Time-varying Mass Research Articles

Revealing pMDI Spray Initial Conditions: Flashing, Atomisation and the Effect of Ethanol.

Sprays from pressurised metered-dose inhalers are produced by a transient discharge of a multiphase mixture. Small length and short time scales have made the investigation of the governing processes difficult. Consequently, a deep understanding of the physical processes that govern atomisation and drug particle formation has been elusive. X-ray phase contrast imaging and quantitative radiography were used to reveal the internal flow structure and measure the time-variant nozzle exit mass density of 50µL metered sprays of HFA134a, with and without ethanol cosolvent. Internal flow patterns were imaged at a magnification of 194pixels/mm and 7759 frames per second with 150ps temporal resolution. Spray projected mass was measured with temporal resolution of 1ms and spatial resolution 6µm × 5µm. The flow upstream of the nozzle comprised large volumes of vapour at all times throughout the injection. The inclusion of ethanol prevented bubble coalescence, altering the internal flow structure and discharge. Radiography measurements confirmed that the nozzle exit area is dominantly occupied by vapour, with a peak liquid volume fraction of 13%. Vapour generation in pMDIs occurs upstream of the sump, and the dominant volume component in the nozzle exit orifice is vapour at all times in the injection. The flow in ethanol-containing pMDIs has a bubbly structure resulting in a comparatively stable discharge, whereas the binary structure of propellant-only flows results in unsteady discharge and the production of unrespirable liquid masses.

Operational modal analysis for linear time-varying continuous dynamic structure based on LMPCA

Based on the theory of time-frozen, this paper proposes a novel operational modal analysis (OMA) for linear time-varying structure using limited memory principal component analysis (LMPCA). Compared with modal coordinate de- composition of non-stationary response signals for linear time-varying continuous beam structure, it is found that PCA can be decomposed to extract time-varying instantaneous modal parameters, which reveal structure characteristics in limited memory window length L. Numerical simulations results on a cantilever beam with slow time-varying mass are presented to verify the TV instantaneous natural frequencies and modal shapes identification capability of the LMPCA.

The ALMA detection of CO rotational line emission in AGB stars in the Large Magellanic Cloud

Context: Low- and intermediate-mass stars lose most of their stellar mass at the end of their lives on the asymptotic giant branch (AGB). Determining gas and dust mass-loss rates (MLRs) is important in quantifying the contribution of evolved stars to the enrichment of the interstellar medium. Aims: Attempt to, for the first time, spectrally resolve CO thermal line emission in a small sample of AGB stars in the Large Magellanic Cloud. Methods: ALMA was used to observe 2 OH/IR stars and 4 carbon stars in the LMC in the CO J= 2-1 line. Results: We present the first measurement of expansion velocities in extragalactic carbon stars. All four C-stars are detected and wind expansion velocities and stellar velocities are directly measured. Mass-loss rates are derived from modelling the spectral energy distribution and Spitzer/IRS spectrum with the DUSTY code. Gas-to-dust ratios are derived that make the predicted velocities agree with the observed ones. The expansion velocities and MLRs are compared to a Galactic sample of well-studied relatively low MLRs stars supplemented with "extreme" C-stars that have properties more similar to the LMC targets. Gas MLRs derived from a simple formula are significantly smaller than derived from the dust modelling, indicating an order of magnitude underestimate of the estimated CO abundance, time-variable mass loss, or that the CO intensities in LMC stars are lower than predicted by the formula derived for Galactic objects. This could be related to a stronger interstellar radiation field in the LMC. Conclusions: Although the LMC sample is small and the comparison to Galactic stars is non-trivial because of uncertainties in their distances it appears that for C stars the wind expansion velocities in the LMC are lower than in the solar neighbourhood, while the MLRs appear similar. This is in agreement with dynamical dust-driven wind models.

The generalized harmonic potential theorem in the presence of a time-varying magnetic field.

We investigate the evolution of the many-body wave function of a quantum system with time-varying effective mass, confined by a harmonic potential with time-varying frequency in the presence of a uniform time-varying magnetic field, and perturbed by a time-dependent uniform electric field. It is found that the wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. In other words, we generalize the harmonic potential theorem to the case when the effective mass, harmonic potential, and the external uniform magnetic field with arbitrary orientation are all time-varying. The results reduce to various special cases obtained in the literature, particulary to that of the harmonic potential theorem wave function when the effective mass and frequency are both static and the external magnetic field is absent.

Adsorption-Induced Surface Effects on the Dynamical Characteristics of Micromechanical Resonant Sensors for In Situ Real-Time Detection

By incorporating modified Langmuir kinetic model, a novel slowly time-varying dynamical model of in situ micromechanical sensors is proposed to real-time monitor atomic or molecular adsorptions on the solid surface in a viscous fluid. First, Langmuir kinetic model is modified by the introduction of time-varying concentrations of analytes. Second, van der Waals (vdW), Coulomb, and biomolecular interactions for uncharged adsorbates, charged ones, and double-stranded DNAs (dsDNAs) are adopted, respectively, to develop the governing equation of time-varying vibrational systems with Hamilton's principle. It can be found that the adsorption-induced surface effects are incorporated into the dynamical equation of sensors due to real-time adsorptions. Third, the dynamical model is validated with the theoretical results of O atoms on Si (100) surface and the experimental data of dsDNAs interactions. The results show that the dynamical behavior is adsorption-induced slowly time-varying vibration due to the time-varying effective mass, stiffness, damping, and equilibrium positions of the microcantilevers. Moreover, comparing the modified Langmuir kinetic model with the unmodified model, the amplitude and phase hysteresis phenomena of frequency shift for resonant sensors can result in huge detection errors. In addition, the fluid effect can dramatically degrade the sensitivity and precision of real-time detection by several orders, which can provide a theoretical foundation to improve the detection sensitivity by reducing the fluid effect. The work demonstrates that it is essential to develop a time-varying dynamical model for in situ real-time label-free detection technique.

An insight into the behaviour of oscillators with a periodically piecewise-defined time-varying mass

Free vibrations of a linear, single-degree-of-freedom oscillator with a periodic piecewise-defined time-varying mass are studied. Two different cases of this variation are investigated: first, the mass increases and then decreases linearly in time, i.e. it changes triangularly, and the second, when the mass changes trapezoidically, which, unlike the previous case, includes the period when it remains constant. Exact solutions for motion are obtained analytically directly from the equations of motion, and the criteria of stability are derived and used to plot stability charts for different system parameters. In addition, the transformed equation of motion is utilized in conjunction with harmonic balancing to derive approximate analytical expressions for the boundaries of the first and second instability region.

ISSM-SESAW v1.0: mesh-based computation of gravitationally consistent sea-level and geodetic signatures caused by cryosphere and climate driven mass change

Abstract. A classical Green's function approach for computing gravitationally consistent sea-level variations associated with mass redistribution on the earth's surface employed in contemporary sea-level models naturally suits the spectral methods for numerical evaluation. The capability of these methods to resolve high wave number features such as small glaciers is limited by the need for large numbers of pixels and high-degree (associated Legendre) series truncation. Incorporating a spectral model into (components of) earth system models that generally operate on a mesh system also requires repetitive forward and inverse transforms. In order to overcome these limitations, we present a method that functions efficiently on an unstructured mesh, thus capturing the physics operating at kilometer scale yet capable of simulating geophysical observables that are inherently of global scale with minimal computational cost. The goal of the current version of this model is to provide high-resolution solid-earth, gravitational, sea-level and rotational responses for earth system models operating in the domain of the earth's outer fluid envelope on timescales less than about 1 century when viscous effects can largely be ignored over most of the globe. The model has numerous important geophysical applications. For example, we compute time-varying computations of global geodetic and sea-level signatures associated with recent ice-sheet changes that are derived from space gravimetry observations. We also demonstrate the capability of our model to simultaneously resolve kilometer-scale sources of the earth's time-varying surface mass transport, derived from high-resolution modeling of polar ice sheets, and predict the corresponding local and global geodetic signatures.

Time-variable gravity fields derived from GPS tracking of Swarm

Abstract Since 2002 Gravity Recovery and Climate Experiment (GRACE) provides monthly gravity fields from K-band ranging (KBR) between two GRACE satellites. These KBR gravity monthlies have enabled the global observation of time-varying Earth mass signal at a regional scale (about 400 km resolution). Apart from KBR, monthly gravity solutions can be computed from onboard GPS data. The newly reprocessed GPS monthlies from 13 yr of GRACE data are shown to yield correct time-variable gravity signal (seasonality, trends, interannual variations) at a spatial resolution of 1300 km (harmonic degree 15). We show that GPS fields from new Swarm mission are of similar quality as GRACE GPS monthlies. Thus, Swarm GPS monthlies represent new and independent source of information on time-variable gravity, and, although with lower resolution and accuracy, they can be used for its monitoring, particularly if GRACE KBR/GPS data become unavailable before GRACE Follow-On is launched (2017 August).

Quantization of time-dependent non-central singular potential systems in three dimensions by using the Nikiforov-Uvarov method

Quantum solutions of a time-dependent Hamiltonian for the motion of a time-varying mass subjected to time-dependent singular potentials in three dimensions are investigated. A time-dependent inverse quadratic potential and a Coulomb-like potential are considered as the components of the singular potential of the system. Because the Hamiltonian is a function of time, special techniques for deriving quantum solutions of the system are necessary. A quadratic invariant operator is introduced, and its eigenstates are derived using the Nikiforov-Uvarov method together with a unitary transformation method. The Nikiforov-Uvarov method enables us to solve the eigenvalue equations of the invariant operator, which are second-order linear diffierential equations, by reducing the original equation to a hypergeometric type. According to the invariant operator theory, the wave functions of the system are represented in terms of the eigenstates obtained in such a way. The difference of the wave functions from the eigenstates of the invariant operator is that the wave functions have time-dependent phases while the eigenstates do not. By determining the phases of the wave functions via the help of the Schr¨odinger equation, we identify the full wave functions of the system and address their physical implications.

A Model Reference Adaptive Control/PID Compound Scheme on Disturbance Rejection for an Aerial Inertially Stabilized Platform

This paper describes a method to suppress the effect of nonlinear and time-varying mass unbalance torque disturbance on the dynamic performances of an aerial inertially stabilized platform (ISP). To improve the tracking accuracy and robustness of the ISP, a compound control scheme based on both of model reference adaptive control (MRAC) and PID control methods is proposed. The dynamic model is first developed which reveals the unbalance torque disturbance with the characteristic of being nonlinear and time-varying. Then, the MRAC/PID compound controller is designed, in which the PID parameters are adaptively adjusted based on the output errors between the reference model and the actual system. In this way, the position errors derived from the prominent unbalance torque disturbance are corrected in real time so that the tracking accuracy is improved. To verify the method, the simulations and experiments are, respectively, carried out. The results show that the compound scheme has good ability in mass unbalance disturbance rejection, by which the system obtains higher stability accuracy compared with the PID method.

Damage Detection Using Measurement Response Data of Beam Structure Subject to a Moving Mass

THE MOVING LOAD PROBLEM IS DIVIDED INTO TWO TYPICAL TYPES: MOVING FORCE AND MOVING MASS. THE MOVING MASS PROBLEM INCLUDES THE TIME-VARYING MASS EFFECT. THIS WORK CONSIDERS DAMAGE DETECTION OF THE BEAM STRUCTURE SUBJECT TO A MOVING LOAD INCLUDING THE INERTIA EFFECT BASED ON THE ONLY MEASUREMENT DATA FROM STRAIN GAGES AND ACCELEROMETERS WITHOUT ANY BASELINE DATA. THIS EXPERIMENT COMPARES THE FEASIBILITY OF DAMAGE DETECTION METHODS DEPENDING ON THE MEASUREMENT SENSORS OF STRAIN GAGES AND ACCELEROMETERS. THE MEASUREMENT DATA ARE TRANSFORMED TO THE PROPER ORTHOGONAL MODES (POMS) IN THE TIME DOMAIN AND THE FREQUENCY DOMAIN, RESPECTIVELY. THE MAGNITUDE OF THE MOVING MASS AND ITS VELOCITY ARE ALSO EVALUATED AS TEST VARIABLES IN THIS EXPERIMENT. IT IS SHOWN IN THE BEAM TESTS THAT THE MEASURED STRAIN DATA CAN BE MORE EXPLICITLY UTILIZED IN DETECTING DAMAGE THAN THE ACCELERATION DATA, AND THE MASS MAGNITUDE AND ITS VELOCITY AFFECT THE FEASIBILITY OF DAMAGE DETECTION.

HIERARCHICAL GRAVITATIONAL FRAGMENTATION. I. COLLAPSING CORES WITHIN COLLAPSING CLOUDS

We investigate the Hierarchical Gravitational Fragmentation scenario through numerical simulations of the prestellar stages of the collapse of a marginally gravitationally isothermal sphere immersed in a strongly gravitationally unstable, uniform background medium. The core developes a Bonnor-Ebert (BE)-like density profile, while at the time of singularity (the protostar) formation the envelope approaches a singular-isothermal-sphere (SIS)-like $r^-2$ density profile. However, these structures are never hydrostatic. In this case, the central flat region is characterized by an infall speed, while the envelope is characterized by a uniform speed. This implies that the hydrostatic SIS initial condition leading to Shu's classical inside-out solution is not expected to occur, and therefore neither should the inside-out solution. Instead, the solution collapses from the outside-in, naturally explaining the observation of extended infall velocities. The core, defined by the radius at which it merges with the background, has a time-variable mass, and evolves along the locus of the ensemble of observed prestellar cores in a plot of $M/M_{BE}$ vs. $M$, where $M$ is the core's mass and $M_{BE}$ is the critical Bonnor-Ebert mass, spanning the range from the to the unstable regimes, even though it is collapsing at all times. We conclude that the presence of an background allows a core to evolve dynamically from the time when it first appears, even when it resembles a pressure-confined, stable BE-sphere. The core can be thought of as a ram-pressure confined BE-sphere, with an increasing mass due to the accretion from the background.

Parametric excitations and lock-in of flexible hydrofoils in two-phase flows

This work introduces a reduced-order method to study the parametric excitations and lock-in of flexible hydrofoils caused by unsteady two-phase (cavitating) flow. The reduced-order method is based on a 1-DOF structural model coupled with a van der Pol wake oscillator with empirically derived relations for the variation in lift, cavity-length, and cavity-shedding frequency as a function of a non-dimensional cavitation parameter. The results are compared with several available data from both numerical simulations and experimental measurements. The frequency content of both the predicted and measured vibrations suggested that, in addition to the primary cavity-shedding frequency and the hydrofoil natural frequencies, unsteady two-phase flows may excite additional modulated frequencies due to time-varying fluid-added mass effects. The results show that these frequency modulations might cause the flexible hydrofoil to undergo higher-order resonances, as well as parametric resonances. While the maximum deformations for the primary and higher-order resonances were observed to damp out, parametric resonances might persist even with realistic fluid damping coefficients (4–12%). It was observed that with higher effective foil flexibility, the cavity-shedding frequencies may be significantly modified from the rigid foil trends, and may instead lock-in with the system natural frequencies.

Characterization of particulate matters and total VOC emissions from a binder jetting 3D printer

Binder jetting 3D printing is a popular type of additive manufacturing and a powerful tool for creating parts and prototypes. Due to continuous movement of dry powders inside printer chambers and injection of resin-like binder fluid during printing, binder jetting 3D printers are a potential emission source of fine particulate matters (PM) and volatile organic compounds (VOCs). In this study, real-time measurements of total VOC (TVOCs) and aerosol (10 nm–10 μm) during a 2-h continuous operation of a binder jetting printer were incorporated into a time-varying mass balance model to obtain the emission rates. The particle sizes between 205 and 407 nm had the highest emission rates by count. Time weighted average PM2.5 and PM10 and TVOC over a 24-h period all exceeded the USEPA ambient air quality standards. Continuous operation of the 3D printer led to a PM2.5 level 10 times greater than the standard (344 vs 35 μg/m3) and a PM10 level 3 times higher than the standard (474 vs 150 μg/m3). TVOC concentrations with a maximum value of 1725 μg/m3 exceeded upper limit concentrations recommended by the Environment Institute of European Commission, and USGBC-LEED. Ultrafine particles emitted from the binder jetting 3D printer were 104–105 times lower than those from typical fused deposition modeling (FDM) type of 3D printers using polylactic acid (PLA), but production of particles larger than 200 nm was significantly higher. The results suggest installing binder jetting 3D printers in an enclosure with proper ventilation for reducing the health risks.

Response Sensitivity and the Assessment of Nonlinear Vibration Using a Nonlinear Lateral–Torsional Coupling Model of Vehicle Transmission System

The eigensensitivity analysis does not meet the increasing industrial requirements of the dynamic performance of a vehicle transmission system. To reduce vibration, it is necessary to include response sensitivity in the guideline in the design stage. In this study, we developed a nonlinear lateral–torsional coupling spur gear system model considering the effect of time-varying mesh stiffness, clearance, mass eccentricity, and transmission error. Then the dynamic response sensitivity to system parameters was systematically analyzed by taking the shaft torsional stiffness, for example. The equation of response sensitivity was deduced by a direct method (DM) based on the fitting of the clearance function curve using a polynomial function. In allusion to the characteristic of the aperiodicity of response sensitivity curves of the nonlinear system in the time domain, a novel assessment method—differential sensitivity based on the root mean square (RMS) of response is proposed. This method provides statistical results in a certain range, thus avoiding the inaccuracy of the partial amplitude. The vibrational energy of modified system (MS) can also be estimated. All the abovementioned characteristics make it possible to provide the theoretical support for dynamic modification, model updating, and optimal design.

水力压裂过程中水管理模拟-最优化模型

A combined simulation-optimization model was developed to minimize the freshwater footprint at multi-well hydraulic fracturing sites. The model seeks to reduce freshwater use by blending it with brackish groundwater and recovered water. Time-varying water quality and quantity mass balance expressions and drawdown calculations using the Theis solution along with the superposition principle were embedded into the optimization model and solved using genetic algorithms. The model was parameterized for representative conditions in the Permian Basin oil and gas play region with the Dockum Formation serving as the brackish water source (Texas, USA). The results indicate that freshwater use can be reduced by 25–30 % by blending. Recovered water accounted for 2–3 % of the total blend or 10–15 % of total water recovered on-site. The concentration requirements of sulfate and magnesium limited blending. The evaporation in the frac pit constrained the amount blended during summer, while well yield of the brackish (Dockum) aquifer constrained the blending during winter. The Edwards-Trinity aquifer provided the best quality water compared to the Ogallala and Pecos Valley aquifers. However, the aquifer has low diffusivity causing the drawdown impacts to be felt over large areas. Speciation calculations carried out using PHREEQC indicated that precipitation of barium and strontium minerals is unlikely in the blended water. Conversely, the potential for precipitation of iron minerals is high. The developed simulation-optimization modeling framework is flexible and easily adapted for water management at other fracturing sites.

Improved methods for observing Earth's time variable mass distribution with GRACE using spherical cap mascons

AbstractWe discuss several classes of improvements to gravity solutions from the Gravity Recovery and Climate Experiment (GRACE) mission. These include both improvements in background geophysical models and orbital parameterization leading to the unconstrained spherical harmonic solution JPL RL05, and an alternate JPL RL05M mass concentration (mascon) solution benefitting from those same improvements but derived in surface spherical cap mascons. The mascon basis functions allow for convenient application of a priori information derived from near‐global geophysical models to prevent striping in the solutions. The resulting mass flux solutions are shown to suffer less from leakage errors than harmonic solutions, and do not necessitate empirical filters to remove north‐south stripes, lowering the dependence on using scale factors (the global mean scale factor decreases by 0.17) to gain accurate mass estimates. Ocean bottom pressure (OBP) time series derived from the mascon solutions are shown to have greater correlation with in situ data than do spherical harmonic solutions (increase in correlation coefficient of 0.08 globally), particularly in low‐latitude regions with small signal power (increase in correlation coefficient of 0.35 regionally), in addition to reducing the error RMS with respect to the in situ data (reduction of 0.37 cm globally, and as much as 1 cm regionally). Greenland and Antarctica mass balance estimates derived from the mascon solutions agree within formal uncertainties with previously published results. Computing basin averages for hydrology applications shows general agreement between harmonic and mascon solutions for large basins; however, mascon solutions typically have greater resolution for smaller spatial regions, in particular when studying secular signals.

Active linear quadratic Gaussian control of the vibration of a flexible beam with a time-varying mass

A linear quadratic Gaussian method for active vibration control of a flexible beam with a time-varying mass is studied in this article. As the time-varying mass can change the resonance frequencies of system and induce instability of system, the vibration control of time-varying mass systems using piezoelectric actuators has been the subject of recent interest. The equation of motion of a beam with a time-varying concentrated mass is obtained by using admissible functions and the principle of separation of variables. Then, active control using piezoelectric actuators is simulated for the time-varying mass system. The linear quadratic Gaussian control strategy is employed for the suppression of transverse vibration of the beam with time-varying mass under different conditions. The numerical results show that the proposed scheme can attenuate the vibration of the variable mass system effectively in the interested frequency range. The control method can be used for the beam with constant mass or time-varying mass.

Radially accelerated trajectories for variable mass spacecraft

This paper proposes a new approach for mission design of a spacecraft with a time-variable mass and subjected to a continuous propulsive thrust in the radial direction. Two different mission scenarios are discussed according to whether the thrust remains constant along the whole mission or its modulus varies inversely proportional to the distance between the spacecraft and the primary body. In the first case a graphical solution is discussed for evaluating the spacecraft performance during an escape mission scenario. In the second case a closed-form solution, which makes use of the trigonometric integral functions, is found for describing the spacecraft trajectory in a polar reference frame. Some examples are discussed where the methodology is applied to a spacecraft with an electric thruster or a mini-magnetospheric propulsion system.

Excess body mass index- and waist circumference-years and incident cardiovascular disease: the CARDIA study.

ObjectiveDetermine the influence of the total cumulative exposure to excess overall and abdominal adiposity on the incidence of cardiovascular disease (CVD).DesignProspective study of 4,061 white and black adults without CVD at baseline in 1985-86 (age 18-30 years) from the multicenter, community-based CARDIA study. Time-varying excess body mass index (BMI) and waist circumference (WC)-years were calculated as products of the degree and duration of excess overall (BMI ≥25 kg/m2) and abdominal adiposity [WC >94 cm (men) and >80 cm (women)], respectively, collected at up to eight examinations.ResultsDuring a median of 24.8 years, there were 125 incident CVD, 62 coronary heart disease (CHD), and 33 heart failure (HF) events. Adjusted hazard ratios for CVD, CHD, and HF for each additional 50 excess BMI-years were 1.20 (1.08, 1.34), 1.25 (1.07, 1.46), and 1.45 (1.23, 1.72), respectively. For each 50 excess WC-years, these hazard ratios were 1.10 (1.04, 1.18), 1.13 (1.03, 1.24), and 1.22 (1.11, 1.34), respectively. Akaike information criterion values were lowest in models containing time-varying excess BMI- or WC-years than those including time-varying BMI or WC only.ConclusionsExcess BMI- and WC-years are predictors of the risk of CVD and may provide a better indicator of the cumulative exposure to excess adiposity than BMI or WC only.