Onset Of Dynamical Instability Research Articles

Development of a desmodromic variable pitch system for hydrokinetic turbines

The use of vertical-axis turbines is raising interest in the field of hydropower production from rivers or water channels, where suitable mass flows are available, without the need of high water jumps or large construction sites. Like their wind-based counterparts, these machines have many advantages in terms of installation and maintenance, but suffer from an inherently complex rotor hydrodynamics, characterized by a continuous variation of the blade angle of attack beyond the static stall limit and the corresponding onset of dynamic instabilities. In virtue of their typically lower rotational speed nonetheless, hydrokinetic machines can benefit from the possibility of active blade pitch control, which is barely feasible in case of wind turbines due to their high characteristic operation frequencies. Moving from this background, a novel control strategy, based on a double-cam desmodromic pitching system, has been developed in the present study by means of a combination of medium- and high-fidelity numerical approaches. In order to tailor the corresponding pitching law, here implemented in a parametric form, to this class of machines, a dedicated automatic optimization framework has been developed in the ANSYS® WORKBENCH® 20.2 suite. The latter combines a Multi-Objective Genetic Algorithm (MOGA) optimizer with an advanced two-dimensional Actuator Line Model (ALM) model of the turbine, developed by the authors. This optimization approach has then been applied to a test rotor with the objective of maximising the turbine power coefficient while containing the rotor stream- and cross-wise force oscillations. The resulting optimal configurations have been eventually verified via high-fidelity, fully-resolved CFD simulations. Results show that variable pitch can represent a promising solution for increasing the performance of vertical-axis hydrokinetic turbines, leading to a +35% efficiency enhancement as well as to a reduction of the machine unsteady loads.

Collapse strength ratios for weak first-story buildings under soft soil intraslab earthquakes

Weak first-story buildings are susceptible to experience severe structural damage, and even collapse, during strong earthquakes as was evidenced during the September 19, 2017 (Mw = 7.1) intraslab earthquake that hit Mexico City. Such type of buildings are prone to exhibit a negative slope in their capacity curve due to weak first-story mechanism that might lead to dynamic instability during earthquake excitation. Therefore, this paper presents the main results of an investigation focused on evaluating the collapse strength ratios, Rc (i.e., the normalized lateral strength ratio in the onset of dynamic instability) of single-degree-of-freedom (SDOF) systems whose force-displacement nonlinear envelope (backbone) behavior is representative of that observed in existing multistory weak first-story buildings. Particularly, their envelope exhibit several levels of negative slope after a post-yield displacement ductility capacity. Median and dispersion of Rc ratios were obtained for degrading SDOF systems subjected to a set of 136 earthquake ground motions recorded in soft soil sites of Mexico City from instraslab earthquakes. Results of this investigation showed that Rc ratios depend on the normalized period of vibration with respect to the predominant period of the ground motion, T/Tg, the displacement ductility capacity, μc, and the negative slope after peak strength, αc. Additionally, the spectral trend of Rc ratios at soft soil sites is different to that reported for firm soil sites. A continuous functional form is introduced to obtain estimates of median Rc ratios for the preliminary seismic assessment of weak first-story buildings in this seismic environment.

Estimating the outcomes of common envelope evolution in triple stellar systems

ABSTRACT We present a new model describing the evolution of triple stars that undergo common envelope evolution, using a combination of analytical and numerical techniques. The early stages of evolution are driven by dynamical friction with the envelope, which causes the outer triple orbit to shrink faster than the inner binary. In most cases, this leads to a chaotic dynamical interaction between the three stars, culminating in the ejection of one of the stars from the triple. This ejection and resulting recoil on the remnant binary are sufficient to eject all three stars from the envelope, which expands and dissipates after the stars have escaped. These results have implications for the properties of post-common envelope triples: they may only exist in cases where the envelope was ejected before the onset of dynamical instability, the likelihood of which depends on the initial binary separation and the envelope structure. In cases where the triple becomes dynamically unstable, the triple does not survive and the envelope dissipates without forming a planetary nebula.

A census of main-sequence interactions in the Multiple Star Catalogue

ABSTRACT Statistics of hierarchical systems containing three or more stars are continuously improving. The Multiple Star Catalogue (MSC) is currently the most comprehensive catalogue of multiple-star systems and contains component masses, orbital periods, and additional information. The systems in the MSC are interesting for several reasons, including the long-term dynamical evolution of few-body systems. Although the secular evolution of triples and quadruples has been explored before, a systematic study of the systems in the MSC including also quintuples and sextuples has not been carried out. Here, we explore the main-sequence (MS) evolution of stars from the MSC based on approximately 2 × 105 secular dynamical integrations. We estimate statistical probabilities for strong interactions during the MS such as tidal evolution and mass transfer, and the onset of dynamical instability. Depending on the assumed model for the unknown orbital elements, we find that the fraction of non-interacting systems is largest for triples (∼0.9), and decreases to ∼0.6–0.8 for sextuples. The fraction of strong interactions increases from ∼0.1 to ∼0.2 from triples to sextuples, and the fraction of dynamically unstable systems increases from ∼0.001 to ∼0.1–0.2. The larger fractions of strong interactions and dynamical instability in systems with increasing multiplicity can be attributed to increasingly complex secular evolution in these systems. Our results indicate that a significant fraction of high-multiplicity systems interact or become dynamically unstable already during the MS, with an increasing importance as the number of stars increases.

Equilibrium and stability of thin spherical shells in Newtonian and relativistic gravity

We consider thin spherical shells of matter in both Newtonian gravity and general relativity and examine their equilibrium configurations and dynamical stability. Thin-shell models are admittedly a poor substitute for realistic stellar models. But the simplicity of the equations that govern their dynamics, compared to the much more complicated mechanics of a self-gravitating fluid, allows us to deliver, in a very direct and easy manner, powerful insights into their equilibria and stability. We explore, in particular, the link between the existence of a maximum mass along a sequence of equilibrium configurations and the onset of dynamical instability. Such a link is well-established in the case of fluid bodies in both Newtonian gravity and general relativity, but the demonstration of this link is both subtle and difficult. The proof is very simple, however, in the case of thin shells, and it is constructed with nothing more than straightforward algebra and a little calculus.

A Magnetic Field Suppresses Plastic Strain Jumps during Low-Temperature Deformation of Two-Component Alloys

The motion of dislocations during low-temperature deformation of two-component alloys has been studied. The condition is found under which the appearance of a region with negative slope of strain-rate dependence of the yield stress is possible that leads to the onset of dynamic instability and jumpwise straining. An analytic expression for the critical magnetic field capable of suppressing these jumps is obtained.

On the Instability of Polytropic Maclaurin and Roche Ellipsoids

Abstract The ellipsoidal configurations studied by Lai et al. belong to the special class of adiabatic polytropes, and most results are applicable only in the interval 0 ≤ n < 1 of polytropic indices n. This restricts the applicability of their models mainly to rapidly rotating neutron stars or binaries with a neutron-star component. We show that their results are incorrect for the following three topics: (1) the stability against equatorial mass loss of polytropic Maclaurin and Jacobi ellipsoids, (2) the onset of dynamical instability in polytropic Maclaurin and Roche binary ellipsoids under the influence of the adiabatic exponent, and (3) the onset of secular instability in polytropic Roche binary ellipsoids. For uniformly rotating polytropes of index n = 1.5, 2, and 3, we get precise numerical values of the critical adiabatic exponent at the onset of dynamical instability, in close agreement with the general theoretical formula of Ledoux. In the Appendix, it is shown that for one of the Rosenkilde toroidal modes, secular and dynamical instability in homogeneous Maclaurin ellipsoids are not correlated, occurring in two distinct overlapping eccentricity intervals. For this mode, the Maclaurin ellipsoid can be secularly stable or unstable if it is dynamically stable or unstable. This rectifies previous conclusions of Lyttleton and Chandrasekhar on this subject.

Towards an initial mass function for giant planets

The distribution of exoplanet masses is not primordial. After the initial stage of planet formation is complete, the gravitational interactions between planets can lead to the physical collision of two planets, or the ejection of one or more planets from the system. When this occurs, the remaining planets are typically left in more eccentric orbits. Here we use present-day eccentricities of the observed exoplanet population to reconstruct the initial mass function of exoplanets before the onset of dynamical instability. We developed a Bayesian framework that combines data from N-body simulations with present-day observations to compute a probability distribution for the planets that were ejected or collided in the past. Integrating across the exoplanet population, we obtained an estimate of the initial mass function of exoplanets. We find that the ejected planets are primarily sub-Saturn type planets. While the present-day distribution appears to be bimodal, with peaks around $\sim 1 M_{\rm J}$ and $\sim 20 M_\oplus$, this bimodality does not seem to be primordial. Instead, planets around $\sim 60 M_\oplus$ appear to be preferentially removed by dynamical instabilities. Attempts to reproduce exoplanet populations using population synthesis codes should be mindful of the fact that the present population has been depleted of intermediate-mass planets. Future work should explore how the system architecture and multiplicity might alter our results.

Family of columns isospectral to gravity-loaded columns with tip force: A discrete approach

A discrete model is introduced to analyze transverse vibration of straight, clamped-free (CF) columns of variable cross-sectional geometry under the influence of gravity and a constant axial force at the tip. The discrete model is used to determine critical combinations of loading parameters - a gravity parameter and a tip force parameter - that cause onset of dynamic instability in the CF column. A methodology, based on matrix-factorization, is described to transform the discrete model into a family of models corresponding to weightless and unloaded clamped-free (WUCF) columns, each with a transverse vibration spectrum isospectral to the original model. Characteristics of models in this isospectral family are dependent on three transformation parameters. A procedure is discussed to convert the isospectral discrete model description into geometric description of realistic columns i.e. from the discrete model, we construct isospectral WUCF columns with rectangular cross-sections varying in width and depth. As part of numerical studies to demonstrate efficacy of techniques presented, frequency parameters of a uniform column and three types of tapered CF columns under different combinations of loading parameters are obtained from the discrete model. Critical combinations of these parameters for a typical tapered column are derived. These results match with published results. Example CF columns, under arbitrarily-chosen combinations of loading parameters are considered and for each combination, isospectral WUCF columns are constructed. Role of transformation parameters in determining characteristics of isospectral columns is discussed and optimum values are deduced. Natural frequencies of these WUCF columns computed using Finite Element Method (FEM) match well with those of the given gravity-loaded CF column with tip force, hence confirming isospectrality.

Dynamic instability of dielectric elastomer actuators subjected to unequal biaxial prestress

The paper presents a Hamiltonian approach for extracting the dynamic instability parameters of homogeneously deforming dielectric elastomer actuators subjected to an unequal biaxial prestress, and driven by a suddenly applied electric load. The approach relies on setting up the balance between the kinetic, strain, and electrostatic energy at the point of maximum overshoot in an oscillation cycle. The equation of the stagnation curve, obtained by invoking aforestated statement of energy-balance, is operated upon by the condition of instability to determine the instability parameters. The underlying principles of the approach are elucidated by considering the Ogden family of hyperelastic material models. The approach is however portrayed generically, and hence, can be extended to the other hyperelastic material models of interest. The estimates of the dynamic instability parameters are corroborated by examining the saddle-node bifurcation points in the time-history response obtained by integrating the equation of motion. A parametric study is conducted to bring out the effect of unequal biaxial prestress, and the trends of variation of the critical electric field and the thickness-stretch on the onset of dynamic instability are presented. A quantitative comparison with the static instability parameters reveals that the dynamic instability gets triggered for electric fields that are lower than those corresponding to the static instability. In contrast, the maximum stretch experienced by the actuator at the dynamic instability is significantly higher than that at the static instability. The crucial inferences can find their potential use in the design of DEAs subjected to a transient motion.

Large Wind Shears and Their Implications for Diffusion in Regions With Enhanced Static Stability: The Mesopause and the Tropopause

AbstractThe NCAR Whole Atmosphere Community Climate Model, with a quasi‐uniform horizontal resolution of ∼25 km and a vertical resolution of 0.1 scale height, produces large vertical shear of horizontal wind with peaks around the mesopause and the tropical and midlatitude tropopause. In these regions, the static stability also reaches peak values and therefore allows large vertical shears before the onset of dynamical instability. The wind shear peaks near the mesopause and the tropopause from the simulation compare well with those identified in observations, including the magnitude, latitudinal dependence, and large shear statistics. By analyzing the probability density functions of the wind shears and their dependence on the zonal scales, it is found that smaller scale processes, likely gravity waves, contribute significantly to the large shears and may play a dominant role in producing the largest shears. Climatological tidal waves have secondary contribution to the large winds and shears, but spectral analysis suggests that they can modulate wind shear perturbations by gravity waves in the mesosphere and lower thermosphere. Implications for tracer transport and mixing in these regions are explored by estimating diffusion coefficients based on the root‐mean‐square winds, shears, and corresponding spatial scales from model results.

Instability in Nonlinear Oscillation of Dielectric Elastomers

A membrane of a dielectric elastomer oscillates when subject to AC voltage. Its oscillation is nonlinear due to large deformation and nonlinear electromechanical coupling. Dynamic instability in dielectric elastomers—the oscillation with an unbounded amplitude—is investigated in this paper. The critical amplitude of AC voltage for dynamic instability varies with the frequency of AC voltage and reaches a valley when the superharmonic, harmonic, or subharmonic resonance is excited. Prestretches can improve dielectric elastomer actuators' capabilities to resist dynamic instability. The critical deformation at the onset of dynamic instability can be much larger than that at the onset of static instability. Oscillation of dielectric elastomers can be used for applications, such as vibration shakers for haptic feedback, soft loudspeakers, soft motors, and soft pumps. We hope that the current analyses can improve the understanding of dynamic behavior of dielectric elastomers and enhance their stability and reliability.

SIGNATURES OF DYNAMICAL INSTABILITY OF BOSE–EINSTEIN CONDENSATES IN 1D OPTICAL LATTICES

The onset of dynamical instabilities of Bose–Einstein condensates in optical lattices due to the dephasing of the condensate wavefunction is observed through the decay of the visibility of the interference pattern in time-of-flight and the growth of the radial width of the condensate.

Increasing blood glucose variability is a precursor of sepsis and mortality in burned patients.

High glycemic variability, rather than a mean glucose level, is an important factor associated with sepsis and hospital mortality in critically ill patients. In this retrospective study we analyze the blood glucose data of 172 nondiabetic patients 18–60 yrs old with second and third-degree burns of total body surface area greater than 30% and 5%, respectively, admitted to ICU in 2004–2008. The analysis identified significant association of increasing daily glucose excursion (DELTA) accompanied by evident episodes of hyperglycemia (>11 mmol/l) and hypoglycemia (<2.8 mmol/l), with sepsis and forthcoming death, even when the mean daily glucose was within a range of acceptable glycemia. No association was found in sepsis complication and hospital mortality with doses of intravenous insulin and glucose infusion. A strong increase in DELTA before sepsis and death is treated as fluctuation amplification near the onset of dynamical instability.

Planet–planet scattering in circumstellar gas disks

Context. Hydrodynamical simulations of two giant planets embedded in a gaseous disk have shown that in case of a smooth convergent migration they end up trapped into a mean motion resonance. These findings have led to the conviction that the onset of dyna mical instability causing close encounters between the planets can occur only after the dissipation of the gas when the eccentricity damping is over. Aims. We show that a system of three giant planets may undergo planet-planet scattering when the gaseous disk, with density val ues comparable to that of the Minimum Mass Solar Nebula, is still interacting with the planets. Methods. The hydrodynamical code FARGO‐2D‐1D is used to model the evolution of the disk and planets, modified to properly handle close encounters between the massive bodies. Results. Our simulations predict a variety of different outcomes of the scattering phase which includes orbital exchange, planet merging and scattering of a planet in a hyperbolic orbit. Conclusions. This implies that the final fate of a multiplanet system under the action of the disk torques is not necessarily a packed resonant configuration.

Cluster Formation in Contracting Molecular Clouds

We explore, through a simplified, semianalytic model, the formation of dense clusters containing massive stars. The parent cloud spawning the cluster is represented as an isothermal sphere. This sphere is in near-force balance between self-gravity and turbulent pressure. Self-gravity, mediated by turbulent dissipation, drives slow contraction of the cloud, eventually leading to a sharp central spike in density and the onset of dynamical instability. We suggest that, in a real cloud, this transition marks the late and rapid production of massive stars. We also offer an empirical prescription, akin to the Schmidt law, for low-mass star formation in our contracting cloud. Applying this prescription to the Orion Nebula Cluster, we are able to reproduce the accelerating star formation previously inferred from the distribution of member stars in the HR diagram. The cloud turns about 10% of its mass into low-mass stars before becoming dynamically unstable. Over a cloud free-fall time, this figure drops to 1%, consistent with the overall star formation efficiency of molecular clouds in the Galaxy.

Instability-induced localization of matter waves in moving optical lattices

By using a one-dimensional nonpolynomial nonlinear mean-field model, we numerically analyze the process of the loading of the Bose-Einstein condensate into a moving one-dimensional optical lattice. We demonstrate that the recently observed dynamical instability of the Bloch states of a repulsive condensate in a moving optical lattice can lead to formation of trains of spatially localized wave packets that can be associated with matter-wave gap solitons. We study the characteristic features of this matter-wave localization under realistic conditions by modeling the dynamics of the condensate beyond the onset of dynamical instability.

Transverse vibration of an uniform Euler–Bernoulli beam under linearly varying axial force

This paper is concerned with the transverse vibration of uniform Euler–Bernoulli beams under linearly varying fully tensile, partly tensile or fully compressive axial force distribution. The system parameters are the constant part of the axial force and the constant of proportionality of the varying part. The mode shape differential equation is linear with variable coefficients. The general solution is derived and expressed as the super-position of four independent power series solution functions. The frequency equations of the 16 combinations of classical boundary conditions are listed. The first three frequency parameters are tabulated for example combinations of the system parameters. Increase in the values of one or both of the system parameters ‘stiffens’ the system and results in increase in the frequency parameter. If one or both system parameters are negative, combinations exist for which a frequency parameter is zero. This is the Euler buckling condition i.e., onset of dynamic instability. Example combinations of the system parameters when buckling occurs are tabulated. The results tabulated may be used to judge frequencies, buckling parameter combinations obtained by other methods.

Stability and collapse of rapidly rotating, supramassive neutron stars: 3D simulations in general relativity

We perform 3D numerical simulations in full general relativity to study the stability of rapidly rotating, supramassive neutron stars at the mass-shedding limit to dynamical collapse. We adopt an adiabatic equation of state with $\ensuremath{\Gamma}=2$ and focus on uniformly rotating stars. We find that the onset of dynamical instability along mass-shedding sequences nearly coincides with the onset of secular instability. Unstable stars collapse to rotating black holes within about one rotation period. We also study the collapse of stable stars which have been destabilized by pressure depletion (e.g., via a phase transition) or mass accretion. In no case do we find evidence for the formation of massive disks or any ejecta around the newly formed Kerr black holes, even though the progenitors are rapidly rotating.

Rotational Effects on the Dynamical Instability of Luminous Blue Variables

Rotation influences the dynamical stability of a star in both direct and indirect ways. Directly, it supplies rotational kinetic energy to the star and changes the star's hydrostatic structure. Indirectly, it influences the possible course of stellar evolution. Calculations show that, for a luminous blue variable (LBV), rotation is not expected to greatly affect the onset of dynamical instability in any direct way, but could be important through its indirect evolutionary effect on the star's luminosity-to-mass ratio. If the classical LBV's are evolving in an advanced stage of central helium burning, when their envelopes are most prone to dynamical instability, the luminosity-to-mass ratio would probably be increased by rotation. It is shown that a brightening of the star lessens its dynamical stability and so leads to a somewhat hotter effective temperature during the phase of dynamical instability. How rotation modifies the Eddington luminosity limit is also discussed.