Arbitrary Phase Angle Research Articles

Simulation of Indexing and Clocking with a New Multidimensional Time Harmonic Balance Approach

Alongside the capability to simulate rotor–stator interactions, a central aspect within the development of frequency-domain methods for turbomachinery flows is the ability of the method to accurately predict rotor–rotor and stator–stator interactions on a single-passage domain. To simulate such interactions, state-of-the-art frequency-domain approaches require one fundamental interblade phase angle, and therefore it can be necessary to resort to multi-passage configurations. Other approaches neglect the cross-coupling of different harmonics. As a consequence, the influence of indexing on the propagation of the unsteady disturbances is not captured. To overcome these issues, the harmonic balance approach based on multidimensional Fourier transforms in time, recently introduced by the authors, is extended in this work to account for arbitrary interblade phase angle ratios on a single-passage domain. To assess the ability of the approach to simulate the influence of indexing on the steady, as well as on the unsteady, part of the flow, the proposed extension is applied to a modern low-pressure fan stage of a civil aero engine under the influence of an inhomogeneous inflow condition. The results are compared to unsteady simulations in the time-domain and to state-of-the-art frequency-domain methods based on one-dimensional discrete Fourier transforms.

Spacecraft Rendezvous in Closed Keplerian Orbits Using Constant Radial Thrust Acceleration

An analytical solution for spacecraft rendezvous within closed Keplerian orbits is presented using continuous radial thrust. The two spacecraft are assumed to be initially placed within the same closed orbit with arbitrary phase angle separation. The target spacecraft is assumed to always remain in the same initial orbit. The chaser vehicle, however, uses a judiciously designed maneuver sequence comprising constant-acceleration radial thrust phases interspersed with coast phases. Importantly, the proposed maneuver design is analytically characterized by one or two (depending on whether the parking orbit is circular or elliptical, respectively) nonlinear algebraic equations that determine the time intervals for the different phases. The set of initial conditions from which rendezvous is feasible is also characterized. Additionally, orbit rotation (that is, changing the orbit argument of periapsis in plane) is also demonstrated for the elliptical parking orbit case. Finally, the remarkable emergence of the golden and silver ratios, as well as their connections to Kepler’s triangle, is demonstrated for a specific sequence of thrust and coast arcs.

Constant intensity acoustic propagation in the presence of non-uniform properties and impedance discontinuities: Hermitian and non-Hermitian solutions.

Propagation of sound through a non-uniform medium without scattering is possible, in principle, if the density and acoustic compressibility assume complex values, requiring passive and active mechanisms, also known as Hermitian and non-Hermitian solutions, respectively. Two types of constant intensity wave conditions are identified: in the first, the propagating acoustic pressure has constant amplitude, while in the second, the energy flux remains constant. The fundamental problem of transmission across an impedance discontinuity without reflection or energy loss is solved using a combination of monopole and dipole resonators in parallel. The solution depends on an arbitrary phase angle that can be chosen to give a unique acoustic metamaterial with both resonators undamped and passive, requiring purely Hermitian acoustic elements. For other phase angles, one of the two elements must be active and the other passive, resulting in a gain/loss non-Hermitian system. These results prove that uni-directional and reciprocal transmission through a slab separating two half spaces is possible using passive Hermitian acoustic elements without the need to resort to active gain/loss energetic mechanisms.

Force sensing and cooling for the mechanical membrane in a hybrid optomechanical system

A study on force sensing and cooling for the mechanical membrane in a dissipative optomechanical system (OMS) with a degenerate optical parametric amplifier (OPA) and an optical Kerr medium is presented. The optimal phase angle can contribute to achieve much better force sensing than the case of the arbitrary phase angle. Specifically, at the blue detuning between the cavity field and the input laser the coexistence of the OPA and the Kerr medium plays an important role in improving the force sensitivity over the case of a bare OMS, while at the red detuning the bare OMS demonstrates more effective force sensitivity than the case of the coexistence of the OPA and the Kerr medium. The coexistence of the OPA and the Kerr medium is helpful to achieve more stable force sensitivity, which results from the change of the normalized cavity detuning having little effect on the force sensitivity of the system. In addition, for the existence of only nonlinear gain of the OPA, the study shows that at the blue detuning the temperature of the mechanical membrane can be achieved more effectively than in the case of the bare OMS, while at the red detuning, with increasing value of the nonlinear gain of the OPA, the cooling of the membrane is weakened. For the existence of the Kerr medium, at continuous detuning the effective temperature of the mechanical membrane is below the temperature of the environment. In quantum engineering, this scheme may have potential applications in precision measurement and quantum manipulation.

Fracture Initiation Mechanisms of Multibranched Radial-Drilling Fracturing

Abstract Compared with conventional hydraulic fracturing, radial-drilling fracturing presents remarkable advantages and can effectively develop low-permeability reservoirs. The radial borehole can reduce formation fracture pressure and guide the fracture initiation and propagation. Due to the large radial borehole azimuth or the strong anisotropy of the reservoir, the single radial borehole may not efficiently guide the fracture propagation. The researchers proposed multibranched radial-drilling fracturing. However, the research on fracture initiation of multibranched radial-drilling fracturing is inadequate. Radial boreholes usually need certain dip angles to avoid penetrating the interlayer, but the effect of dip angle on the stress field has never been considered before. In this paper, an analytical model for predicting stress distribution around the main wellbore with multiradial boreholes of arbitrary dip angle, azimuth angle, and phase angle is established for the first time, taking full account of the influences of in situ stress, internal pressure, and fracture fluid infiltration on the stress field. The model is utilized to calculate the fracture initiation pressure (FIP) and point out the specific fracture initiation location (FIL). The influences of azimuth angle, dip angle, phase angle, depth difference, and the stress profile radius on fracture initiation pressure, fracture initiation location, and maximum tensile stress distribution are investigated, and a series of sensitivity analyses are carried out. The results show that the areas between the radial boreholes and closer to the walls of radial boreholes are more prone to tensile failure, which provides a theoretical basis for radial boreholes guiding fracture initiation. The reduction of phase angle and depth difference enhances the interference between radial wells, which is conductive to the formation of hydraulic fracture networks between them. As the dip angle increases, the stress becomes increasingly concentrated, and the preferential rock tensile failure becomes increasingly easy. The farther the stress profile is from the main wellbore axis, the smaller it will be influenced by the main wellbore. When the distance exceeds 2R, the maximum tensile stress distribution on the profile remains constant. The research enriches the fracture initiation mechanism of multibranched radial-drilling fracturing and provides guidance for optimizing radial borehole layout parameters of hydraulic fracturing directed by multiradial boreholes.

Spin-gapped magnets with weak anisotropies I: Constraints on the phase of the condensate wave function

We study the thermodynamic properties of dimerized spin-gapped quantum magnets with and without exchange anisotropy (EA) and Dzyaloshinsky and Moriya (DM) anisotropies within the mean-field approximation (MFA). For this purpose we obtain the thermodynamic potential Ω of a triplon gas taking into account the strength of DM interaction up to second order. The minimization of Ω with respect to self-energies Σn and Σan yields the equation for X1,2=Σn±Σan−μ, which define the dispersion of quasiparticles Ek=ϵk+X1ϵk+X2 where ϵk is the bare dispersion of triplons. The minimization of Ω with respect to the magnitude ρ0 and the phase Θ of triplon condensate leads to coupled equations for ρ0 and Θ. We discuss the restrictions on ρ0 and Θ imposed by these equations for systems with and without anisotropy. The requirement of dynamical stability conditions (X1>0,X2>0) in equilibrium, as well as the Hugenholtz–Pines theorem, particularly for isotropic Bose condensate, impose certain conditions to the physical solutions of these equations. It is shown that the phase angle of a purely homogenous Bose–Einstein condensate (BEC) without any anisotropy may only take values Θ=πn (n=0, ±1,±2...) while that of BEC with even a tiny DM interaction results in Θ=π∕2+2πn. In contrast to the widely used Hartree–Fock–Popov approximation, which allows arbitrary phase angle, our approach predicts that the phase angle may have only discrete values, while the phase of the wave function of the whole system remains arbitrary as expected. The consequences of this phase locking for interference of two Bose condensates and to their possible Josephson junction is studied. In such quantum magnets the emergence of a triplon condensate leads to a finite staggered magnetization M⊥, whose direction in the xy-plane is related to the condensate phase Θ. We also discuss the possible Kibble–Zurek mechanism in dimerized magnets and its influence on M⊥.

Dual Josephson impedance bridge: towards a universal bridge for impedance metrology

This paper presents a full characterization of a Dual Josephson Impedance Bridge (DJIB) at frequencies up to 80 kHz by using the DJIB to compare the best available impedance standards that are (a) directly traceable to the quantum Hall effect, (b) used as part of international impedance comparisons, or (c) believed to have calculable frequency dependence. The heart of the system is a dual Josephson Arbitrary Waveform Synthesizer (JAWS) source that offers unprecedented flexibility in high-precision impedance measurements. The JAWS sources allow a single bridge to compare impedances with arbitrary ratios and phase angles in the complex plane. The uncertainty budget shows that both the traditional METAS bridges and the DJIB have comparable uncertainties in the kilohertz range. This shows that the advantages of the DJIB, including the flexibility which allows the comparison of arbitrary impedances, the wide frequency range and the automated balancing procedure, are obtained without compromising the measurement uncertainties. These results demonstrate that this type of instrument can considerably simplify the realization and maintenance of the various impedance scales. In addition, the DJIB is a very sensitive tool for investigating the frequency-dependent systematic-errors that can occur in impedance construction and in the voltage provided by the JAWS source at frequencies greater than 10 kHz.

Efficient magic state factories with a catalyzed|CCZ⟩to2|T⟩transformation

We present magic state factory constructions for producing|CCZ⟩states and|T⟩states. For the|CCZ⟩factory we apply the surface code lattice surgery construction techniques described in \cite{fowler2018} to the fault-tolerant Toffoli \cite{jones2013, eastin2013distilling}. The resulting factory has a footprint of12d×6d(wheredis the code distance) and produces one|CCZ⟩every5.5dsurface code cycles. Our|T⟩state factory uses the|CCZ⟩factory's output and a catalyst|T⟩state to exactly transform one|CCZ⟩state into two|T⟩states. It has a footprint25%smaller than the factory in \cite{fowler2018} but outputs|T⟩states twice as quickly. We show how to generalize the catalyzed transformation to arbitrary phase angles, and note that the caseθ=22.5∘produces a particularly efficient circuit for producing|T⟩states. Compared to using the12d×8d×6.5d|T⟩factory of \cite{fowler2018}, our|CCZ⟩factory can quintuple the speed of algorithms that are dominated by the cost of applying Toffoli gates, including Shor's algorithm \cite{shor1994} and the chemistry algorithm of Babbush et al. \cite{babbush2018}. Assuming a physical gate error rate of10−3, our CCZ factory can produce∼1010states on average before an error occurs. This is sufficient for classically intractable instantiations of the chemistry algorithm, but for more demanding algorithms such as Shor's algorithm the mean number of states until failure can be increased to∼1012by increasing the factory footprint∼20%.

Calibration of an $LCR$ -Meter at Arbitrary Phase Angles Using a Fully Automated Impedance Simulator

A fully automated impedance simulator, called iSimulator, capable of simulating impedances ranging from $1~\Omega $ to 10 $\text{M}\Omega $ , at arbitrary phase angles, over a large frequency range (from 100 Hz to 20 kHz) is presented. The validation of the instrument is performed by calibrating a commercial $LCR$ -meter up to 20 kHz along the axis of the complex plane. The results of the iSimulator calibration are in good agreement with measurements carried out using the classical artifact-based method. This validation clearly demonstrated the unique capabilities of the iSimulator, based on its flexibility, broad impedance and frequency range, full coverage of the complex plane, and its full automation. In the near future, impedance simulators will definitely play a privileged role in the entire impedance calibration field both in National Metrology Institutes and in industrial calibration laboratories.

A Three-Arm Current Comparator Digitally Assisted Bridge for the Comparison of Arbitrary Four Terminal-Pair Impedances

High accuracy impedance measurements are performed with coaxial transformer bridges, whose conventional design allows the comparison of like impedances—pure resistors or capacitors. Here, we present a current comparator bridge suited for the measurement of impedances of arbitrary magnitudes and phase angles. The bridge has three arms, to connect the impedance under measurement and two calibrated standards. The bridge is digitally assisted and its operation is based on a polyphase digital sine wave synthesizer. To allow the measurement of midimpedance to low-impedance magnitudes, the bridge network and the balancing procedure are designed to approximate the four terminal-pair definition of the three impedance standards. The bridge has been extensively tested with conventional impedance standards and custom designed phase standards. The relative base accuracy is in the 10−5 to 10−6 range at kilohertz frequency.

An approach to lifetime prediction for a wrought Ni-base alloy under thermo-mechanical fatigue with various phase angles between temperature and mechanical strain

The damage and lifetime behaviour of Ni-base alloy NiCr22Co12Mo9 (comparable to Inconel Alloy 617) under thermo-mechanical fatigue (TMF) loading with varying phase angles between strain and temperature and optional dwell times at the maximum temperature was studied. Based on the results, a new lifetime prediction approach is proposed.Strain controlled TMF tests with a temperature range of 100–850°C were conducted in air. Phase angles between temperature and mechanical strain were 0° (in-phase, IP), 180° (out-of-phase, OP), +90° (clockwise diamond, CD) and −90° (counter clockwise diamond, CCD). In some tests, optional dwell times of 2, 5 or 30min were introduced at 850°C. The TMF-lifetime depends significantly on the phase angle and increases in the sequence IP<CCD<OP<CD. While for IP and CCD loading intergranular damage dominates, the damage in OP and CD tests is mainly transgranular. For all phase angles, wedge-type cracks at grain boundary triple points could be found. The orientation of these wedge type cracks is perpendicular to the loading axis for IP and CCD loading and parallel to the loading axis for OP and CD loading. This behaviour could be explained by phase angle dependent grain boundary sliding. Introducing dwell times leads to lower stress amplitudes and higher plastic strain amplitudes compared to tests without dwells. For OP and CD loading the two effects apparently compensate each other and the overall effect of dwell times on the lifetime is small. For IP and CCD loading, the intergranular damage is reduced due to lower tensile stress at high temperatures. That way, introducing dwells increases the IP and CCD lifetime. Based on the findings, a life prediction approach incorporating two separate damage parameters for intergranular and transgranular damage was developed. For loading cycles with arbitrary phase angles and dwells both parameters yield a lifetime. The parameter giving the shorter lifetime is used for lifetime prediction and also indicates the dominant damage mechanism. The approach allows for a satisfying life prediction within a wide range of testing conditions.

Josephson-based full digital bridge for high-accuracy impedance comparisons**Contribution of the National Institute of Standards and Technology, US Department of Commerce, not subject to copyright in the United States.

This paper describes a Josephson-based full digital impedance bridge capable of comparing any two impedances, regardless of type (R-C, R-L, or L-C), over a large frequency range (from 1 kHz to 20 kHz). At the heart of the bridge are two Josephson arbitrary waveform synthesizer systems that offer unprecedented flexibility in high-precision impedance calibration, that is, it can compare impedances with arbitrary ratios and phase angles. Thus this single bridge can fully cover the entire complex plane. In the near future, this type of instrument will considerably simplify the realization and maintenance of the various impedance scales in many National Metrology Institutes around the world.

A Three-Arm Current Comparator Bridge for Impedance Comparisons Over the Complex Plane

We present here the concept of three-arm current comparator impedance bridge, which allows one to perform comparisons among three unlike impedances. Its purpose is the calibration of impedances having arbitrary phase angles against calibrated nearly pure impedances. An analysis of the bridge optimal setting and proper operation is presented. To test the concept, a two-terminal-pair digitally assisted bridge has been realized; preliminary measurements of an air-core inductor and of an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$RC$ </tex-math></inline-formula> network versus decadic resistance and capacitance standards, at kilohertz frequency, have been performed. The bridge measurements are compatible with previous knowledge of the standard values with relative deviations of parts in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-5}$ </tex-math></inline-formula> .

A modified unequal power divider with a complex isolation component for enhanced isolation

ABSTRACTThis article presents a modified unequal power divider with a complex isolation component for enhanced physical and electrical isolation between output ports. In the proposed power divider, the complex isolation component is positioned at an arbitrary phase angle inside a quarter‐wave transmission line. A theoretical analysis is performed to derive the design equations for the proposed unequal power divider. For validating the performance of the proposed unequal power divider, samples of the device operating at the center frequency of 2 GHz were fabricated and tested. The test results are in good agreement with the simulation results. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:322–324, 2015

Comprehensive Compensation Method for Harmonics and Negative Sequence Current in High-speed Railway under Grid Voltage Distortion

As the grid voltage of the V/v power supply system for high-speed railway is distorted, the detection method for harmonic and negative sequence current is complex, and there are errors in the detection result. A method is proposed in order to solve these issues, which is capable of carrying out fast and accurately comprehensive compensation for grid current without the PLL circuit. During the detection process, a group of sine and cosine function with arbitrary initial phase angle is needed, the grid fundamental positive sequence voltage is extracted to participate into the detection of fundamental active power component to obtain the command signal. The calculation process is fast and simple and not affected by the distorted grid voltage. The correctness and feasibility of this method is verified by the result of simulation

Trantanella Wilkinson power divider with additional transmission lines for simple layout

By adding extra transmission lines between 90° transmission lines at an arbitrary phase angle from the input terminal, a modified Trantanella Wilkinson power divider with a simple layout is presented. Design equations for characteristic impedances and complex isolation components are derived from even- and odd-mode analysis. Parallel and series RC circuits are chosen to realise the complex isolation components, and bandwidths are also discussed. For both parallel and series RC circuits, two experimental circuits were fabricated under the same conditions. The experimental results showed good agreement with the results of simulation.

Active stabilization of a Michelson interferometer at an arbitrary phase with subnanometer resolution.

We report on the active stabilization of a Michelson interferometer at an arbitrary phase angle with a precision better than 1° at λ=632.8 nm, which corresponds to a precision in the optical path difference between the two arms of less than 1nm. The stabilization method is ditherless, and the error signal is computed from the spatial shift of the interference pattern of a reference laser, measured in real-time with a CCD array detector. We discuss the usefulness of this method for nanopositioning, optical interferometry, and quantum optical experiments.

Wilkinson Power Divider With Complex Isolation Component and Its Miniaturization

By adding a complex isolation component between two 90 ° transmission lines at an arbitrary phase angle from the input terminal, a small Wilkinson power divider provides physical separation and electrical isolation between two output ports. General design equations for the complex isolation component are derived from even- and odd-mode analysis. Parallel and series RLC circuits are chosen to realize complex isolation components, respectively. Considering the bandwidths of S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">22</sub> , S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> , and S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">32</sub> , inductors in both parallel and series RLC components are omitted to get the widest bandwidths; mathematical proof and design examples are also presented in this paper. A coupled line section with a compensating capacitor is introduced to reduce the circuit size, where characteristic impedances between even and odd mode are different in the coupled line section, and their electrical lengths are also different in inhomogeneous medium. Mathematical equations and simulation examples prove that the compensating capacitor compensates the characteristic impedance difference in the homogeneous medium and the electrical length difference in the inhomogeneous medium. Finally, an experimental circuit shows good agreement with the theoretical simulation.

Profiles of quick access to the orbital station for modern spacecraft

The problems of decreasing the duration of the autonomous flight of a spacecraft (SC) before the docking with an orbital station (OS) are considered in this paper. Modern SCs should be docked with the International Space Station (ISS) with an arbitrary initial phase angle; for this reason, the rendezvous of the Russian Soyuz-TMA spacecraft with the ISS is performed for 2 days. The paper presents to consideration some new flight profiles with essentially smaller duration. The results of modeling the developed rendezvous profiles are presented and solutions to emergency situations are considered.

Process Identification Using Relay Feedback with a Fractional Order Integrator

In this work, a novel relay feedback experiment method is proposed for system identification by connecting a fractional order integrator in front of a basic relay component. With this approach, a linear time invariant process model can be estimated at an arbitrary phase angle in the third or fourth quadrant on the Nyquist curve. Another contribution of this paper is to present a pseudo frequency response concept to generalize the describing function method so as to make it compatible with the frequency response operations. The proposed setup is illustrated through mathematical derivation using the proposed concept. Simulations are provided to verify the effectiveness.