Time-varying Equation Of State Research Articles

A Reliability-Based Robust Design Optimization Method for Rolling Bearing Fatigue under Cyclic Load Spectrum

Reliability-based robust design methods have been widely used in the field of product design; however, they are difficult to apply to the fatigue reliability design process of rolling bearings due to the problems of determining fatigue accumulated damage caused by the internal cyclic time-varying load distribution of rolling bearings and the computational cost of time-varying reliability. Therefore, a reliability-based robust design method for rolling bearing fatigue failure is proposed, which derives the formula for fatigue accumulated damage of a rolling bearing under cyclic load spectrum and significantly reduces the computational cost of rolling bearing time-varying reliability compared with existing methods. First, the state response of a rolling bearing under random design parameters is obtained by finite element simulation. Then, the adaptive kriging method is used to characterize the correlation between the random parameters and the state response. The Miner fatigue cumulative damage theory is improved and the rolling bearing fatigue time-varying equation of state under cyclic load spectrum is derived. Subsequently, a fatigue time-varying reliability model based on an improved fourth-order moment method is developed, and a reliability robust optimization design method is proposed. Finally, a rolling bearing example is presented to demonstrate that the method achieves time-varying fatigue reliability design under cyclic load spectrum and effectively improves the reliability and robustness of the product design.

Trajectory tracking control of upper limb rehabilitation robot based on optimal discrete sliding mode control

In this paper, an optimal sliding mode control method for trajectory tracking of discrete-time systems based on linear quadratic regulator is proposed to improve the trajectory tracking control accuracy and robustness of upper limb rehabilitation robot under the condition of highly nonlinearities, external disturbances, and unmodeled dynamics. Firstly, considering the uncertainty of the mass and moment of inertia of the connecting rod arm of the upper limb rehabilitation robot and the uncertainty of external interference, the dynamic model of the upper limb rehabilitation robot is established by using the Euler Lagrange method, and the linear time-varying state equation of the rehabilitation robot system under the influence of both nonlinear and uncertain factors is derived. Secondly, directing at the chattering problem in sliding mode control, a sliding mode control method based on a new discrete time reaching law is designed to reduce the amplitude of chattering in the control input signal of the upper limb rehabilitation robot system and improve the tracking speed. Furthermore, combined with linear quadratic optimal control, the optimal discrete integral sliding mode control law (LQRSMC) is finally obtained. Meanwhile, for the sake of reducing the influence of the uncertain signal on the system, a robust control law is adopted to estimate and compensate the uncertain interference. The stability of the upper limb rehabilitation robot system is verified by the sliding mode approach condition of the discrete system. Finally, the genetic algorithm is used to further optimize the weighted value, and MATLAB/Simulink is used to simulate the state trajectory of the upper limb rehabilitation robot under various weighted values. The control strategy can not only effectively weaken the trajectory tracking oscillation problem of the upper limb rehabilitation robot, but also overcome the external disturbance and modeling uncertainty, while ensuring the robustness of the rehabilitation robot system.

Reliability Evaluation of Smart Substation Based on Time-Varying Probabilistic Hybrid Attack Graph

A substation is the portion of a power grid that forms a link between the cyber system and the physical system. Reliability evaluation of smart substations based on a time-varying probabilistic hybrid attack graph (TVPHAG) is studied in this paper. First, the topology network of the smart substation is established, whose attributes are represented by probability. Then, in order to solve the problem of asynchrony in the cyber-physical system and the hybrid caused by heterogeneity, time-varying state equation in topology and cuts in algebra are introduced to TVPHAG. Based on TVPHAG, the evaluation of the reliability of cyber-physical systems with multiple equipment and multiple timescales is established. On this basis, the influences of physical conditions, cyberattacks, physical attacks, and cyber-physical attacks on substations are analyzed, respectively. Finally, the simulation shows that the method is effective in evaluating the reliability of smart substations, providing a new method for the evaluation of reliability.

Reconstructing the statefinder hierarchy for an interacting cosmology

This paper studies an interacting cosmology in a spatially flat universe. Here, we have reconstructed the interaction term, Q, between a cold dark matter (DM) fluid and a dark energy (DE) fluid, as well as a time-varying equation of state (EoS) parameter ωDE, and have explored its evolutionary trajectories in the second members of the statefinder hierarchy, allowing us to establish differences when they are compared with those obtained in other non-interacting models. Likewise, both Q and ωDE have been modeled in terms of the Chebyshev polynomials. Then, via a Markov chain Monte Carlo (MCMC) method, we have constrained the model parameter space by using a combined analysis of geometric data. Our results show that an interacting model can be distinguished well from the standard concordance model at the present time by using any combination of the second members of the statefinder hierarchy. In this way, different DE scenarios could be compared and distinguished between them.

The promising future of a robust cosmological neutrino mass measurement

We forecast the sensitivity of thirty-five different combinations of future Cosmic Microwave Background and Large Scale Structure data sets to cosmological parameters and to the total neutrino mass. We work under conservative assumptions accounting for uncertainties in the modelling of systematics. In particular, for galaxy redshift surveys, we remove the information coming from non-linear scales. We use Bayesian parameter extraction from mock likelihoods to avoid Fisher matrix uncertainties. Our grid of results allows for a direct comparison between the sensitivity of different data sets. We find that future surveys will measure the neutrino mass with high significance and will not be substantially affected by potential parameter degeneracies between neutrino masses, the density of relativistic relics, and a possible time-varying equation of state of Dark Energy.

Time-delay cosmography: increased leverage with angular diameter distances

Strong lensing time-delay systems constrain cosmological parameters via the so-called time-delay distance and the angular diameter distance to the lens. In previous studies, only the former information was used in forecasting cosmographic constraints. In this paper, we show that the cosmological constraints improve significantly when the latter information is also included. Specifically, the angular diameter distance plays a crucial role in breaking the degeneracy between the curvature of the Universe and the time-varying equation of state of dark energy. Using a mock sample of 55 bright quadruple lens systems based on expectations for ongoing/future imaging surveys, we find that adding the angular diameter distance information to the time-delay distance information and the Planck's measurements of the cosmic microwave background anisotropies improves the constraint on the constant equation of state by 30%, on the time variation in the equation of state by a factor of two, and on the Hubble constant in the flat ΛCDM model by a factor of two. Therefore, previous forecasts for the statistical power of time-delay systems were overly pessimistic, i.e., time-delay systems are more powerful than previously appreciated.

Adiabatic initial conditions for perturbations in interacting dark energy models

We present a new systematic analysis of the early radiation era solution in an interacting dark energy model to find the adiabatic initial conditions for the Boltzmann integration. In a model where the interaction is proportional to the dark matter density, adiabatic initial conditions and viable cosmologies are possible if the early-time dark energy equation of state parameter is $w_e > -4/5$. We find that when adiabaticity between cold dark matter, baryons, neutrinos and photons is demanded, the dark energy component satisfies automatically the adiabaticity condition. As supernovae Ia or baryon acoustic oscillation data require the recent-time equation of state parameter to be more negative, we consider a time-varying equation of state in our model. In a companion paper [arXiv:0907.4987] we apply the initial conditions derived here, and perform a full Monte Carlo Markov Chain likelihood analysis of this model.

Observational constraints on an interacting dark energy model

We use observations of cosmic microwave background anisotropies, supernova luminosities and the baryon acoustic oscillation signal in the galaxy distribution to constrain the cosmological parameters in a simple interacting dark energy model with a time-varying equation of state. Using a Monte Carlo Markov Chain technique we determine the posterior likelihoods. Constraints from the individual data sets are weak, but the combination of the three data sets confines the interaction constant $\Gamma$ to be less than 23% of the expansion rate of the Universe $H_0$; at 95% CL $-0.23 < \Gamma/H_0 < +0.15$. The CMB acoustic peaks can be well fitted even if the interaction rate is much larger, but this requires a larger or smaller (depending on the sign of interaction) matter density today than in the non-interacting model. Due to this degeneracy between the matter density and the interaction rate, the only observable effect on the CMB is a larger or smaller integrated Sachs-Wolfe (ISW) effect. While SN or BAO data alone do not set any direct constraints on the interaction, they exclude the models with very large matter density, and hence indirectly constrain the interaction rate when jointly analysed with the CMB data. To enable the analysis described in this paper, we present in a companion paper [arXiv:0907.4981] a new systematic analysis of the early radiation era solution to find the adiabatic initial conditions for the Boltzmann integration.

High-redshift star formation rate up to z ∼ 8.3 derived from gamma-ray bursts and influence of background cosmology

Abstract The high-redshift star formation rate (SFR) is difficult to measure directly even by modern approaches. Long-duration gamma-ray bursts (GRBs) can be detected to the edge of the visible universe because of their high luminosities. The collapsar model of long GRBs indicates that they may trace the star formation history. So, long GRBs may be a useful tool of measuring the high-redshift SFR. Observations show that long GRBs prefer to form in a low-metallicity environment. We study the high-redshift SFR up to z∼ 8.3 considering the Swift GRBs tracing the star formation history and the cosmic metallicity evolution in different background cosmological models including Λ cold dark matter (ΛCDM), quintessence, quintessence with a time-varying equation of state and brane-world model. We use latest Swift GRBs including two highest-z GRBs, GRB 080913 at z= 6.7 and GRB 090423 at z= 8.3. We find that the SFR at z &amp;gt; 4 shows a steep decay with a slope of ∼−5.0 in ΛCDM. In the other three models, the high-redshift SFR is slightly different from ΛCDM model and also shows a steep decay.

Estimation of Time-Varying Connectivity Patterns Through the Use of an Adaptive Directed Transfer Function

Frequency-derived identification of the propagation of information between brain regions has quickly become a popular area in the neurosciences. Of the various techniques used to study the propagation of activation within the central nervous system, the directed transfer function (DTF) has been well used to explore the functional connectivity during a variety of brain states and pathological conditions. However, the DTF method assumes the stationarity of the neural electrical signals and the time invariance of the connectivity among different channels over the investigated time window. Such assumptions may not be valid in the abnormal brain signals such as seizures and interictal spikes in epilepsy patients. In the present study, we have developed an adaptive DTF (ADTF) method through the use of a multivariate adaptive autoregressive model to study the time-variant propagation of seizures and interictal spikes in simulated electrocorticogram (ECoG) networks. The time-variant connectivity reconstruction is achieved by the Kalman filter algorithm, which can incorporate time-varying state equations. We study the performance of the proposed method through simulations with various propagation models using either sample seizures or interictal spikes as the source waveform. The present results suggest that the new ADTF method correctly captures the temporal dynamics of the propagation models, while the DTF method cannot, and even returns erroneous results in some cases. The present ADTF method was tested in real epileptiform ECoG data from an epilepsy patient, and the ADTF results are consistent with the clinical assessments performed by neurologists.

Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe

We investigate the third-order density perturbation and the one-loop correction to the linear power spectrum in the dark-energy cosmological model. Our main interest is to understand the dark-energy effect on baryon acoustic oscillations in a quasi-nonlinear regime ($k \approx 0.1h$/Mpc). Analytical solutions and simple fitting formulae are presented for the dark-energy model with the general time-varying equation of state $w(a)$. It turns out that the power spectrum coincides with the approximate result based on the EdS (Einstein de-Sitter) model within 1% for $k<0.4h/$Mpc at $z=0$ in the WMAP (Wilkinson Microwave Anisotropy Probe) 5yr best-fitting cosmological model, which suggests that the cosmological dependence is very small.

Covariance of dark energy parameters and sound speed constraints from large H i surveys

A B ST R A C T An interesting probe ofthe nature ofdark energy isthe m easure ofitssound speed, cs.W e review the signicance for constraining sound speed m odels ofdark energy using large neutralhydrogen (HI)surveyswith the Square Kilom etre Array (SKA). Our analysis considers the eect on the sound speed m easurem ent that arises from thecovarianceof cs with thedark energy density, de,and a tim e-varyingequation of state, w(a)= w0 + (1 a)wa.W end thattheapproxim atedegeneracy between dark energy param etersthatarisesin powerspectrum observationsis lifted through red- shifttom ography ofthe HI-galaxy angularpowerspectrum ,resulting in sound speed constraints that are not severely degraded.The cross-correlation ofthe galaxy and theintegrated Sachs-W olfe(ISW )eectspectra contributesapproxim ately 10percent oftheinform ation thatisneeded to distinguish variationsin thedark energy param - eters,and m ostofthe discrim inating signalcom esfrom the galaxy auto-correlation spectrum .W ealsond thatthesound speed constraintsareweakly sensitivetotheHI biasm odel.These constraintsdo notim provesubstantially fora signicantly deeper HIsurvey sincem ostoftheclusteringsensitivity tosound speed variationsarisesfrom z �1:5.A detection ofm odelswith sound speedsclose to zero, cs�0:01; ispossible fordark energy m odelswith w � 0:9. K ey w ords: cosm ologicalparam eters-large-scalestructureoftheuniverse-cosm ic m icrowavebackground -radio lines:galaxies

Probing the early universe with inflationary gravitational waves

Near comoving wave number $k$, the gravitational-wave background (GWB) from inflation carries information about the physical conditions near two moments in cosmic history: the moment when $k$ ``left the horizon'' during inflation, and the moment when it ``re-entered the horizon'' after inflation. We investigate the extent to which this information can be extracted if the GWB is measured by a combination of cosmic-microwave-background polarization experiments on large scales and space-based laser-interferometer experiments on small scales. To disentangle this information, we derive a new gravitational-wave transfer function that incorporates a number of physical effects that were treated less accurately, less generally, or were missing altogether in previous treatments. In particular, it incorporates: (i) dark energy with time-varying equation of state $w(z)$; (ii) tensor anisotropic stress due to free-streaming relativistic particles in the early universe; and (iii) a variety of physical effects that cause deviations from the standard equation of state $w=1/3$ during the radiation era. Based on this transfer function, we consider the degree to which the GWB can be used to test inflation and to probe the ``primordial dark age'' between the end of inflation and the electroweak phase transition.

Gamma-ray burst neutrinos, Lorenz invariance violation and the influence of backgroundcosmology

Modern ideas in quantum gravity predict the possibility of Lorenz invariance violation(LIV) manifested, for example, by energy-dependent modification of the standardrelativistic dispersion relation. In a recent paper, Jacob and Piran proposed that time offlight delays in high-energy neutrinos emitted by gamma-ray bursts (GRBs) located atcosmological distances can become a valuable tool for setting limits on LIV theories.However, current advances in observational cosmology suggest that our Universeis dominated by dark energy with relatively little guidance on its nature, thusleading to several cosmological scenarios that are compatible with observations.In this paper we raise the issue of how important, in the context of testing LIV theories, is ourknowledge of the background cosmological model. Specifically we calculate expected time lagsfor high-energy (100 TeV) neutrinos in different cosmological models. Out of many particularmodels of dark energy we focus on five as representative for various competing approaches:ΛCDM, quintessence, quintessence with time-varying equation of state, brane-world andgeneralized Chaplygin gas.The conclusion is that better understanding of a dark energy dominated Universe is crucialfor testing LIV theories with cosmological sources like GRBs. Theoretically one may alsoinvert this argument by saying that if an LIV dispersion relation was provenexperimentally and its parameters were constrained then time delays from GRBs couldbecome a new kind of cosmological test.

Power-law parametrized quintessence model

We propose a simple power-law parametrized quintessence model with time-varying equation of state and obtain corresponding quintessence potential of this model. This model is compared with Supernova Type Ia (SNIa) Gold sample data, size of baryonic acoustic peak from Sloan Digital Sky Survey (SDSS), the position of the acoustic peak from the CMB observations and structure formation from the 2dFGRS survey and put constrain on the parameters of model. The parameters from the best fit indicates that the equation of state of this model at the present time is ${w}_{0}=\ensuremath{-}{1.40}_{\ensuremath{-}0.65}^{+0.40}$ at $1\ensuremath{\sigma}$ confidence level. Finally we calculate the age of universe in this model and compare it with the age of old cosmological objects.

Virialization of cosmological structures in models with time-varying equation of state

We study the virialization of the cosmic structures in the framework of flat cosmological models where the dark energy component plays an important role in the global dynamics of the Universe. In particular, our analysis focuses on the study of the spherical matter perturbations, as the latter decouple from the background expansion, start to 'turn around' and finally collapse. We generalize this procedure, taking into account models with an equation of state which vary with time, and provide a complete formulation of the cluster virialization attempting to address the non-linear regime of structure formation. In particular, assuming that clusters have collapsed prior to the epoch of z f ≃ 1.4, in which the most distant cluster has been found, we show that the behaviour of the spherical collapse model depends on the functional form of the equation of state.

Dark energy evolution and the curvature of the universe from recent observations

We discuss the constraints on the time-varying equation of state for dark energy and the curvature of the universe using observations of type Ia supernovae from Riess et al. and the most recent Supernova Legacy Survey (SNLS), the baryon acoustic oscillation peak detected in the SDSS luminous red galaxy survey and cosmic microwave background. Because of the degeneracy among the parameters which describe the time dependence of the equation of state and the curvature of the universe, the constraints on them can be weakened when we try to constrain them simultaneously, in particular, when we use a single observational data. However, we show that we can obtain relatively severe constraints when we use all data sets from observations above even if we consider the time-varying equation of state and do not assume a flat universe. We also found that the combined data set favors a flat universe even if we consider the time variation of the dark energy equation of state.

Strong lensing efficiency of galaxy clusters in dark energy cosmologies

We study the efficiency for producing strong gravitational lensing events of galaxy clusters numerically simulated in different dark-energy cosmologies with constant and time-variable equation of state, and we compare the results with those obtained in standard ACDM and OCDM models. Our main results are (1) that the expected abundance of gravitational arcs with large length-to-width ratio depends on the equation of state of dark energy at the epoch of formation of the halo; and (2) that the high sensitivity of strong-lensing cross sections of galaxy clusters to dynamical processes like mergers, which was found in earlier studies, varies substantially between different cosmologies, being stronger for models in which halos are less concentrated. As expected, the largest differences in the lensing optical depth occur at intermediate and high redshift.

Strong lensing by cluster-sized halos in dark energy cosmologies

We perform a set of ray-tracing simulations, using numerical cluster models, aiming at evaluating how the galaxy cluster efficiency for producing strong lensing events changes in different cosmological models with dark energy. The sample of investigated clusters for which we present our results here is composed by seven dark matter halos. Each of them was simulated in eight different cosmological models with constant and time-variable equation of state of dark energy. For all the clusters in the sample, we have measured the lensing cross-sections for producing giant arcs, i.e., arcs having a minimum length-to-width ratio. We find that the lensing cross-section for giant arcs is sensitive to the equation of state of quintessence. Indeed, the optical depth, which can be translated into a number of arcs by multiplying by the correct density of source galaxy on the sky, spans more than one order of magnitude among different cosmological models.

Phenomenological parameterization of quintessence

We propose a simple phenomenological parameterization of quintessence with a time-varying equation of state. In particular, it accounts for the possibility of early dark energy. The quintessence potential can be reconstructed in terms of the present fraction in dark energy, the present equation of state and the amount of early dark energy.