Stability Threshold Research Articles

Nonlinear standing waves in an array of coherently coupled Bose-Einstein condensates

Stationary solitary waves are studied in an array of $M$ linearly-coupled one-dimensional Bose-Einstein condensates (BECs) by means of the Gross-Pitaevskii equation. Solitary wave solutions with the character of overlapping dark solitons, Josephson vortex - antivortex arrays, and arrays of half-dark solitons are constructed for $M>2$ from known solutions for two coupled BECs. Additional solutions resembling vortex dipoles and rarefaction pulses are found numerically. Stability analysis of the solitary waves reveals that overlapping dark solitons can become unstable and susceptible to decay into arrays of Josephson vortices. The Josephson vortex arrays have mixed stability but for all parameters we find at least one stationary solitary wave configuration that is dynamically stable. The different families of nonlinear standing waves bifurcate from one another. In particular we demonstrate that Josephson-vortex arrays bifurcate from dark soliton solutions at instability thresholds. The stability thresholds for dark soliton and Josephson-vortex type solutions are provided, suggesting the feasibility of realization with optical lattice experiments.

Strong Shear-Flow Modulation of Instabilities in Rapid Directional Solidification

We examine the effect of a strong shear flow on morphological instabilities that occur in the directional solidification of a dilute, binary alloy when the interface departs from local thermal equilibrium in a frozen-temperature, one-sided model. In particular, the flow velocity U∞ is much larger than the rate of solidification V and the Schmidt number is arbitrary. In contrast to solidification processes under small or no flow, for which both a cellular and an oscillatory mode of instability appear, the liquid-solid interface under flows of large magnitude is susceptible to a single mode of instability. All experiments on banding occur in the overlap region between these modes under no flow and since these two primary modes coalesce into one time-dependent, spatially-dependent mode, there is no mechanism for the production of bands anymore in the large-flow regime. No experiments have been conducted to date on this rapid solidification under flow and this suggests that such experiments would show no bands. The flow significantly stabilizes and selects higher wavenumbers for the preferred form of instability in comparison to systems involving small or no flow. The introduction of a strong flow provides an effective mechanism to eliminate instabilities at high solidification rates. However, stability thresholds at low solidification rates remain mainly indifferent to the presence of flow.

Double-diffusive Soret convection phenomenon in porous media: effect of Vadasz inertia term

The onset of double-diffusive convection in horizontal porous layers for the thermo-diffusive Soret phenomenon in the case of a generalized Darcy model including inertia term is investigated. Via a linearization principle recently introduced in Rionero (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Natur 28:21–47, 2017) the coincidence between linear and nonlinear (global) stability thresholds of the thermo-solutal conduction solution, is proved. Necessary and sufficient conditions guaranteeing the onset of steady or oscillatory convection in a closed algebraic form are obtained.

Multi-Spectral Water Index (MuWI): A Native 10-m Multi-Spectral Water Index for Accurate Water Mapping on Sentinel-2

Accurate water mapping depends largely on the water index. However, most previously widely-adopted water index methods are developed from 30-m resolution Landsat imagery, with low-albedo commission error (e.g., shadow misclassified as water) and threshold instability being identified as the primary issues. Besides, since the shortwave-infrared (SWIR) spectral band (band 11) on Sentinel-2 is 20 m spatial resolution, current SWIR-included water index methods usually produce water maps at 20 m resolution instead of the highest 10 m resolution of Sentinel-2 bands, which limits the ability of Sentinel-2 to detect surface water at finer scales. This study aims to develop a water index from Sentinel-2 that improves native resolution and accuracy of water mapping at the same time. Support Vector Machine (SVM) is used to exploit the 10-m spectral bands among Sentinel-2 bands of three resolutions (10-m; 20-m; 60-m). The new Multi-Spectral Water Index (MuWI), consisting of the complete version and the revised version (MuWI-C and MuWI-R), is designed as the combination of normalized differences for threshold stability. The proposed method is assessed on coincident Sentinel-2 and sub-meter images covering a variety of water types. When compared to previous water indexes, results show that both versions of MuWI enable to produce native 10-m resolution water maps with higher classification accuracies (p-value < 0.01). Commission and omission errors are also significantly reduced particularly in terms of shadow and sunglint. Consistent accuracy over complex water mapping scenarios is obtained by MuWI due to high threshold stability. Overall, the proposed MuWI method is applicable to accurate water mapping with improved spatial resolution and accuracy, which possibly facilitates water mapping and its related studies and applications on growing Sentinel-2 images.

A frequency domain-based correlation approach for structural assessment and damage identification

Abstract The objective of this work is to demonstrate the feasibility of utilising vibration data to generate a set of spectral domain-based indicators purposed to assess the degradation and reinforcement on structures. These indicators are derived from the complex frequency domain assurance criterion (CFDAC) matrices, corresponding to the altered and pristine state of a monitored structure. The CFDAC operator is similar to the MAC (modal assurance criterion) but formulated in the complex spectral domain. The indicators, referred to as spectral correlation indices (SCI), are aimed to quantify the strength of correlation between an altered state and a reference state so structural alteration can be assessed. In this paper, a numerical and experimental investigation on the feasibility of the proposed approach for structural assessment is presented, by examining the spectral correlation indices in front of multiple alteration scenarios on a square aluminium plate under one-edge-clamped boundary conditions. A comprehensive parametric, sensitivity and stability analysis in front of the FRF synthesis and acquisition parameters is undertaken, both experimentally and numerically, to deepen the knowledge concerning stability properties of the indicators. Once stability thresholds are identified, experimental results are compared to numeric outcomes, allowing conclusions to be drawn regarding the capability and suitability of proposed SCI indicators for structural assessment and damage identification. This research is aimed to serve as a first step towards the development of a fully functional SHM system based on spectral domain indices.

Stability of quasi-equilibrium states and supercritical regimes of thermal vibrational convection of a Williamson fluid in zero gravity conditions

In this paper we investigate a linear stability of quasi-equilibrium states and supercritical regimes of thermal vibrational convection of a Williamson fluid between two rigid parallel plates, maintained at constant different temperatures in zero gravity conditions. Calculations are made for different angles of inclination of the vibration axis relative to the layer. It has been found that, as in the case of a Newtonian fluid, most dangerous are the hydrodynamic monotonic perturbations. Enhancement of viscoplastic properties of a fluid has a destabilizing effect at all angles of inclination of the vibration axis. An increase in the Prandtl number stabilizes the quasi-equilibrium states of the pseudoplastic fluids. In the viscoplastic limit, the critical value of the modified Rayleigh number, which determines the quasi-equilibrium stability threshold, does not depend on the Prandtl number and rheological parameters. The critical value of the perturbation wave number for pseudo- and viscoplastic fluids depends only on the angle of inclination of the vibration axis. The type of the convection excitation and the structure of the supercritical convective flows under longitudinal vibrations have been studied on the basis of full nonlinear equations of thermal vibrational convection. It has been found that the supercritical bifurcation takes place.

Finite element based optimization design for a one-piece zirconia ceramic dental implant under dynamic loading and fatigue life validation

This study presents an optimization procedure for the design of a one-piece zirconia ceramic dental implant that uses finite element simulation with dynamic loads and experimental validation using a fatigue test. The key dimensions of the implant’s shape are the factors for the simulation. Their effect on micromotion is determined using a uniform design of experiment. The Kriging interpolation method and a genetic algorithm (KIGA) are used to optimize the geometric features, in order produce an optimized one-piece dental implant model. The model is fabricated using a three-dimensional slurry printer. The lifetime of the zirconia implant is evaluated using a fatigue test. The numerical result for the objective function shows that the micromotion for the optimized dental implant is 27.58 μm, which is less than the value of 72.62 μm for the original numerical prediction. The safety factor also increases to 1.54 from 1.16. This demonstrates that the optimized dental implant is better than the original design because the degree of micromotion is much lower than the stability threshold. The fatigue test also shows that the safety factor increases to 1.54. Therefore, the proposed procedure produces a dental implant with an optimized shape.

Two AMOC States in Response to Decreasing Greenhouse Gas Concentrations in the Coupled Climate Model MPI-ESM

This study analyzes the response of the Atlantic meridional overturning circulation (AMOC) to different CO2 concentrations and two ice sheet configurations in simulations with the coupled climate model MPI-ESM. With preindustrial (PI) ice sheets, there are two different AMOC states within the studied CO2 range: one state with a strong and deep upper overturning cell at high CO2 concentrations and one state with a weak and shallow upper cell at low CO2 concentrations. Changes in AMOC variability with decreasing CO2 indicate two stability thresholds. The strong state is stable above the first threshold near 217 ppm, and the weak state is stable below the second threshold near 190 ppm. Between the two thresholds, both states are marginally unstable, and the AMOC oscillates between them on millennial time scales. The weak AMOC state is stable when Antarctic Bottom Water becomes dense and salty enough to replace North Atlantic Deep Water (NADW) in the deep North Atlantic and when the density gain over the North Atlantic becomes too weak to sustain continuous NADW formation. With Last Glacial Maximum (LGM) ice sheets, the density gain over the North Atlantic and the northward salt transport are enhanced with respect to the PI ice sheet case. This enables active NADW formation and a strong AMOC for the entire range of studied CO2 concentrations. The AMOC variability indicates that the simulated AMOC is far away from a stability threshold with LGM ice sheets. The nonlinear relationship among AMOC, CO2, and prescribed ice sheets provides an explanation for the large intermodel spread of AMOC states found in previous coupled LGM simulations.

Vulnerability to Flash Floods: A Simplified Structural Model for Masonry Buildings

AbstractUrban and land use planning is conditioned by flood risk analyses and is a great research challenge. While methods are available for quantitative hazard and risk modeling, there is still a major gap related to reliable rational approaches for vulnerability assessment. This is particularly true for assessing vulnerability of buildings to floods. This vulnerability, which is important for economic reasons as well as for the safety of individuals and communities, is usually conceptualized on an empirical basis. Such empirical approaches, however, are plagued by considerable uncertainties, mostly because the damage‐causing mechanisms on the building envelope are poorly represented. In order to advance this area, this paper focuses on the structural vulnerability of traditional masonry buildings in alpine areas exposed to flash floods. A simplified physically based conceptual model which requires a limited amount of input data is proposed. The resistance of a wall impacted by a flash flood is studied in a limit analysis framework, considering different geometric ratios and building configurations. The resulting stability thresholds, expressed in dimensionless form as a function of the water depth, were positively compared with the results provided by numerical finite element models of the investigated geometries. The application of the proposed vulnerability model in risk mitigation strategies provides reliable information, suitable for a first‐level risk assessment on large building stocks.

Synthesis, growth, structural and optical properties of a novel organic third order nonlinear optical crystal: Piperazinediium trichloroacetate

An organic centric compound Piperazinium trichloroacetate (PPTC) was successfully synthesized and grown first time from water solvent by applying slow evaporation technique. The crystal structure and its lattice inter perfection were identified from XRD analysis. The chemical groups of title compound were confirmed by FTIR spectral studies. Lower cutoff and optical band gap were determined from the UV–vis spectral studies using solid crystal sample. Threshold of optical stability has been investigated by using laser damage threshold studies. The thermal resistance was observed by using TG/DTA analysis. Mechanical stability was found from load dependant microhardness study. Dislocation and growth mechanism of PPTC was determined from etching studies. The dielectric permittivity and dielectric loss measured using dielectric study as a function of different frequency and temperature. The electronic polarizability was calculated from dielectric related solid state parameters for the PPTC crystal. The saturable absorption and defocusing phenomena were found from observed Z-scan results which are applicable in optical limiting and switching applications.

On the stability of direct time-domain boundary element methods for elastodynamics

Numerical stability has been a fundamental challenge in direct time-domain boundary element methods (TD-BEM) for elastodynamics. In this paper, an analytical framework for the evaluation of the critical aspect is presented. By casting a convolution integral-based TD-BEM algorithm in the form of a linear multi-step method with a hybrid amplification matrix and the incorporation of some fundamental characteristics of commonly-used transient Green's functions, a rigorous assessment of the problem is shown to be reducible to a standard spectral analysis in matrix theory by which the stability threshold can be clearly defined. Apt to be relevant to the evaluation of other TD-BEMs, the approach is applied to a regularized time-domain direct boundary element method with optional collocation weights and orders of solution variable projections as illustration. By virtue of the proposed formalism and a systematic parametric study, a proper resolution of the critical aspect for some past schemes as well as the versatility of the generalized TD-BEM algorithm as they pertain to the benchmark finite-domain square-bar and the infinite-domain cavity elastodynamic problems are given as examples.

Dynamic coefficients and stability analysis of finite-length journal bearings considering approximate analytical solutions of the Reynolds equation

The paper presents linearized coefficients for finite-length journal bearings based on the HD forces with multiplicative correction polynomials applied to the infinitely short and the infinitely long solutions under the assumption of π-film boundary condition. Based on the linear theory, stability thresholds and their dependence on the length-to-diameter ratio are investigated. Moreover, using the numerical continuation method the change of the generalized Hopf bifurcation which separates regions with subcritical and supercritical Hopf is documented. All results are compared with those of the solution obtained using the finite differences method.

Stability analysis of a couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity using a thermal non-equilibrium model

A nonlinear stability threshold for convection in a couple stress fluid saturating a porous medium with temperature and pressure dependent viscosity using a thermal non-equilibrium model is found to be exactly the same as the linear instability boundary. This optimal result is important because it shows that linear theory has completely captured the physics of the onset of convection. The effects of couple stress fluid parameter (F), temperature and pressure dependent viscosity (Γ), interface heat transfer coefficient (H), Darcy–Brinkman number (D˜a) and porosity modified conductivity ratio (γ) on the onset of convection have been investigated. Asymptotic analysis for both small and large values of interface heat transfer coefficient (H) is also presented. An excellent agreement is found between the exact solutions and asymptotic solutions.

Corrugated Heterojunction Metal-Oxide Thin-Film Transistors with High Electron Mobility via Vertical Interface Manipulation.

A new strategy is reported to achieve high-mobility, low-off-current, and operationally stable solution-processable metal-oxide thin-film transistors (TFTs) using a corrugated heterojunction channel structure. The corrugated heterojunction channel, having alternating thin-indium-tin-zinc-oxide (ITZO)/indium-gallium-zinc-oxide (IGZO) and thick-ITZO/IGZO film regions, enables the accumulated electron concentration to be tuned in the TFT off- and on-states via charge modulation at the vertical regions of the heterojunction. The ITZO/IGZO TFTs with optimized corrugated structure exhibit a maximum field-effect mobility >50 cm2 V-1 s-1 with an on/off current ratio of >108 and good operational stability (threshold voltage shift <1 V for a positive-gate-bias stress of 10 ks, without passivation). To exploit the underlying conduction mechanism of the corrugated heterojunction TFTs, a physical model is implemented by using a variety of chemical, structural, and electrical characterization tools and Technology Computer-Aided Design simulations. The physical model reveals that efficient charge manipulation is possible via the corrugated structure, by inducing an extremely high carrier concentration at the nanoscale vertical channel regions, enabling low off-currents and high on-currents depending on the applied gate bias.

A Modulated Voltage Waveform for Enhancing the Travel Range of Dielectric Elastomer Actuators

This paper presents a method to achieve high deformability levels in dielectric elastomer actuators (DEAs) by applying a modulated voltage waveform. The method relies on supplying the electrostatic energy during the specific phase of the oscillation cycle, resulting in the enhanced travel range at a relatively low driving voltage. We consider a standard sandwich configuration of the DE actuator with neo-Hookean material model and outline an energy-based approach for delineating the underlying principles of the proposed method. A comparison of the deformability levels achieved using the quasi-static, Heaviside step, and the modulated input waveforms is presented. Significant reduction in instability voltages together with a considerable increase in the stable actuation limit is observed in the case of the modulated voltage input. The estimates of the stability thresholds are validated by integrating the equation of motion obtained using Hamilton's principle. The effect of energy dissipation is assessed by considering variations in the quality factor. Further, a qualitative comparison with experimental observations is presented highlighting the practical feasibility of the method. This investigation can find its potential use in the design and development of DEAs subjected to a time-dependent motion.

Landslide state of activity maps by combining multi-temporal A-DInSAR (LAMBDA)

In this paper, a new methodology was developed to automatically update Landslide state of Activity Maps by combining multi-temporal A-DInSAR data (LAMBDA). LAMBDA procedure was tested using ERS-1/2 (1992–2000), Radarsat-1/2 (2003–2009) and COSMO-SkyMed data (2011–2014) over an area of 2199 km2 located in Alps context of Piedmont region (north-western Italy). For the first time, a multidimensional landslide activity matrix was implemented to update the landslide state of activity during the monitored time span. For the definition of the state of activity, the representative velocity of each landslide was divided by the standard deviation of the velocities along the slope of the whole dataset. Thus, a common stability threshold of ±1 was introduced for multi-sensors A-DInSAR data, allowing to distinguish a phenomenon with stable targets (PS-DS) or unstable PS-DS. By combining activity classes estimated during different time spans allows to determine if a phenomenon is active, reactivated, or dormant. Furthermore, an innovative confidence degree assessment was carried out to verify the reliability of the procedure, by considering the measuring points distribution and the variability of the movements for each landslide. The results were validated using the landslide inventory of the study area and in-situ monitoring systems for representative case studies. Thanks to this approach an updated state of activity until 2014 was assigned to 507 landslides out the 1657 which were previously mapped in the study area.

Refined stability thresholds for localized spot patterns for the Brusselator model in

In the singular perturbation limit ε → 0, we analyse the linear stability of multi-spot patterns on a bounded 2-D domain, with Neumann boundary conditions, as well as periodic patterns of spots centred at the lattice points of a Bravais lattice in $\mathbb{R}^2$, for the Brusselator reaction–diffusion model $$ \begin{equation*} v_t = \epsilon^2 \Delta v + \epsilon^2 - v + fu v^2 \,, \qquad \tau u_t = D \Delta u + \frac{1}{\epsilon^2}\left(v - u v^2\right) \,, \end{equation*} $$ where the parameters satisfy 0 &amp;lt; f &amp;lt; 1, τ &amp;gt; 0 and D &amp;gt; 0. A previous leading-order linear stability theory characterizing the onset of spot amplitude instabilities for the parameter regime D = ${\mathcal O}$(ν−1), where ν = −1/log ϵ, based on a rigorous analysis of a non-local eigenvalue problem (NLEP), predicts that zero-eigenvalue crossings are degenerate. To unfold this degeneracy, the conventional leading-order-in-ν NLEP linear stability theory for spot amplitude instabilities is extended to one higher order in the logarithmic gauge ν. For a multi-spot pattern on a finite domain under a certain symmetry condition on the spot configuration, or for a periodic pattern of spots centred at the lattice points of a Bravais lattice in $\mathbb{R}^2$, our extended NLEP theory provides explicit and improved analytical predictions for the critical value of the inhibitor diffusivity D at which a competition instability, due to a zero-eigenvalue crossing, will occur. Finally, when D is below the competition stability threshold, a different extension of conventional NLEP theory is used to determine an explicit scaling law, with anomalous dependence on ϵ, for the Hopf bifurcation threshold value of τ that characterizes temporal oscillations in the spot amplitudes.

Random Error Analysis of MEMS Gyroscope Based on an Improved DAVAR Algorithm

In view that traditional dynamic Allan variance (DAVAR) method is difficult to make a good balance between dynamic tracking capabilities and the confidence of the estimation. And the reason is the use of a rectangular window with the fixed window length to intercept the original signal. So an improved dynamic Allan variance method was proposed. Compared with the traditional Allan variance method, this method can adjust the window length of the rectangular window adaptively. The data in the beginning and terminal interval was extended with the inverted mirror extension method to improve the utilization rate of the interval data. And the sliding kurtosis contribution coefficient and kurtosis were introduced to adjust the length of the rectangular window by sensing the content of shock signal in terminal interval. The method analyzed the window length change factor in different stable conditions and adjusted the rectangular window’s window length according to the kurtosis, sliding kurtosis contribution coefficient. The test results show that the more the kurtosis stability threshold was close to 3, the stronger the dynamic tracking ability of DAVAR would be. But the kurtosis stability threshold was too close to 3, there was a misjudgement in kurtosis analysis of signal stability, resulting in distortion of DAVAR analysis results. When using the improved DAVAR method, the kurtosis stability threshold can be close to 3 to improve the tracking ability and the estimation confidence in stable interval. Therefore, it solved the problem that the dynamic Allan variance tracking ability and confidence level were difficult to take into account, and also solved the problem of misjudgement in the stability analysis of kurtosis.

Rollover threshold investigation of a heavy-duty vehicle during cornering based on multi-body dynamics

The objective of this article is to investigate the rollover threshold of a heavy-duty vehicle during cornering. Based on the multi-body dynamics theory, a high-fidelity model is established, which takes account of the chassis flexibility, the suspension nonlinear characteristics, the tire handling model, and Ackermann steering strategy. Furthermore, by the inverse fast Fourier transform method, a three-dimensional stochastic road in space domain is employed in the model to improve the accuracy. A full-size heavy-duty vehicle test was carried out to validate the model. Based on the validated model, the rollover stability and rollover threshold of the heavy-duty vehicle during cornering are investigated. Lateral acceleration, yaw rate, roll angle, and vehicle torsional deflection in different cornering conditions are analyzed. The rollover threshold is summarized by the response surface methodology for the safe cornering purpose. The result shows the practical meaning of improving transportation safety of heavy-duty vehicles and also provides useful insights for developing the rollover warning system.

Sharp stability results in LTNE rotating anisotropic porous layer

Thermal convection of a fluid filling an anisotropic porous medium, uniformly rotating about a vertical axis, with local thermal non equilibrium, is studied. The linear and nonlinear stability analysis are performed. In particular the coincidence between linear instability and nonlinear (global) stability thresholds is proved.