops and for transmission coefficients and phase times for any value of N. Experimental and numerical results show the existence of large gaps in these structures. These gaps originate both from the periodicity of the system and the loop resonant states that create zeroes of transmission. The gap widths depend on the lengths of the finite segment and the loop diameters. Defect modes may occur in these bandgaps by introducing defective segments in the structure. The localized states appear as very narrow peaks both in the transmission spectrum and in the transmission phase time of finite serial loop structures. The localized state behavior is analyzed as a function of the length and of the position of the defect segment. The transmission phase measurements enable us to derive the group velocity as well as the density of states in these structures. The experimental results are obtained using coaxial cables in the frequency range of few hundreds of MHz.

Nonlinear electrical properties of polyaniline: role of conjugation length

Undoped polyaniline (emeraldine base) exhibits nonlinear effects at high electric field. Conductivity measurements, as a function of a) temperature and b) aging induced disorder, are presented. Current-voltage curves are modeled in a space charge limited current scheme with a field dependent mobility and a non vanishing free carrier density. All the variations of the modeling parameters (cases a and b) are accounted for by models in which transport occurs by hopping between conjugated segments of finite length. For the first time, the relationship between the conjugation length distribution and the mobility behavior is evidenced in conjugated systems.

Scattering losses from planar waveguides with material inhomogeneity

We consider the propagation of guided waves in a planar waveguide that has a finite-length segment of inhomogeneous media. Except for the inhomogeneous segment, which varies in length from 0 to 160λ, the waveguide is piecewise homogeneous everywhere. The inhomogeneity is modelled by two-dimensional random permittivity fluctuations that are numerically generated from an assumed Gaussian correlation function. In 2D, the Maxwell equations are solved in the frequency domain for both TE and TM polarization by using modal expansion methods, perfectly matched absorbing boundary layers and the R -matrix transfer matrix algorithm. The guided waves are excited by a Gaussian beam incident on the waveguide aperture. For various waveguide design parameters, numerical results are given for waveguide power loss per unit length of waveguide inhomogeneity. The power loss curves are calculated as the average from numerous realizations of the random permittivity and the coefficient of variation is also given.

Observation of large photonic band gaps and defect modes in one-dimensionalnetworked waveguides

The photonic band structures and transmission spectra of serial loop structures(SLSs), made of loops pasted together with segments of finite length, areinvestigated experimentally and theoretically. These monomode structures,composed of one-dimensional dielectric materials, may exhibit large stop bandswhere the propagation of electromagnetic waves is forbidden. The width of theseband gaps depends on the geometrical and compositional parameters of thestructure and may be drastically increased in a tandem geometry made upof several successive SLSs which differ in their physical characteristics.These SLSs may have potential applications as ultrawide-band filters.

Magnonic spectral gaps and discretetransmission in serial loop structures

In the frame of the long-wavelength Heisenberg model, themagnonic bandgaps and the selective transmission in a serialloop structure, made of loops pasted together with segments offinite length, are investigated theoretically. The loops and thesegments are assumed to be one-dimensional ferromagneticmaterials. Using a Green function method, we obtainedclosed-form expressions for the band structure and thetransmission coefficients for an arbitrary value of the numberN of loops in the serial loop structure. It was found that thegaps originated from the periodicity of the system. The width ofthese forbidden bands depends on the structural andcompositional parameters. We also present analytical andnumerical results for the transmission coefficient through adefective geometry where the length of one finite branch hasbeen modified. It was demonstrated that the presence of thisdefect in the structure can give rise to localized states insidethe gaps. We show especially that these localized states arevery sensitive to the size of the loops and to the periodicity aswell as to the length and the location of the defect branch.