Infinite Transmission Research Articles

Torsional vibration band gaps in a shaft with 1D-piezoelectric phononic crystals

A kind of phononic crystal shaft with piezoelectric ceramic circular rings is proposed in this paper. Based on the wave equation, the propagating characteristics of torsional wave are calculated by the transfer matrix method. The torsional wave band structures of infinite piezoelectric phononic crystal shaft (PPC shaft) and transmission curves of finite PPC shaft are analyzed, then simulations are carried out to verify the theoretical results by using ANSYS software. Furthermore, the effects of outer active control on the torsional wave band gaps are considered by changing feedback control gains. The influences of the ratios of length and cross-sectional area on the band gaps are also discussed in detail. Results show that there exist band gaps of torsional vibration in this special PPC shaft and the width together with the position of the band gaps can be adjusted effectively by varying structural parameters and outer active control gains.

Energy efficient resource allocation for quantity of information delivery in parallel channels

AbstractThis paper deals with the problem of minimising the energy required to transmit a certain amount of information bits. If there is no constraint, in a Gaussian channel, the solution leads us to the use an infinite transmission time or an infinite bandwidth. In particular, the minimum required signal‐to‐noise ratio to transmit one bit is equal to −1.59 dB. To allow the development of new green communication services, a finite bandwidth and a finite time have to be used in practice. Thus, we focus on the transmission of a given number of bits over a set of parallel Gaussian channels when there is an energy constraint, and we have the goal of minimising either the highest transmission time (amongst the channels) or the average channel occupancy time. This is a resource allocation problem that is formulated by targeting a certain energy consumption factor, herein defined as the ratio between the energy required in the asymptotic regime and the energy required to transmit a certain quantity of information with limited (time, bandwidth) resources. The Pareto front for the joint optimization of the maximum transmission time and the average channel occupancy time is also derived. Several explicative numerical results of the derived resource allocation algorithms for energy efficient communications are also reported. Copyright © 2014 John Wiley & Sons, Ltd.

Regularization of the spectral singularity inPT-symmetric systems by all-order nonlinearities: Nonreciprocity and optical isolation

Spectral singularities are ubiquitous with PT-symmetry leading to infinite transmission and reflection coefficients. Such infinities imply the divergence of the fields in the medium thereby breaking the very assumption of the linearity of the medium used to obtain such singularities. We identify saturable nonlinearity retaining contributions from all orders of the field to limit the infinite growth and regularize the spectral singularity. We present explicit numerical results to demonstrate regularization. The all order nonlinear PT-symmetric device is shown to exhibit very effective isolation or optical diode action, since transmission through such a system is nonreciprocal. In contrast, a linear system or a system with Kerr nonlinearity is known to have only reciprocal transmission. Further we demonstrate optical bistability for such a system with high contrast.

On the performance evaluation of query-based wireless sensor networks

We present a queueing-theoretic framework to evaluate the performance of large-scale, query-based wireless sensor networks whose nodes detect and advertise significant events that are useful for only a limited time; queries generated by sensor nodes are also time-limited. The main performance parameter is the steady state proportion of generated queries that fail to be answered on time. Using an infinite transmission range model, we first provide an approximation for this parameter that is insensitive to the size of the network. Subsequently, we approximate the proportion of failed queries when the transmission range is limited and show that this proportion converges to its infinite range counterpart as the sensor transmission range tends to infinity. The analytical approximations are shown to be remarkably accurate when compared with benchmark values obtained using a commercial network simulator.

Function-indexed empirical processes based on an infinite source Poisson transmission stream

We study the asymptotic behavior of empirical processes generated by measurable bounded functions of an infinite source Poisson transmission process when the session length have infinite variance. In spite of the boundedness of the function, the normalized fluctuations of such an empirical process converge to a non-Gaussian stable process. This phenomenon can be viewed as caused by the long-range dependence in the transmission process. Completing previous results on the empirical mean of similar types of processes, our results on non-linear bounded functions exhibit the influence of the limit transmission rate distribution at high session lengths on the asymptotic behavior of the empirical process. As an illustration, we apply the main result to estimation of the distribution function of the steady state value of the transmission process.

Current limiting performance test of 3-phase tri-axial transformer-type SFCL with re-wound structure at 3-line-to-ground fault in lab-scale transmission system

We have proposed a transformer-type SFCL of a re-wound structure, which can produce a limiting reactance (L-limiting) for smaller fault current and, for larger one, additively give a limiting resistance (L+R limiting). The single-phase proposed model SFCL had been tested and shown good limiting characteristics and excellent recovery performance. A 3-phase tri-axial SFCL of the proposed type had been designed and made using BSCCO2223. This paper describes demonstration tests of the model SFCL carried out using a lab-scale one-machine infinite bus transmission model system. The experimental results on the current limiting performance of the SFCL at the 3-line-to-ground (3LG) fault were shown and discussed. The peak fault current 560 A without SFCL was reduced to 230A with SFCL immediately. The 3-phase SFCL successfully worked without large inter-phase interaction. The SFCL recovered to the stand-by mode under a typical Circuit Breaker (CB) operation sequence.

The singular point transition concept: A novel continuously variable transmission comprising planetary gear trains and a variator

The singular point transition concept relates a novel type of continuously variable transmission. This transmission comprises a pair of planetary gear trains and a couple of electric motors, used to control the overall speed ratio. Its singularity lies in the topology of operation, with less than 10% of nominal power circulating through the electric path. This low power level is achieved by segmenting the range of operation of the transmission.To validate this technology, a test bed was built. The transmission presented here is able to provide any output/input speed ratio within the interval of 0:1.55, meaning that it also offers the function of an infinite variable transmission. Description of the system and results of experimental tests are presented. The results showed that the transmission is able to function in the whole range of operation. They also showed that under load conditions the fraction of power transmitted through the electric path is maintained around the design value.

Resonance phenomenon related to spectral singularities, complex barrier potential, and resonating waveguides

A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission coefficients. This property reveals an interesting resonance effect with possible applications in waveguide physics. We study the spectral singularities of a complex barrier potential and explore their application in designing a waveguide that functions as a resonator. We show that for the easily accessible sizes of the waveguide and its gain region, we can realize the spectral singularity-related resonance phenomenon at almost every wavelength within the visible spectrum or outside it.

Reflection and transmission by a slab with randomly distributed isotropic point scatterers

The problem of how a wave propagates in an infinite medium filled with scatterers has revealed the notion of an effective medium: the mean wave propagates as in an homogeneous medium with complex index. Is this notion of an effective medium still valid when the scatterers are bounded in space? The problem is treated here for isotropic point scatterers. It is shown that (i) the waves propagate inside the slab with an effective wavenumber K being the same as that in an infinite medium, (ii) the reflection and transmission coefficients of the slab mainly behave as R ≃ ( 1 − e i K L ) ( k − K ) / 2 k and T ≃ e i K L at leading order, (iii) the reflection and transmission coefficients of a single interface are related to R and T with the usual law of optics and (iv) the boundary conditions to be applied at the interface are the continuity of the field and its first derivative for isotropic scatterers. Finally, numerical experiments in one dimension show satisfactory agreement with the presented theory.

Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at Real Energies

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a waveguide modeled using such a potential operates like a resonator at the frequencies of spectral singularities. As a concrete example, we explore the spectral singularities of an imaginary PT-symmetric barrier potential and demonstrate the above resonance phenomenon for a certain electromagnetic waveguide.

Finite and Infinite Transmission Zeros for Infinite-Dimensional Systems

In this article various definitions and features of transmission zeros for finite-dimensional systems are represented. Then possibilities to generalize these definitions for infinite-dimensional systems are discussed.

Improvement of Power System Stability by Use of Superconducting Fault Current Limiter With ZnO Device and Resistor in Parallel

Superconducting fault current limiters (SCFCLs) are expected to improve the reliability and stability of power systems. SCFCLs can be classified into R-types (resistive) and L-types (inductive) by the fault current limiting impedance. An L-type FCL is more effective in suppressing the voltage drop during a fault. On the other hand, a R-type FCL is more effective in consuming the acceleration energy of generators at the fault. Both functions lead to the improvement of the transient stability of the power system. We have proposed and fabricated the FCL unit, which is expected to have both functions. It consists of an inductive superconducting fault current limiter with a resistor and a ZnO device in parallel. In this paper, the simulation analysis on one machine and an infinite bus transmission system including the proposed FCL unit was carried out. EMTP (electro-magnetic transients program) was used in order to analyze the power system characteristics of the FCL unit. A rotor angle of the generator and a critical fault clearing time were analyzed to evaluate the effects of the FCL unit on the improvement of the transient stability of the model power system. A contribution share of the voltage drop suppression and the acceleration energy consumption to the improvement of the power system stability were clarified with various conditions, such as, generator output and fault clearing time.

Current imbalance in superconducting strand-to-strand joint and its relaxation in multistage cable-in-conduit conductor

This paper presents non-uniformity or imbalance in the transport current of the superconducting toroidal-field coil (TFC) made of multistage cable-in-conductor (CICC) due to inductive current in a strand-to-strand (STS) soldered joint of cylindrical shape and also the relaxation of the inductive current in the conductor. Using an NbTi CICC consisting of 486 strands, a joint sample is fabricated and experimented. An external magnetic field of symmetric trapezoidal waveform is vertically applied to the sample joint. The field maximum and the ramp rate (d B/d t) maximum are 1 T and 0.25 T/s, respectively. Voltage taps and Hall probes are utilized to measure the inductive voltage and current. Experimental results are analyzed numerically using an infinite electrical transmission line model, which is found to explain our sample system well. The flattop induced current is proportional to the d B/d t. Being different from our expectation that the inductive current will distribute widely over the cross-sectional surface of the joint, it localizes to a narrow region; a triplet located in the outer-most side of the joint, for instance. The relaxation phenomenon in the induced current is observed experimentally. From numerical analysis, the relaxation length is found to increase logarithmically with decreasing d B/d t and saturate at a certain value of d B/d t.

A Feynman path analysis of the Fano effect in electronic transport through a parallel double quantum dot structure

We carry out a comprehensive analysis of Fano effect in electronic transport process through a parallel double quantum dot (QD) structure. First, we establish an expression of the linear conductance in the standard Fano form. This expression provides a uniform way to explain the presence of the Fano antiresonance (or a lack of thereof) in various double QD structures. Then, by virtue of the language of Feynman path, we find that there are infinite electron transmission paths to contribute to the Fano interference. In the absence of a magnetic field, the high-order paths play a nontrivial role in the formation of the Fano lineshape. Finally, we find that it is possible to eliminate the contributions of all the high-order paths by tuning the magnetic field to some specific values. Thus, just two lowest-order Feynman paths remain. Only in such a case, the Fano effect can be unambiguously understood to arise from a quantum interference between a resonant and a nonresonant paths.

A Periodically Loaded Transmission Line Excited by an Aperiodic Source—A Green's Function Approach

A simple and closed-form expression for the Green's function of a periodically loaded infinite transmission line is derived. The spatial-domain formulation is based on distinguishing three coordinate systems, i.e., the observation, primary source, and secondary source coordinates. The Fourier transform is subsequently employed to transform the primary source spatial domain to a spectral domain, wherein Floquet's theorem is applicable. While applying Floquet's theorem, the observation coordinate is Fourier transformed to another spectral parameter that is a function of the primary source spectral parameter. The spatial-domain expression for the Green's function is obtained upon identifying the poles in the spectral parameter complex plane. The derived expression is verified by comparing the values of the voltage along the line obtained analytically with those obtained using a circuit simulator. The effect of the various parameters on the voltage distribution along the line and the dispersion curves is investigated.

Design of an anisotropic quarter-wave polariser without insertion loss caused by mismatch

The authors present novel high-performance polariser designs. The polarisers provide perfect linear-to-circular polarisation transformation without insertion loss at the centre frequency. Four designs are discussed for use in two situations. In the first situation, a polariser is inserted into an isotropic medium and, in the second, a polariser is sandwiched between two isotropic media with different intrinsic impedances. For the first situation, two designs are proposed based on the dielectric window and impedance matching. For the second, two further designs are proposed. In the first, two anisotropic media are cascaded in a special manner to perform the polarisation transformation without insertion loss. For a simpler uniaxial medium, the design utilises an impedance transformer and the polariser mentioned in the first situation. One of the resulting polarisers has an infinite transmission bandwidth, if the medium is nondispersive. Hence, the bandwidth of the polariser is solely determined by the axial ratio bandwidth. Based on the two-transmission-lines model, the polariser can be examined easily using commercial radio-frequency software. Some examples and simulated results are presented to validate these designs.

Loss in an Infinite Transmission Line

An infinitely long transmission line appears to have an ohmic conductance even when loss in circuit elements approaches zero. We show that the real part of the admittance of the transmission line derives from a dense distribution of resonance absorption lines.

Hyperreal waves on transfinite, terminated, distortionless and lossless, transmission lines

A prior work (Graphs and Networks: Transfinite and Nonstandard, Chapter 8. Birkhauser: Boston, Cambridge, MA, 2004) examined the propagation of an electromagnetic wave on a transfinite transmission line—transfinite in the sense that infinitely many one-way infinite transmission lines are connected in cascade. That there are infinitely many such one-way infinite lines results in the wave propagating without ever reflecting at some discontinuity. The present work examines the case where the cascade terminates after only finitely many one-way infinite transmission lines, with the result that reflected waves are now produced at both the far end as well as at the initial end of the transfinite transmission line. The questions whether the reflected waves are infinitesimal or appreciable and whether they sum to an infinitesimal or appreciable amount are resolved for both distortionless and lossless lines. Finally, the generalization to higher ranks of transfiniteness is briefly summarized. Copyright © 2005 John Wiley & Sons, Ltd.

Quasistatic capacitance and frequency-dependent effective permittivity of multilayer microstrip patch antennas

A variational method in the spectral domain is used to determine the quasistatic capacitance of a patch antenna within a nonhomogeneous multilayer structure. The patch is modelled both by a one dimensional analysis using a segment of an infinite transmission line and by a full two-dimensional representation. A new technique is presented for determining the relative permittivity of an equivalent single-layer structure, from which the frequency-dependent effective permittivity is obtained. Results for a number of different antenna structures are given and show good agreement with measured values.

Computation of capacitance coefficients of rectangular thick patches on multilayered substrates

This article presents an alternative method to compute the capacitance coefficients of a system of rectangular thick patches on a multilayered substrate. Following the M-strips, previously developed to analyze infinite length transmission lines, the conductors are modeled by a set of zero-thickness plates at the same potential. The capacitance coefficients of the model structure are obtained after applying the Galerkin's method in the spatial domain. A suitable approach for computing the static spatial Green's function is also presented. © 1996 John Wiley & Sons, Inc.