Small Imperfections Research Articles

Multi-parameter actuation of a neutrally stable shell: a flexible gear-less motor.

We have designed and tested experimentally a morphing structure consisting of a neutrally stable thin cylindrical shell driven by a multi-parameter piezoelectric actuation. The shell is obtained by plastically deforming an initially flat copper disc, so as to induce large isotropic and almost uniform inelastic curvatures. Following the plastic deformation, in a perfectly isotropic system, the shell is theoretically neutrally stable, having a continuous set of stable cylindrical shapes corresponding to the rotation of the axis of maximal curvature. Small imperfections render the actual structure bistable, giving preferred orientations. A three-parameter piezoelectric actuation, exerted through micro-fibre-composite actuators, allows us to add a small perturbation to the plastic inelastic curvature and to control the direction of maximal curvature. This actuation law is designed through a geometrical analogy based on a fully nonlinear inextensible uniform-curvature shell model. We report on the fabrication, identification and experimental testing of a prototype and demonstrate the effectiveness of the piezoelectric actuators in controlling its shape. The resulting motion is an apparent rotation of the shell, controlled by the voltages as in a 'gear-less motor', which is, in reality, a precession of the axis of principal curvature.

Robustness of error-suppressing entangling gates in cavity-coupled transmon qubits

Superconducting transmon qubits comprise one of the most promising platforms for quantum information processing due to their long coherence times and to their scalability into larger qubit networks. However, their weakly anharmonic spectrum leads to spectral crowding in multiqubit systems, making it challenging to implement fast, high-fidelity gates while avoiding leakage errors. To address this challenge, we use a protocol known as SWIPHT [Phys. Rev. B 91, 161405(R) (2015)], which yields smooth, simple microwave pulses designed to suppress leakage without sacrificing gate speed through spectral selectivity. Here, we determine the parameter regimes in which SWIPHT is effective and demonstrate that in these regimes it systematically produces two-qubit gate fidelities for cavity-coupled transmons in the range 99.6%-99.9% with gate times as fast as 23 ns. Our results are obtained from full numerical simulations that include current experimental levels of relaxation and dephasing. These high fidelities persist over a wide range of system parameters that encompass many current experimental setups and are insensitive to small parameter variations and pulse imperfections.

Propagation of phase transformation fronts in pseudoelastic NiTi tubes under uniaxial tension

Under tension a pseudoelastic NiTi tube traces a closed hysteresis with an upper stress plateau associated with transformation from the austenitic to the martensitic phase during loading, and the reverse with a lower stress plateau on unloading. The transformations induce multi-helical localization patterns of higher/lower strain that propagate as the two stress plateaus develop. The experiment is simulated numerically by implementing a recently developed constitutive model for the pseudoelastic behavior of NiTi in a finite element analysis using solid elements. The unstable behavior of the material is modeled by introducing softening that spans the two stress plateaus recorded in the structural response. Localized deformation of nearly 7% initiates from a small thickness imperfection at one end of the model and propagates via a multi-helical front with ten prongs symmetric about a plane passing through the imperfection and the center of the circular tube. The specimen initially unloads homogeneously, but reverts to a single helical band of lower strain, which broadens as it propagates along the length of the tube. A parametric study demonstrates that the shape of localization patterns is influenced by the type and location of the imperfection used to initiate instability, by the imposed boundary conditions, and to some degree by the strength of the softening modulus adopted.

Non-modal stability of Jeffery-Hamel flow

The destabilization of modal perturbations in the classical diverging Jeffery-Hamel (JH) flow has been long-known. The converging JH flow is far less-studied, but it is known that convergence suppresses modal instabilities. We make a parallel-flow approximation following previous studies, to examine its non-modal stability at small convergent and divergent angles and show that non-modal growth is extremely sensitive to the angle of convergence/divergence at high Reynolds numbers. The transient growth of energy is significantly suppressed at high Reynolds numbers as the wall angle is varied from divergence to convergence by just a few hundredths of a degree. This finding is especially relevant for convergent channels, where the flow is stable to linear modal perturbations up to the Reynolds numbers of the order of 105 or larger. In all the cases, streamwise-aligned rolls (which are a characteristic of the lift-up mechanism) are the initial perturbations that display the largest energy growth. The spanwise separation between the rolls decreases significantly with channel convergence. Our findings indicate that extremely small imperfections in the wall alignment in channel flows can drastically affect the experimental measurements of algebraic growth of the disturbance kinetic energy, as minute amounts of wall convergence can strongly reduce the maximum transient growth.

Accurate and efficient a posteriori account of geometrical imperfections in Koiter finite element analysis

SummaryThe Koiter method recovers the equilibrium path of an elastic structure using a reduced model, obtained by means of a quadratic asymptotic expansion of the finite element model. Its main feature is the possibility of efficiently performing sensitivity analysis by including a posteriori the effects of the imperfections in the reduced nonlinear equations. The state‐of‐art treatment of geometrical imperfections is accurate only for small imperfection amplitudes and linear pre‐critical behaviour. This work enlarges the validity of the method to a wider range of practical problems through a new approach, which accurately takes into account the imperfection without losing the benefits of the a posteriori treatment. A mixed solid‐shell finite element is used to build the discrete model. A large number of numerical tests, regarding nonlinear buckling problems, modal interaction, unstable post‐critical and imperfection sensitive structures, validates the proposal. Copyright © 2017 John Wiley & Sons, Ltd.

Global dynamics of imperfect axially forced microbeams

This paper, for the first time, analyses the size-dependent global dynamics of imperfect axially forced microbeams and shows that how a small initial imperfection (due to improper manufacturing of microbeams) can substantially change the size-dependent global dynamical behaviour of the microsystem; moreover, it investigates the effect of small size of the microbeam on the appearance and vanishing of different chaotic and quasiperiodic motions. More specifically, the continuous expressions for the size-dependent potential energy as well as kinetic energy of the microsystem are constructed and dynamically balanced via an energy method. A transformation to a reduced-order model is performed via a weighted-residual method. The bifurcation diagrams of Poincaré maps are constructed by means of direct time-integrating the reduced-order model for the imperfect microsystem. Poincaré sections, phase-plane diagrams, time histories, and fast Fourier transforms are also plotted for some cases in order to shed light on the microsystem size-dependent global dynamics.

Parametric vibrations of imperfect Timoshenko microbeams

This paper examines the size-dependent nonlinear parametric vibrations of imperfect Timoshenko microbeams subject to a time-dependent axial load. Taking into account rotary inertia and shear deformation, the modified couple stress theory is employed so as to derive a continuous expression for the elastic potential energy of the system; the geometric imperfection is modelled via a small initial deflection in the transverse direction. The continuous model of the system is obtained via an energy balance method. A reduced-order model is obtained by means of a weighted residual method together with an assumed-mode technique. The double-dimensionalised form of the reduced-order model is solved by means of different numerical techniques and stability is analysed. It is shown that even small geometric imperfections may change the parametric response of the system not only quantitatively, but also qualitatively.

Observation of persistent photoconductivity in Ni-doped MoS2

In this study, Ni-doped MoS2 was grown by chemical vapor transportation. Photoconductivity results reveal that Ni-doped MoS2 has an obvious doping level of 1.2 eV and an electrical conductivity of σ ≅ 9.92 × 10−7 S cm−1 at room temperature, which is lower than that of undoped MoS2 (σ ≅ 7.913 × 10−5 S cm−1) owing to the impurity state caused by Ni atoms. Hall effect measurement results indicate that Ni-doped MoS2 sample is of the n-type and has a higher resistance and a lower mobility than undoped MoS2. We further fabricated undoped and Ni-doped MoS2 photodetectors to understand the operation characteristics of MoS2-based photodetectors. Persistent photoconductivity shows that both rise and fall times decreased from 0.33/0.68 to 0.14/0.43 s as Ni atoms were doped in MoS2 PDs. This work shows that Ni atoms could cause small lattice imperfections to form trap states leading to high resistance, low mobility, small activation energy and short decay time. Therefore, doping Ni atoms in MoS2 is beneficial for the application of photodetectors.

Nonlinear Vibrations of Fluid-Filled Cylindrical Shells with Initial Imperfections

Theoretical approaches to studying the free vibrations of imperfect (with small geometrical imperfections) orthotropic cylindrical shells filled with a fluid are proposed. A geometrically nonlinear problem is solved. The emphasis is on the interaction and energy exchange between the “conjugate” flexural modes in the dynamic radial deflection. The effect of initial deflections on the interaction of the initial deflection modes is analyzed

Publisher's Note

This paper, for the first time, analyses the size-dependent global dynamics of imperfect axially forced microbeams and shows that how a small initial imperfection (due to improper manufacturing of microbeams) can substantially change the size-dependent global dynamical behaviour of the microsystem; moreover, it investigates the effect of small size of the microbeam on the appearance and vanishing different chaotic and quasiperiodic motions. More specifically, the continuous expressions for the size-dependent potential energy as well as kinetic energy of the microsystem are constructed and dynamically balanced via an energy method. A transformation to a reduced-order model is performed via a weighted-residual method. The bifurcation diagrams of Poincare maps are constructed by means of direct time-integrating the reduced-order model for the imperfect microsystem. Poincare sections, phase-plane diagrams, time histories, and fast Fourier transforms are also plotted for some cases in order to shed light on the size-dependent microsystem global dynamics.

Optomechanical damping of a nanomembrane inside an optical ring cavity

We experimentally and theoretically investigate mechanical nanooscillators coupled to the light in an optical ring resonator made of dielectric mirrors. We identify an optomechanical damping mechanism that is fundamentally different to the well known cooling in standing wave cavities. While in a standing wave cavity the mechanical oscillation shifts the resonance frequency of the cavity, in a ring resonator the frequency does not change. Instead the position of the nodes is shifted with the mechanical excursion. We derive the damping rates and test the results experimentally with a silicon-nitride nanomembrane. It turns out that scattering from small imperfections of the dielectric mirror coatings has to be taken into account to explain the value of the measured damping rate. We extend our theoretical model and consider a second reflector in the cavity that captures the effects of mirror back scattering. This model can be used to also describe the situation of two membranes that both interact with the cavity fields. This may be interesting for future work on synchronization of distant oscillators that are coupled by intracavity light fields.

The Pelayo Family Plays Roulette: The Prequel

The case presents data from 70,340 spins of four roulette wheels: three of which are real (imperfect) and one of which is simulated (perfect). The challenge posed is to identify which of the four is the simulated wheel. After weeks spent recording spin results at their local casino, the members of the Pelayo family think they have identified three imperfect wheels. Before they start betting, they want to be certain that the three wheels they identified as imperfect are easily distinguishable from a theoretically perfect wheel.This case has been used successfully in Darden's MBA elective about data analysis. That course introduced pivot tables and the chi-squared goodness-of-fit test using the case “The Roulette Wheel” (UVA-QA-0718). Discussion of the “The Pelayo Family Plays Roulette” probably will not require an entire class period. One option would be to hand out this case during the discussion of “The Roulette Wheel” as something of a follow-on. Excerpt UVA-QA-0847 Jun. 20, 2016 The Pelayo Family Plays Roulette: The Prequel Dear Student, For six weeks, my extended family (six people total) spent five to six hours a night at the Casino Gran Madrid (Figure 1) recording the outcomes of thousands of spins of roulette wheels. Each morning, I entered these data into my personal computer. I believe there is no such thing as a perfect wheel (Figure 2), and that it takes lots of observations to find the small imperfections that must exist in every wheel. We believe we have found three wheels with imperfections large enough to be discovered, and I would like to ask you to use your data analysis skills to help make sure. . . .

Coalescence of resonances in dissipationless resonant tunneling structures and [formula omitted]-symmetry breaking

We study the phenomenon of spontaneous symmetry breaking in dissipationless resonant tunneling structures (RTS). To describe the quantum transport in this system we apply both the nonequilibrium Green function formalism based on a tight-binding model and a numerical solution of the Schrödinger equation within the envelope wavefunction formalism. An auxiliary non-Hermitian Hamiltonian is introduced. Its eigenvalues determine exactly the transparency peak positions. In spatially symmetric RTS the corresponding auxiliary non-Hermitian Hamiltonian becomes PT-symmetric and possesses real eigenvalues, which can coalesce at exceptional points of this Hamiltonian. A coalescence of the auxiliary non-Hermitian Hamiltonian eigenvalues means a coalescence of perfect resonances in RTS, which can be accompanied be symmetry breaking of the electron wavefunction probability distribution (at a given direction of the particle flow). Also we construct a classification of different types of the coalescence of resonances in terms of the catastrophe theory and investigate the impact of small imperfections (scattering and asymmetry) on these phenomena.

Cointegration and spatial price transmission among wheat and wheat-flour markets in Afghanistan

ABSTRACTThis article examines cointegration and spatial price transmission among Afghan wheat and flour markets as well as their linkages with those of supplier countries and global markets. Unit root tests, consistent momentum threshold autoregressive (M-TAR) models and vector error correction models (asymmetric and symmetric) are employed to achieve research objectives. The results suggest that provincial wheat and flour markets may have a long-run relationship with principal market of Kabul. Afghan wheat and flour markets may also be cointegrated with their respective global, Kazakh and Pakistani markets. While provincial wheat markets might adjust to divergence from their long-run equilibrium with Kabul wheat market, some of the provincial flour markets may not respond to deviation from their long-run equilibrium with Kabul flour market. The speed of adjustment towards the long-run Afghan–Pakistani and Afghan–Kazakh equilibrium may be faster for Afghan flour than wheat markets. The equilibrium adjustment coefficients are generally small and market imperfections may exist, however. A shock in Kabul wheat and flour markets may have long-lasting effect on the respective provincial markets whereas a shock in global wheat and Pakistani, and Kazakh wheat and flour markets might have transitory effect on the corresponding Afghan markets.

Bifurcation analysis of laminar isothermal planar opposed-jet flow

For a fixed geometric configuration, hydrodynamic instabilities and bifurcation processes of laminar isothermal planar opposed-jet flows with symmetric and slightly asymmetric inlet boundary conditions are investigated numerically using a high-resolution approach based on spectral element method. In current configuration, when inlet boundary conditions are symmetric, in the range of the Reynolds number considered (Re ≤ 200), multiple new symmetry-breaking bifurcations are observed and four new flow patterns are identified. Their hydrodynamic characteristics are analyzed, in particular their symmetries. In addition, the case that inlet boundary conditions are slightly asymmetric is investigated. It is found that bifurcation processes are extremely sensitive to this small symmetry-breaking imperfection and much different from those in the symmetric case. Furthermore, model equations are constructed by symmetry consideration to explain the numerical results based on hydrodynamic equations.

Buckling delamination induced microchannel: Flow regulation in microfluidic devices

The buckling delamination induced microchannel is employed to regulate fluid flow as a microvalve which can be utilized in microfluidic devices. This microvalve consists of a soft substrate and a stiff thin film, between which there is a pre-set small imperfection. Two critical strain values, namely, on-off strain and failure strain, have been proposed to determine the working strain interval using analytical predictions. Within this interval, the cross-sectional area of the microchannel can be controlled and predicted by different compressive strains of the film/substrate system. The fluid flow rate within this microchannel can be then estimated by both analytical and numerical simulations and adjusted to satisfy different values by alternating the compressive strain. In addition, a demonstrative experiment has been taken to verify the feasibility of this approach. This flexible microvalve has potential in the application where the use of traditional rigid microvalves is improper in flexible microfluidic devices. The method and approach of this paper can provide a general guide for flow rate control in microfluidic devices.

Design Considerations for Single-Mode Microring Lasers Using Parity-Time-Symmetry

Coupled microring arrangements with balanced gain and loss, also known as parity-time symmetric systems, are investigated both analytically and experimentally. In these configurations, stable single-mode lasing can be achieved at pump powers well above threshold. This self-adaptive mode management technique is broadband and robust to small fabrication imperfections. The results presented in this paper provide a new avenue in designing mode selective chip-scale in-plane semiconductor lasers by utilizing the complex dynamics of coupled gain/loss cavities.

Design Considerations for Single-Mode Microring Lasers Using Parity–Time Symmetry

Coupled microring arrangements with balanced gain and loss, also known as parity-time symmetric systems, are investigated both analytically and experimentally. In these configurations, stable single-mode lasing can be achieved at pump powers well above threshold. This self-adaptive mode management technique is broadband and robust to small fabrication imperfections. The results presented in this paper provide a new avenue in designing mode selective chip-scale in-plane semiconductor lasers by utilizing the complex dynamics of coupled gain/loss cavities.

Focusing properties of a spherical perfect lens with eccentric deformations

A spherical perfect lens made of a shell of negative refractive index material is known not only for its subwavelength resolution of images but also for the magnification of the near-field image due to its curved geometry. We investigate the effects on the image resolution arising from geometric deformations of the spherical perfect lens, whereby an eccentricity in the spherical shell is introduced. Using a first-order perturbative method valid for small deformations in the near-field (quasi-static) limit, we find that small deformations (∼1% of the inner radius of the shell) appear to affect the strength of the multipoles in the image by only few percent and do not have any drastic effects. Our results indicate that near-field imaging can be robust against small geometric imperfections in these imaging devices, which is expected to be highly encouraging to nanoscale/microscale design in optical engineering.

Optical and Transport Properties of Ni-MoS2

In this paper, MoS2 and Ni-MoS2 crystal layers were fabricated by the chemical vapor transport method with iodine as the transport agent. Two direct band edge transitions of excitons at 1.9 and 2.1 eV were observed successfully for both MoS2 and Ni-MoS2 samples using temperature-dependent optical reflectance (R) measurement. Hall effect measurements were carried out to analyze the transport behavior of carriers in MoS2 and Ni-MoS2, which indicate that the Ni-MoS2 sample is n-type and has a higher resistance and lower mobility than the MoS2 sample has. A photoconductivity spectrum was performed which shows an additional Ni doping level existing at 1.2 eV and a higher photocurrent generating only for Ni-MoS2. The differences between MoS2 and Ni-MoS2 could be attributed to the effect of Ni atoms causing small lattice imperfections to form trap states around 1.2 eV. The temperature-dependent conductivity shows the presence of two shallow levels with activation energies (84 and 6.7 meV in MoS2; 57 and 6.5 meV in Ni-MoS2). Therefore, the Ni doping level leads to high resistance, low mobility and small activation energies. A series of experimental results could provide useful guidance for the fabrication of optoelectronic devices using MoS2 structures.