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1

Szary, Marek L., and Peter Weber. "The Study of Behavior of Vibrating Systems Controllable by Devices with Rheological Fluid." Archives of Acoustics 38, no. 2 (June 1, 2013): 217–22. http://dx.doi.org/10.2478/aoa-2013-0026.

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Abstract The nonlinear mathematical model of behavior of controllable viscosity fluid (CVF) under applied external field is presented. A large family of these fluids is commonly used to control responding forces of dampers in vibration control applications. The responding force of a damper with CVF has two components. The first one - uncontrollable - is proportional to the viscosity of a base fluid and velocity of its motion, the second one, which is controllable, depends on the strength of the applied external field. Both are involved in the process of dissipation of unwanted energy from the vibrating systems. An equivalent damping factor based on the principle of energy dissipated during one cycle of damper work under a constant strength external field was calculated. When mass or stiffness is variable the equivalent damping factor can be set accordingly by adjusting the strength of external field to have vibrating damped system purposely/continuously working in the critical or other chosen state. This paper also presents cases of applying periodically changing strengths of an external field synchronized with cycles of periodical motion of the vibrating system to continuously control the damping force within each cycle.
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2

Sefler, J. F., and A. P. Pisano. "The Design, Experimentation, and Simulation of a Novel Coulomb Friction Device for Automotive Valve Spring Damping." Journal of Mechanical Design 115, no. 4 (December 1, 1993): 871–76. http://dx.doi.org/10.1115/1.2919281.

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This investigation contains experimental and computer modeling results of an alternative method for damping automotive valve springs, in which a nondestructive elastomeric sleeve that slides over the spring with an interference fit is used to provide coulomb damping on the outside of the valve spring coils. The damper and valve spring dynamics are modeled using the wave equation with a damping term composed of both viscous and coulomb components. Although the damper is very simple and inexpensive, the reduction in residual spring vibrations are shown to be significant without loss of valve spring performance. Experimental data taken from a 1983 Pontiac family-II, 1.8 liter, four cylinder, single overhead cam engine equipped both with and without the new elastomeric dampers is used to verify the results of the computer simulation and demonstrate the effectiveness of the damper.
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3

Modi, V. J., A. Akinturk, and W. Tse. "A Family of Efficient Sloshing Liquid Dampers for Suppression of Wind-Induced Instabilities." Journal of Vibration and Control 9, no. 3-4 (March 2003): 361–86. http://dx.doi.org/10.1177/107754603030773.

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Bluff structures in the form of tall buildings, smokestacks, control towers, bridges, etc., are susceptible to vortex resonance and galloping type of instabilities. One approach to vibration control of such systems is through energy dissipation using sloshing liquid dampers. In this paper we focus on enhancing the energy dissipation efficiency of a rectangular liquid damper through the introduction of two-dimensional obstacles as well as floating particles. The investigation has two phases. To begin with, a parametric free vibration study aimed at the optimization of the obstacle geometry is undertaken to arrive at configurations promising increased damping ratio and hence higher energy dissipation. The study is complemented by an extensive wind tunnel test program, which substantiates the effectiveness of this class of damper in suppressing both vortex resonance and galloping type of instabilities. Simplicity of design, ease of implementation, minimal maintenance, reliability as well as high efficiency make such liquid dampers quite attractive for real-life applications.
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4

Hayashi, Ken-Ichi. "Lysmata dispar sp. nov., a new shrimp from the Dampier Archipelago, Western Australia, with notes on other species of the family Hippolytidae (Crustacea: Decapoda: Caridea)." Records of the Western Australian Museum, Supplement 73, no. 1 (2007): 85. http://dx.doi.org/10.18195/issn.0313-122x.73.2007.085-095.

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5

Martorell, F., Vicenç Torra, Antonio Isalgué, M. L. Perea, Patrick Terriault, and Francisco C. Lovey. "Damping by SMA in Civil Engineering Structures." Advances in Science and Technology 56 (September 2008): 92–97. http://dx.doi.org/10.4028/www.scientific.net/ast.56.92.

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The particular properties of Shape Memory Alloys associated to their thermoelastic martensitic transformation with hysteresis permits applications of SMA as a damper via the conversion of the work absorbed in each cycle in heat. The guaranteed behavior requires the appropriateness of SMA for the complete requirements of the application. This work shows two complementary aspects of the SMA application in Civil Engineering, the first of them, the SMA dampers in earthquake damping of a family house. The second aspect relates an elementary approach to the damping of stayed cables in bridges, using some data from the Iroise Bridge. The application in the first case needs long time constancy of properties and then around 200 cycles during an earthquake. In the second case, the fatigue life of SMA imposes that only small strains in the alloy can be accepted. Finally, it is emphasized the importance of working conditions, including temperature and time.
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6

Fu, Bo, Huanjun Jiang, and Jin Chen. "Substructure Shake Table Testing of Frame Structure–Damper System Using Model-Based Integration Algorithms and Finite Element Method: Numerical Study." Symmetry 13, no. 9 (September 18, 2021): 1739. http://dx.doi.org/10.3390/sym13091739.

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Substructure shake table testing (SSTT) is an advanced experimental technique that is suitable for investigating the vibration control of secondary structure-type dampers such as tuned mass dampers (TMDs). The primary structure and damper are considered as analytical and experimental substructures, respectively. The analytical substructures of existing SSTTs have mostly been simplified as SDOF structures or shear-type structures, which is not realistic. A common trend is to simulate the analytical substructure via the finite element (FE) method. In this study, the control effects of four dampers, i.e., TMD, tuned liquid damper (TLD), particle damper (PD) and particle-tuned mass damper (PTMD), on a frame were examined by conducting virtual SSTTs. The frame was modeled through stiffness-based beam-column elements with fiber sections and was solved by a family of model-based integration algorithms. The influences of the auxiliary mass ratio, integration parameters, time step, and time delay on SSTT were investigated. The results indicate that the TLD had the best performance. In addition, SSTT using model-based integration algorithms can provide satisfactory results, even when the time step is relatively large. The effects of integration parameters and time delay are not significant.
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7

Gérard, Patrick, Sandrine Grellier, and Zihui He. "Turbulent cascades for a family of damped Szegő equations." Nonlinearity 35, no. 9 (August 16, 2022): 4820–49. http://dx.doi.org/10.1088/1361-6544/ac7e13.

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Abstract In this paper, we study the transfer of energy from low to high frequencies for a family of damped Szegő equations. The cubic Szegő equation has been introduced as a toy model for a totally non-dispersive degenerate Hamiltonian equation. It is a completely integrable system which develops growth of high Sobolev norms, detecting transfer of energy and hence cascades phenomena. Here, we consider a two-parameter family of variants of the cubic Szegő equation and prove that, adding a damping term unexpectedly promotes the existence of turbulent cascades. Furthermore, we give a panorama of the dynamics for such equations on a six-dimensional submanifold.
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8

Dampier, Carlton, Elizabeth Ely, Leela Aertker, Darcy Brodecki, Karen Kesler, and Marie Stuart. "Pain In Infants and Young Children with Sickle Cell Disease-a Prospective Longitudinal Analysis." Blood 116, no. 21 (November 19, 2010): 841. http://dx.doi.org/10.1182/blood.v116.21.841.841.

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Abstract Abstract 841 Pain is the hallmark symptom of vaso-occlusion in sickle cell disease (SCD), but has not been well studied, particularly in children. Previous studies of pain in very young children with SCD have largely been limited to episodes sufficiently severe as to require acute care visits or hospitalizations. Our previous studies in school-aged children and adolescents (Dampier CD et al. J Pediatr Hematol Oncol 2004), as well as those in adults (Smith W et al Ann Inter Med 2009) suggest that vaso-occlusive pain is frequently managed at home outside of acute care medical settings. We sought to obtain similar data about the home pain experience of infants and young children with SCD as reported by parents or guardians, and to explore the relationship between the pain experience and hematological biomarkers. Enrollment and data collection was conducted from Jan 1999-Mar 2008 at the Marian Anderson Sickle Cell Center as part of the Comprehensive Sickle Cell Centers program. Families with SCD infants identified by newborn screening were first approached about the study after completion of confirmatory diagnosis and initial SCD-related education, usually between 4 to 6 months of age. After informed consent, parents/guardians were trained in pain assessment and daily reporting. When sickle cell related pain events occurred, parents/guardians reported pain occurrence, location, associated symptoms and the treatment that they provided. Daily paper diaries were generally used in the first year of life to familiarize families with pain assessment and reporting. Subsequently a novel daily pager system was used to provide a method allowed daily reporting, but with reduced participant burden. A monthly telephone system in conjunction with a daily calendar was used for those families unable to effectively comply with providing daily reports. All pain reports were adjudicated by consensus of study staff and PI/Co-PI. Children were removed from the study for any period of chronic transfusion for clinical events (splenic sequestration, recurrent acute chest syndrome, surgery). Over the study period, 103 children (58% male) were enrolled beginning at a median age of 7.3 months (range 1.5, 65.2 months). This represented about 50% of SCD children referred to the Center by newborn screening during these time periods; the most common reasons for refusal were inability to complete daily reporting and geographic distance from the Center. An SS genotype was present in 50 children (48.5%), SC in 32 (31.1%), SB0thalassemia in 6 (5.8%), SB+thalassemia in 15 (14.6%). Children were actively followed for a median of 3.8 years (range 0.3–7.6 years). The total number of days children were assessed for pain was 141,197 days with an additional 28,079 days of missing data (16%). The total number of days that children had reported pain was 2,288 days (1.6%), which represented 768 distinct episodes of pain. Over 80% of children reported to have pain in the 0–12 month age interval had pain locations (hands/feet) and characteristics (swelling or tenderness) consistent with dactylitis, which became progressively less prevalent in older age intervals. Significantly more SS/SB0 patients (58%) had >2 days of average dactylitis pain during 0–12 months or 12–24 months (53%) intervals compared to SC/SB+ patients (0%) (p=0.04). The timing of the first reported dactylitis event (<2 years or ≥2 years) significantly predicted the frequency of SCD pain events per person year, with earlier onset associated with more frequent pain events during the study period (p=0.02), for both the SS/SB0 and SC/SB+ (P=0.03) groups. Our study demonstrates the feasibility of initial recruitment and subsequent daily reporting of clinical events by families of infants and young children with SCD over many years, particularly when careful consideration is given to enhance family support and minimizing respondent burden. The onset of an initial dactylitis episode prior 2 years of age, even if treated at home, was associated with more frequent pain throughout childhood, irrespective of hemoglobinopathy type. Such children may be appropriate for interventions, such as oral hydroxyurea, that reduce excessive pain frequency. Supported by NIHHL-051495 and HL-083705. Disclosures: Dampier: Anthera Pharmaceuticals Inc:; Glycomimetics Inc: .
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9

Skalski, Paweł, and Klaudia Kalita. "Role of Magnetorheological Fluids and Elastomers in Today’s World." Acta Mechanica et Automatica 11, no. 4 (December 1, 2017): 267–74. http://dx.doi.org/10.1515/ama-2017-0041.

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AbstractThis paper explains the role of magnetorheological fluids and elastomers in today’s world. A review of applications of magnetorheological fluids and elastomers in devices and machines is presented. Magnetorheological fluids and elastomers belong to the smart materials family. Properties of magnetorheological fluids and elastomers can be controlled by a magnetic field. Compared with magnetorheological fluids, magnetorheological elastomers overcome the problems accompanying applications of MR fluids, such as sedimentation, sealing issues and environmental contamination. Magnetorheological fluids and elastomers, due to their ability of dampening vibrations in the presence of a controlled magnetic field, have great potential present and future applications in transport. Magnetorheological fluids are used e.g. dampers, shock absorbers, clutches and brakes. Magnetorheological dampers and magnetorheological shock absorbers are applied e.g. in damping control, in the operation of buildings and bridges, as well as in damping of high-tension wires. In the automotive industry, new solutions involving magnetorheological elastomer are increasingly patented e.g. adaptive system of energy absorption, system of magnetically dissociable [hooks/detents/grips], an vibration reduction system of the car’s drive shaft. The application of magnetorheological elastomer in the aviation structure is presented as well.
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10

Bollimpalli, D. A., M. Wielgus, D. Abarca, and W. Kluźniak. "Atmospheric oscillations provide simultaneous measurement of neutron star mass and radius." Monthly Notices of the Royal Astronomical Society 487, no. 4 (June 10, 2019): 5129–42. http://dx.doi.org/10.1093/mnras/stz1597.

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ABSTRACT Neutron stars with near-Eddington observable luminosities were shown to harbour levitating atmospheres, suspended above their surfaces. We report a new method to simultaneously measure the mass and radius of a neutron star based on oscillations of such atmospheres. In this paper, we present an analytic derivation of a family of relativistic, oscillatory, spherically symmetric eigenmodes of the optically and geometrically thin levitating atmospheres, including the damping effects induced by the radiation drag. We discover characteristic maxima in the frequencies of the damped oscillations and show that from a measurement of the frequency maximum and of the luminosity one can determine the mass and radius of the neutron star. In addition to the stellar parameters, observation of the variation of the oscillation frequencies with flux would allow us to estimate the stellar luminosity and therefore the distance to the source with an accuracy of a few per cent. We also show that the ratio of any two undamped eigenfrequencies depends only on the adiabatic index of the atmosphere, while for the damped eigenfrequencies, this ratio varies with the luminosity. The damping coefficient is independent of the mode number of the oscillations. Signatures of the dynamics of such atmospheres will be reflected in the source’s X-ray light curves.
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11

Corpus, William T., and William J. Endres. "Added Stability Lobes in Machining Processes That Exhibit Periodic Time Variation, Part 1: An Analytical Solution." Journal of Manufacturing Science and Engineering 126, no. 3 (August 1, 2004): 467–74. http://dx.doi.org/10.1115/1.1765137.

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An added family of stability lobes, which exists in addition to the traditional stability lobes, has been identified for the case of periodically time varying systems. An analytical solution of arbitrary order is presented that identifies and locates multiple added lobes. The stability limit solution is first derived for zero damping where a final closed-form symbolic result can be realized up to second order. The un-damped solution provides a mathematical description of the added lobes’ locations along the speed axis, an added-lobe numbering convention, and the asymptotes for the damped case. The derivation for the damped case permits a final closed-form symbolic result for first-order only; the second-order solution requires numerical evaluation. The easily computed analytical solution is shown to agree well with the results of the computationally intensive numerical simulation approach. An increase in solution order improves the agreement with numerical simulation; but, more importantly, it allows equivalently more added lobes to be predicted, including the second added lobe that cuts into the speed regime of the traditional high-speed stability peak.
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12

Robinson, P. A. "Dispersion of electron Bernstein waves including weakly relativistic and electromagnetic effects. Part 1. Ordinary modes." Journal of Plasma Physics 37, no. 3 (June 1987): 435–47. http://dx.doi.org/10.1017/s0022377800012290.

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Ordinary solutions of the weakly relativistic, electromagnetic dispersion relation are investigated for waves propagating perpendicular to a uniform magnetic field in a Maxwellian plasma. Weakly relativistic resonance broadening, frequency downshift and damping are found to alter dramatically the dispersion predicted by the corresponding strictly non-relativistic (‘classical’) theory in the neighbourhood of harmonics of the cyclotron frequency Ωe. All classical resonances and cut-offs are removed except the cut-off at the plasma frequency ωp. At frequencies above ωp the infinite family of classically predicted modes is replaced by a single weakly damped mode whose dispersion differs only slightly from that predicted by cold plasma theory. No weakly damped modes exist in the range of harmonics s satisfying (ωp/Ωe)⅔/8 ≲ S < Ωp/Ωe, however, one such mode is located immediately below each harmonic for s ≲ (ωp/Ωe)⅔/8. A companion paper investigates extraordinary solutions of the dispersion relation.
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13

Goto, Yutaka. "Highly Accurate Frequency Interpolation of Apodized FFT Magnitude-Mode Spectra." Applied Spectroscopy 52, no. 1 (January 1998): 134–38. http://dx.doi.org/10.1366/0003702981942465.

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“Generalized” interpolation (called GIα here) of fast Fourier transform (FFT) spectra apodized by a family of sinα ( X) windows has previously been proposed. The GIα gives the highly accurate interpolated frequency by calculating the simple formula of frequency determination with the use of two squared ratios between three magnitudes nearest to the peak maximum on the apodized FFT spectrum. Although the value of window parameter α, limited to integer values, has been used for the GIα, we show in the present paper that the GIα with a real α value also gives an extremely good estimate of the true frequency from the sinα ( X)-apodized spectra. Thus, we intend to apply the GIα with the optimal values of α to FFT spectra apodized by any other window functions that are often used in Fourier spectroscopy. Simulation results show that the GIα is easier and more accurate than the KCe interpolation, which uses a family of interpolating functions [ KCe(ω) = ( aω2 + bω + c)e] proposed by Keefe and Comisarow. Finally, in the presence of noise we examine effects of damping and windowing on the frequency interpolation of FFT spectra. Because damping and windowing reduce the signal-to-noise ratio (SNR), we define anew the relative SNR by the ratio of the SNR of the apodized spectrum of a damped sinusoid to the SNR of the unapodized spectrum of an undamped sinusoid. Numerical calculation shows that the relative SNR varies, owing to damping rather than windowing. In fact, the observed frequency error roughly increases as the damping ratio increases for any window functions, as is expected from our previous investigation that the frequency error based upon the GIα is inversely proportional to the SNR. However, no obvious differences between the various window functions are observed in the presence of noise.
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14

Atallah-Baraket, Amel, and Clotilde Fermanian Kammerer. "Microlocal defect measures for a degenerate thermoelasticity system." Journal of the Institute of Mathematics of Jussieu 13, no. 1 (April 17, 2013): 145–81. http://dx.doi.org/10.1017/s1474748013000108.

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AbstractIn this paper, we study a system of thermoelasticity with a degenerate second-order operator in the heat equation. We analyze the evolution of the energy density of a family of solutions. We consider two cases: when the set of points where the ellipticity of the heat operator fails is included in a hypersurface and when it is an open set. In the first case, and under special assumptions, we prove that the evolution of the energy density is that of a damped wave equation: propagation along the rays of the geometric optic and damping according to a microlocal process. In the second case, we show that the energy density propagates along rays which are distortions of the rays of the geometric optic.
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15

Hanna, J. A. "An integrable family of torqued, damped, rigid rotors." Mechanics Research Communications 116 (September 2021): 103768. http://dx.doi.org/10.1016/j.mechrescom.2021.103768.

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16

Al-Baali, Mehiddin, and Anton Purnama. "Numerical Experience with Damped Quasi-Newton Optimization Methods when the Objective Function is Quadratic." Sultan Qaboos University Journal for Science [SQUJS] 16 (April 1, 2012): 1. http://dx.doi.org/10.24200/squjs.vol17iss1pp1-11.

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A class of damped quasi-Newton methods for nonlinear optimization has recently been proposed by extending the damped-technique of Powell for the BFGS method to the Broyden family of quasi-Newton methods. It has been shown that this damped class has the global and superlinear convergence property that a restricted class of 'undamped' methods has for convex objective functions in unconstrained optimization. To test this result, we applied several members of the Broyden family and their corresponding damped methods to a simple quadratic function and observed several useful features of the damped-technique. These observations and other numerical experiences are described in this paper. The important role of the damped-technique is shown not only for enforcing the above convergence property, but also for improving the performance of efficient, inefficient and divergent undamped methods substantially (significantly in the latter case). Thus, some appropriate ways for employing the damped-technique are suggested.
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17

Demina, Maria, and Dmitry Sinelshchikov. "Integrability Properties of Cubic Liénard Oscillators with Linear Damping." Symmetry 11, no. 11 (November 6, 2019): 1378. http://dx.doi.org/10.3390/sym11111378.

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We consider a family of cubic Liénard oscillators with linear damping. Particular cases of this family of equations are abundant in various applications, including physics and biology. There are several approaches for studying integrability of the considered family of equations such as Lie point symmetries, algebraic integrability, linearizability conditions via various transformations and so on. Here we study integrability of these oscillators from two different points of view, namely, linearizability via nonlocal transformations and the Darboux theory of integrability. With the help of these approaches we find two completely integrable cases of the studied equation. Moreover, we demonstrate that the equations under consideration have a generalized Darboux first integral of a certain form if and only if they are linearizable.
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Torra, Vicen, Antonio Isalgue, Ferran Martorelli, Francisco C. Lovey, and Patrick Terriault. "Damping in Civil Engineering Using SMA. Part I: Particular Properties of CuAIBe for Damping of Family Houses." Canadian Metallurgical Quarterly 49, no. 2 (April 2010): 179–90. http://dx.doi.org/10.1179/cmq.2010.49.2.179.

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19

Zhang, Meng, Romeo Ortega, Zhitao Liu, and Hongye Su. "A new family of interconnection and damping assignment passivity-based controllers." International Journal of Robust and Nonlinear Control 27, no. 1 (May 3, 2016): 50–65. http://dx.doi.org/10.1002/rnc.3557.

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20

Ishchenko, Anna R., and Dmitry I. Sinelshchikov. "On an integrable family of oscillators with linear and quadratic damping." Chaos, Solitons & Fractals 176 (November 2023): 114082. http://dx.doi.org/10.1016/j.chaos.2023.114082.

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21

Bobylev, A. V., and V. A. Zenkin. "Pneumatic Damper Multicriteria Optimization in the Free-Piston Stirling Engine Displacer." Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, no. 2 (141) (June 2022): 89–100. http://dx.doi.org/10.18698/0236-3941-2022-2-89-100.

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The free-piston Stirling engine is a complex self-oscillating system, which parameters should be strictly coordinated with each other to ensure the unit operability. One of such coordination tasks is to ensure the balance of energy input to and output from the engine displacer. In this case, energy output depends on the dissipative forces, and energy output is provided by the displacer rod and depends on its diameter. The need to select rod diameter complicates and slows down the engine design. In addition, the system possible instability could lead to the engine racing. To solve this problem, it is proposed to install a pneumatic damper on the displacer rod ensuring the dissipative forces growth with an increase in the displacer amplitude above its nominal value. Thermodynamic model was created to evaluate the damper characteristics and select its parameters. MATLAB software package was used as the development environment. The system of differential equations was integrated using the Runge --- Kutta family method. The damper multicriteria optimization problem was formalized, and two objective functions with five independent parameters were compiled. Optimization was performed using the genetic algorithm, and the Pareto front was built. To evaluate results of the work performed, the damper mathematical model was integrated into the Stirling engine mathematical model, and the working process was calculated with selected damper parameters. It is demonstrated that the developed pneumatic damper prevents an increase in the displacer oscillation amplitude ensuring system stability and reducing time for the unit design
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Omidalizarandi, Mohammad, Ralf Herrmann, Boris Kargoll, Steffen Marx, Jens-André Paffenholz, and Ingo Neumann. "A validated robust and automatic procedure for vibration analysis of bridge structures using MEMS accelerometers." Journal of Applied Geodesy 14, no. 3 (July 26, 2020): 327–54. http://dx.doi.org/10.1515/jag-2020-0010.

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AbstractToday, short- and long-term structural health monitoring (SHM) of bridge infrastructures and their safe, reliable and cost-effective maintenance has received considerable attention. From a surveying or civil engineer’s point of view, vibration-based SHM can be conducted by inspecting the changes in the global dynamic behaviour of a structure, such as natural frequencies (i. e. eigenfrequencies), mode shapes (i. e. eigenforms) and modal damping, which are known as modal parameters. This research work aims to propose a robust and automatic vibration analysis procedure that is so-called robust time domain modal parameter identification (RT-MPI) technique. It is novel in the sense of automatic and reliable identification of initial eigenfrequencies even closely spaced ones as well as robustly and accurately estimating the modal parameters of a bridge structure using low numbers of cost-effective micro-electro-mechanical systems (MEMS) accelerometers. To estimate amplitude, frequency, phase shift and damping ratio coefficients, an observation model consisting of: (1) a damped harmonic oscillation model, (2) an autoregressive model of coloured measurement noise and (3) a stochastic model in the form of the heavy-tailed family of scaled t-distributions is employed and jointly adjusted by means of a generalised expectation maximisation algorithm. Multiple MEMS as part of a geo-sensor network were mounted at different positions of a bridge structure which is precalculated by means of a finite element model (FEM) analysis. At the end, the estimated eigenfrequencies and eigenforms are compared and validated by the estimated parameters obtained from acceleration measurements of high-end accelerometers of type PCB ICP quartz, velocity measurements from a geophone and the FEM analysis. Additionally, the estimated eigenfrequencies and modal damping are compared with a well-known covariance driven stochastic subspace identification approach, which reveals the superiority of our proposed approach. We performed an experiment in two case studies with simulated data and real applications of a footbridge structure and a synthetic bridge. The results show that MEMS accelerometers are suitable for detecting all occurring eigenfrequencies depending on a sampling frequency specified. Moreover, the vibration analysis procedure demonstrates that amplitudes can be estimated in submillimetre range accuracy, frequencies with an accuracy better than 0.1 Hz and damping ratio coefficients with an accuracy better than 0.1 and 0.2 % for modal and system damping, respectively.
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MacLean, James, Majid Aleyaasin, and Sumeet S. Aphale. "How Far Should Poles Be Placed? Selecting Positive Feedback Controllers for Damping and Tracking Applications: A Complete Characterisation." Vibration 5, no. 4 (September 20, 2022): 641–58. http://dx.doi.org/10.3390/vibration5040038.

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Designers of Positive Feedback Controllers (PFCs) arbitrarily place poles into the left-hand half-plane of the complex plane without any detailed understanding of where to stop. This works aims to clearly demonstrate, via rigorous mathematical derivation, the conditions for which pole–placement becomes possible. It also highlights the design limits for the family of second–order PFCs—the most popular PFC group. To this end, the complete family of PFCs, namely, Positive Acceleration Velocity Position Feedback and its derivatives, are analysed in great depth with respect to pure damping and also with respect to combined damping and tracking applications. To showcase the practical value and validity of this work, experimental results on a piezoelectric nanopositioner are also presented and discussed.
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24

Krenk, Steen, and Jan Høgsberg. "Equal modal damping design for a family of resonant vibration control formats." Journal of Vibration and Control 19, no. 9 (May 14, 2012): 1294–315. http://dx.doi.org/10.1177/1077546312446796.

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25

Cordero, Alicia, Antonio Franques, and Juan R. Torregrosa. "Chaos and convergence of a family generalizing Homeier’s method with damping parameters." Nonlinear Dynamics 85, no. 3 (April 29, 2016): 1939–54. http://dx.doi.org/10.1007/s11071-016-2807-0.

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26

Hussain, Ali Nasser, F. Malek, Mohd Abdur Rashid, Latifah Mohamed, and Ismail Daut. "UPFC Device Application on Power System Oscillations to Improve the Damping Performance." Advanced Materials Research 694-697 (May 2013): 830–37. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.830.

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UPFC is considered as an important modern device in the flexible ac transmission systems family that provides the controllability and flexibility for transmission lines. It is also capable of enhancing the stability of the power system by the addition of a supplementary damping controller, which can be installed on any control channel of the UPFC inputs to implement the task of power oscillation damping controller. This paper presents the application of UPFC to enhance damping of low frequency oscillations by the simultaneous coordinated design between power system stabilizer and different UPFC supplementary damping controller in order to identify the design that provided the most robust damping performance in a single machine infinite bus. The parameters of the damping controller were tuned in the individual and coordinated design by using a chaotic particle swarm optimization algorithm that optimized the given eigenvalue-based objective function. The results analysis reveals that the proposed coordinated designs have high ability in damping Low-frequency oscillations and improve the system damping over their individual control responses. In addition, the coordinated design PSS & δE provides superior performance in comparison to the all coordinated designs.
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27

McCauley, Robert, and Douglas H. Cato. "The marine fish Terapon theraps calling in tropical Australia." Journal of the Acoustical Society of America 154, no. 4_supplement (October 1, 2023): A316. http://dx.doi.org/10.1121/10.0023650.

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Calling by fish of the family Terapontidae, primarily Terapon theraps, is a dominant component of sea noise recorded in northern Australian tropical coastal waters. These fish produce nightly choruses over a few hours at frequencies from 50 Hz to a few kilohertz, with spectral peaks up to 30 dB above background. Choruses are heard over muddy bottoms &lt;30 m depth. The two commonly heard calls range from 73–260 ms in length and comprised 11–21 pulses with repetition rates of 87–121 Hz. Calls were produced by muscle action on a two chambered swim bladder, and differed by muscle contraction rates, damping, and possibly the opening state of a sphincter separating chambers. Swimbladder carrier frequencies varied from 570–1465 Hz. Source levels varied from 141–154 dB re 1 mPa @ 1 m. Heavily damped alarm calls were sometimes heard. Chorusing fish schools were up to 2 km across although they were diffuse and actively calling fish extended beyond this region. A chorus could be detected out to 8 km from its center, well beyond the detection range of an individual call. Choruses may advertise school location during spawning, be used for mate attraction or mediate gamete release in dark turbid waters.
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Akers, A., and S.-C. J. Lin. "Squeeze-Film Damping of the Motion of a Control Flapper-Nozzle." Proceedings of the Institution of Mechanical Engineers, Part C: Mechanical Engineering Science 204, no. 2 (March 1990): 109–15. http://dx.doi.org/10.1243/pime_proc_1990_204_084_02.

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A squeeze film used in a flapper-nozzle affords stand-alone properties to the flapper motion, meaning that it behaves in a dynamically stable manner. The device constitutes the first stage of a new family of two-stage electrohydraulic control valves. Successful mathematical modelling of it has been reported by Lin and Akers (1,2). Because of the expense of maintaining close manufacturing tolerances within the damper, the investigation included the extent of deterioration of dynamic response when the dimensions of the damper are varied, when the tolerances on the squeeze-film annular area are relaxed and when the annular clearance is increased. As a result of the investigation, the dimensions and other variables, chosen by trial-and-error procedures, appeared to be optimum from the point of view of dynamic performance, convenience of installation and cost.
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29

Pranatha, Aria, and Rika Rostika. "HUBUNGAN ANTARA DUKUNGAN KELUARGA DENGAN KEJADIAN KEKAMBUHAN (RELAPS) PADA PENYALAHGUNA NARKOBADI RUMAH DAMPING TENJO LAUTKABUPATEN KUNINGAN TAHUN 2016." Jurnal Skolastik Keperawatan 3, no. 1 (June 9, 2017): 36. http://dx.doi.org/10.35974/jsk.v3i1.577.

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ABSTRAK Penggunaan obat-obatan secara sipil telah ada di setiap tahun, pada tahun 2008 ada 3.362.527 orang yang menggunakan narkoba kemudian menjadi 5.126.913 pada tahun 2015. Penyalahgunaan obat telah direnovasi dan disembuhkan diizinkan untuk menggunakan narkoba (kambuh). Laporan ini bertujuan untuk meninjau kembali hubungan antara suport keluarga dengan Peristiwa kambuh pelaku narkoba di rumah meredam tenjo laut di kabupaten kuningan 2016. Jenis penelitian yang digunakan adalah desain analitik cross sectional. Instrumen yang digunakan adalah kuesioner yang telah mengalami validitas ada 15 responden, uji validitas menunjukkan bahwa dukungan untuk keluarga 23 pertanyaan 4 tidak valid karena nilai r kurang dari r tabel (0,514). Pelaksanaan penelitian ini pada Mei 2016. Sampel 40 responden menggunakan total sampling dan data analisis menggunakan chi square. Berdasarkan pengolahan data diperoleh dukungan keluarga terhadap kategori baik yaitu sekitar (52,5%) dan kekambuhan mayoritas responden mengalami kekambuhan yaitu sekitar (65%). Dari analisis hubungan keluarga kekambuhan (kambuh) terhadap pelaku narkoba di Rumah Damping Tenjo Laut di Kabupaten Kuningan 2016 adalah p value 0,026. Kesimpulannya ada hubungan positif antara suport keluarga terhadap kejadian kambuh pelaku narkoba di rumah redaman tenjo laut di kabupaten kuningan 2016. Diperkirakan supervisi dan bantuan mantan pengguna narkoba harus lebih optimal untuk mengurangi kejadian kambuh dan penyalahgunaan narkoba bisa hidup sehat tanpa narkoba.  Kata kunci: Dukungan Keluarga, Kambuh  ABSTRACT The civil using drugs in indonesia has been increasing every year , in 2008 there are 3.362.527 people drugs abusers later became 5.126.913 in 2015. There were 51 cases of drug abuses in kuningan district in all 2015. Drugs abusers have renovated and healing allowed to use drugs ( relapse ) .Cause a recurrence can be caused by several factors that may be one of these factors family .This report aims to review the relationship between family suport to events the relapse of drugs abuser at rumah damping tenjo laut in kuningan district 2016. The kind of research use is analytic design cross sectional .Instrument used is a questionnaire that has undergone a validity there are 15 respondents , test validity suggests that support for the family of 23 questions 4 are not valid and variable a recurrence of 20 questions 8 invalid because the value of r less than the r table (0,514 ) .The implementation of this research on may 2016 .The sample 40 respondents were using a total sampling and analysis data using the chi square. Based on data processing obtained a family support of good category that is about ( 52,5 % ) and a recurrence the majority of respondents experienced a recurrence that is about ( 65% ) . From an analysis of the relationship between a family of a recurrence ( relapse ) on drugs abusers at Rumah Damping Tenjo Laut in Kuningan District 2016 is p value 0,026 . The conclusion is there a positive relationship between family suport to events the relapse of drugs abuser at Rumah damping tenjo laut in kuningan district 2016. Expected supervision and assistance former drug users must be more optimal to reduce incidence a recurrence and drugs abusers can healthy life without drugs.Keywords: Family Support, Relapse
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30

Li, Hengyan, and Shaowei Liu. "Traveling Waves in the Underdamped Frenkel–Kontorova Model." Discrete Dynamics in Nature and Society 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/7081804.

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31

Bowie, M. A., J. D. Layes, and M. E. Demont. "DAMPING IN THE HINGE OF THE SCALLOP PLACOPECTEN MAGELLANICUS." Journal of Experimental Biology 175, no. 1 (February 1, 1993): 311–15. http://dx.doi.org/10.1242/jeb.175.1.311.

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The family Pectinaceae are the only bivalves that have been well documented as swimmers (DeMont, 1992), although Ensis minor has been observed to swim (McMahon and McMahon, 1983). The behaviour was once regarded only as an escape response (Gade, 1981; McMahon and McMahon, 1983), but some studies suggest seasonal migrations are involved (Gruffydd, 1976; DeMont, 1990). DeMont (1990) suggests that they swim at the natural frequency of the shell-hinge system for more efficient use of energy.
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32

Lin, Guoguang, and Liping Guan. "Random Attractor Family for a Class of Stochastic Higher-Order Kirchhoff Equations." Journal of Mathematics Research 11, no. 3 (May 8, 2019): 23. http://dx.doi.org/10.5539/jmr.v11n3p23.

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A class of stochastic dynamical systems with strong damped stochastic higher order Kirchhoff equation solutions with white noise is studied. Firstly, the equation is transformed into a stochastic equation with random variables as parameters and without noise by using Ornstein-Uhlenbeck process. Secondly, the bounded stochastic absorption set is obtained by estimating the solution of the equation. Finally, the stochastic dynamical system is obtained by using the isomorphic mapping method and the compact embedding theorem. It is progressively compact, thus proving the existence of random attractors.
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33

Pippenger, Randall Todd. "Lives on hold: the Dampierre family, captivity and the crusades in thirteenth-century Champagne." Journal of Medieval History 44, no. 5 (October 20, 2018): 507–28. http://dx.doi.org/10.1080/03044181.2018.1519716.

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34

Carbinatto, M. C., and K. P. Rybakowski. "On convergence, admissibility and attractors for damped wave equations on squeezed domains." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 132, no. 4 (August 2002): 765–91. http://dx.doi.org/10.1017/s0308210500001876.

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Let be an arbitrary non-empty bounded Lipschitz domain in RM RN. Given > 0, squeeze by the factor in the y-direction to obtain the squeezed domain := {(x, y) | (x, y) }. Let and be positive constants. Consider the following semilinear damped wave equation on , where is the exterior normal vector field on and G is an appropriate nonlinearity, which ensures that (W) generates a (local) flow ̃ on X := H1() L2(). We show that there is a closed subspace X0 of X and a flow ̃0 on X0 that is the limit flow of the family ̃, > 0. We show that, as 0, the family ̃ converges in some singular sense to ̃ and establish a technical singular asymptotic compactness property. As a corollary, we obtain an upper-semicontinuity result for global attractors of the family ̃, 0, generalizing results obtained previously by Hale and Raugel for domains that are ordinate sets of a positive function.The results obtained here are also applied in our paper On a general Conley index continuation principle for singular perturbation problems to establish a singular Conley index continuation principle for damped wave equations on thin domains.
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35

Deng, Dingwen, and Chengjian Zhang. "A family of new fourth-order solvers for a nonlinear damped wave equation." Computer Physics Communications 184, no. 1 (January 2013): 86–101. http://dx.doi.org/10.1016/j.cpc.2012.08.019.

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36

belykh, Vladimir, Igor Blykh, Nikolai Komrakov, and Erik Moseklide. "Invariant manifolds and cluster synchronization in a family of locally coupled map lattices." Discrete Dynamics in Nature and Society 4, no. 3 (2000): 245–56. http://dx.doi.org/10.1155/s1026022600000236.

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This paper presents an analysis of the invariant manifolds for a general family of locally coupled map lattices. These manifolds define the different types of full, partial, and anti-phase chaotic synchronization that can arise in discrete dynamical systems. Existence of various invariant manifolds, self-similarity as well as orderings and embeddings of the manifolds of a coupled map array are established. A general variational equation for the stability analysis of invariant manifolds is derived, and stability conditions for full and partial chaotic synchronization of concrete coupled maps are obtained. The general results are illustrated through examples of three coupled two-dimensional standard maps with damping.
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37

Carvalho, Alexandre N., Jan W. Cholewa, and Tomasz Dłotko. "Equi-exponential attraction and rate of convergence of attractors with application to a perturbed damped wave equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144, no. 1 (January 30, 2014): 13–51. http://dx.doi.org/10.1017/s0308210511001235.

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We consider a family of bounded dissipative asymptotically compact semigroups depending on a parameter, and study the continuity properties of the corresponding family of its global attractors. We exploit the idea of the uniform exponential attraction property to discuss the continuity properties of the family of attractors and estimate the rate of convergence of the approximating attractors to the limit one. Showing a range of applications of an abstract framework, we focus much of our attention on a perturbed damped wave equation. In this latter case our results involve nonlinearities with critical exponents, for which the continuity of the family of attractors is concluded, including the rate of convergence and the regularity of the limit attractor. This complements the results in the literature.
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38

Luo, Yongbing. "Improved decay of solution for strongly damped nonlinear wave equations." Mathematical Biosciences and Engineering 20, no. 3 (2023): 4865–76. http://dx.doi.org/10.3934/mbe.2023225.

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<abstract><p>In this work, we deal with the initial boundary value problem of solutions for a class of linear strongly damped nonlinear wave equations $ u_{tt}-\Delta u -\alpha \Delta u_t = f(u) $ in the frame of a family of potential wells. For this strongly damped wave equation, we not only prove the global-in-time existence of the solution, but we also improve the decay rate of the solution from the polynomial decay rate to the exponential decay rate.</p></abstract>
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39

Huang, Wen-Yi, and Wen-Li Chen. "Global Existence and Blow-Up of Solutions for Nonlinear Klein-Gordon Equation with Damping Term and Nonnegative Potentials." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/142892.

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This paper is concerned with the nonlinear Klein-Gordon equation with damping term and nonnegative potentials. We introduce a family of potential wells and discuss the invariant sets and vacuum isolating behavior of solutions. Using the potential well argument, we obtain a new existence theorem of global solutions and a blow-up result for solutions in finite time.
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40

Reyes-Cortés, Fernando, César Chávez-Olivares, and Emilio J. González-Galván. "A Family of Hyperbolic-Type Explicit Force Regulators with Active Velocity Damping for Robot Manipulators." Journal of Robotics 2018 (2018): 1–15. http://dx.doi.org/10.1155/2018/9324623.

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This paper addresses the explicit force regulation problem for robot manipulators in interaction tasks. A new family of explicit force-control schemes is presented, which includes a term driven by a large class of saturated-type hyperbolic functions to handle the force error. Also, an active velocity damping term with the purpose of obtaining energy dissipation on the contact surface is incorporated plus compensation for gravity. In order to ensure asymptotic stability of the closed-loop system equilibrium point in Cartesian space, we propose a strict Lyapunov function. A force sensor placed at the end-effector of the robot manipulator is used in order to feed back the measure of the force error in the closed-loop, and an experimental comparison of the performanceL2-norm between 5 explicit force control schemes, which are the classical proportional-derivative (PD), arctangent, and square-root controls and two members of the proposed control family, on a two-degree-of-freedom, direct-drive robot manipulator, is presented.
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41

Guo, Ze Ying. "A Taylor Series Integration Method with Coupling in Structural Dynamics." Applied Mechanics and Materials 166-169 (May 2012): 9–13. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.9.

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Based on the coupled precise time integration method and basic assumptions of constant average acceleration method in Newmark family, implicit series solution of structural dynamic equation is put forward by introducing the Taylor series expansion. Relevant time step integration formulas were designed. Stability and accuracy of the method were analyzed. Stability analyses show that the coupling implicit method is stable when damping ratio is equal to 0, and is conditionally stable when damping ratio are other values. The results show that the accuracy of the algorithm can be controlled by choosing the number of truncation order of Taylor series expansion and is better than that of traditional scheme with the increase of time step. Number examples are given to demonstrate the validity of the proposed method.
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42

Jia, Xinyue. "Analytical solutions to the isothermal Euler equations with time-dependent damping." Journal of Physics: Conference Series 2543, no. 1 (July 1, 2023): 012007. http://dx.doi.org/10.1088/1742-6596/2543/1/012007.

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Abstract In this paper, we construct a class of analytical solutions to the one dimensional compressible isothermal Euler equations with time-dependent damping. By introducing a special density function ρ(x, t) = e c(t)x+d(t), we obtain a family of analytical solutions. A sufficient condition for the solution to blow up in finite time is given. On the basis of the conclusion, the analytical solutions to the initial boundary value problem of the pressureless Euler equations are obtained.
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43

Shaw, A. D., A. R. Champneys, and M. I. Friswell. "Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2192 (August 2016): 20160303. http://dx.doi.org/10.1098/rspa.2016.0303.

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Sudden onset of violent chattering or whirling rotor–stator contact motion in rotational machines can cause significant damage in many industrial applications. It is shown that internal resonance can lead to the onset of bouncing-type partial contact motion away from primary resonances. These partial contact limit cycles can involve any two modes of an arbitrarily high degree-of-freedom system, and can be seen as an extension of a synchronization condition previously reported for a single disc system. The synchronization formula predicts multiple drivespeeds, corresponding to different forms of mode-locked bouncing orbits. These results are backed up by a brute-force bifurcation analysis which reveals numerical existence of the corresponding family of bouncing orbits at supercritical drivespeeds, provided the damping is sufficiently low. The numerics reveal many overlapping families of solutions, which leads to significant multi-stability of the response at given drive speeds. Further, secondary bifurcations can also occur within each family, altering the nature of the response and ultimately leading to chaos. It is illustrated how stiffness and damping of the stator have a large effect on the number and nature of the partial contact solutions, illustrating the extreme sensitivity that would be observed in practice.
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44

Salas, Alvaro H., S. A. El-Tantawy, and Noufe H. Aljahdaly. "An Exact Solution to the Quadratic Damping Strong Nonlinearity Duffing Oscillator." Mathematical Problems in Engineering 2021 (January 18, 2021): 1–8. http://dx.doi.org/10.1155/2021/8875589.

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The nonlinear equations of motion such as the Duffing oscillator equation and its family are seldom addressed in intermediate instruction in classical dynamics; this one is problematic because it cannot be solved in terms of elementary functions before. Thus, in this work, the stability analysis of quadratic damping higher-order nonlinearity Duffing oscillator is investigated. Hereinafter, some new analytical solutions to the undamped higher-order nonlinearity Duffing oscillator in the form of Weierstrass elliptic function are obtained. Posteriorly, a novel exact analytical solution to the quadratic damping higher-order nonlinearity Duffing equation under a certain condition (not arbitrary initial conditions) and in the form of Weierstrass elliptic function is derived in detail for the first time. Furthermore, the obtained solutions are camped to the Runge–Kutta fourth-order (RK4) numerical solution.
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45

SEFTON, TOM, MARIA EVANDROU, and JANE FALKINGHAM. "Family Ties: Women's Work and Family Histories and their Association with Incomes in Later Life in the UK." Journal of Social Policy 40, no. 1 (April 12, 2010): 41–69. http://dx.doi.org/10.1017/s0047279410000255.

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AbstractThis article examines the relationship between the family and work histories of older women and their personal incomes in later life, using retrospective data from the first 15 waves of the British Household Panel Survey. The association between women's family histories and their incomes later in life are relatively weak, explaining only a small proportion of the overall variation in older women's incomes. Divorce, early widowhood and re-marriage are not associated with any significant differences in older women's incomes, while motherhood is only associated with a small reduction in incomes later in life. While there are significant differences in the work histories of older women with different family histories, this translates into relatively small differences in their personal incomes, because the types of employment career pursued by most women are not associated with significantly higher retirement incomes and because public transfers dampen work history-related differentials, especially for widows. On the one hand, this could be seen as a positive finding in that the ‘pension penalty’ associated with life-course events such as motherhood and divorce is not as severe as often anticipated. On the other hand, the main reason for this is that the pension returns to working longer are relatively low, particularly for women with few qualifications. The analysis suggests that women retiring over the next two decades are unlikely to benefit significantly from the additional years they have spent in employment, because most of this increase has been in part-time employment. The article highlights the tensions between two objectives: rewarding work, and protecting the most vulnerable, such as carers, long-term disabled and unemployed. Resolving this dilemma involves moving away from a close association between pension entitlements and work history and towards universal entitlement based on a citizen's pension.
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46

Schubert, Till, Jan Martin Brockmann, Johannes Korte, and Wolf-Dieter Schuh. "On the Family of Covariance Functions Based on ARMA Models." Engineering Proceedings 5, no. 1 (July 5, 2021): 37. http://dx.doi.org/10.3390/engproc2021005037.

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In time series analyses, covariance modeling is an essential part of stochastic methods such as prediction or filtering. For practical use, general families of covariance functions with large flexibilities are necessary to model complex correlations structures such as negative correlations. Thus, families of covariance functions should be as versatile as possible by including a high variety of basis functions. Another drawback of some common covariance models is that they can be parameterized in a way such that they do not allow all parameters to vary. In this work, we elaborate on the affiliation of several established covariance functions such as exponential, Matérn-type, and damped oscillating functions to the general class of covariance functions defined by autoregressive moving average (ARMA) processes. Furthermore, we present advanced limit cases that also belong to this class and enable a higher variability of the shape parameters and, consequently, the representable covariance functions. For prediction tasks in applications with spatial data, the covariance function must be positive semi-definite in the respective domain. We provide conditions for the shape parameters that need to be fulfilled for positive semi-definiteness of the covariance function in higher input dimensions.
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47

Du, Jun, Dongling Cui, Yeguo Sun, and Jin Xu. "Approximate Controllability for a Kind of Fractional Neutral Differential Equations with Damping." Mathematical Problems in Engineering 2020 (October 21, 2020): 1–9. http://dx.doi.org/10.1155/2020/7592818.

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This paper gains several meaningful results on the mild solutions and approximate controllability for a kind of fractional neutral differential equations with damping (FNDED) and order belonging to 1,2 in Banach spaces. At first, a new expression for the mild solutions of FNDED via the (p, q)-regularized operator family and the technique of Laplace transform is acquired. Then, we consider the approximate controllability of FNDED by means of the approximate sequence method, and simultaneously, some applicable sufficient conditions are obtained.
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48

Lv, Penghui, Yan Liu, and Shasha Yu. "Long-Term Dynamic Behavior of a Higher-Order Coupled Kirchhoff Model with Nonlinear Strong Damping." Journal of Mathematics 2022 (June 13, 2022): 1–12. http://dx.doi.org/10.1155/2022/7044906.

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In this paper, we study the long-time dynamics problem of a class of higher-order Kirchhoff coupled systems with nonlinear strong damping. The existence and uniqueness of the solutions of these equations in different spaces are proved by prior estimation and Faedo–Galerkin method; secondly, the family of global attractors of these problems is proved by using the compactness theorem. The results of the Kirchhoff coupled group are promoted through research.
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49

Truong, Thi Nhan. "Classification of Blow-up and Global Existence of Solutions to a System of Petrovsky Equations." Electronic Journal of Applied Mathematics 1, no. 2 (September 9, 2023): 29–59. http://dx.doi.org/10.61383/ejam.20231231.

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In this paper, we investigate global existence, uniform decay, and blow-up of solutions for a class of system of Petrovsky equations containing nonlinear damping and sources. By introducing a family of potential wells, we not only obtain the invariant sets and vacuum isolating of solutions but also give some threshold results of global existence and nonexistence of solutions. Furthermore, by using energy techniques, we also establish certain qualitative estimates for solution.
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50

Collier, Angela, Isaac Shlosman, and Clayton Heller. "What makes the family of barred disc galaxies so rich: damping stellar bars in spinning haloes." Monthly Notices of the Royal Astronomical Society 476, no. 1 (February 2, 2018): 1331–44. http://dx.doi.org/10.1093/mnras/sty270.

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