Dynamic State Equations Research Articles

Tightening the reins on nonminimal dark sector physics: Interacting dark energy with dynamical and nondynamical equation of state

We present a comprehensive reassessment of the state of interacting dark energy (DE) cosmology, namely models featuring a nongravitational interaction between dark matter and DE. To achieve high generality, we extend the dark sector physics by considering two different scenarios: a nondynamical DE equation of state w0≠−1, and a dynamical w(a)=w0+wa(1−a). In both cases, we distinguish two different physical regimes resulting from a phantom or quintessence equation of state. To circumvent early time superhorizon instabilities, the energy-momentum transfer should occur in opposing directions within the two regimes, resulting in distinct phenomenological outcomes. We study quintessence and phantom nondynamical and dynamical models in light of two independent cosmic microwave background (CMB) experiments—the Planck satellite and the Atacama Cosmology Telescope. We analyze CMB data both independently and in combination with supernovae distance moduli measurements from the catalog and baryon acoustic oscillations from the SDSS-IV eBOSS survey. Our results update and extend the state-of-the-art analyses, significantly narrowing the parameter space allowed for these models and limiting their overall ability to reconcile cosmological tensions. Although considering different combinations of data leaves some freedom to increase H0 towards the value measured by the SH0ES collaboration, our most constraining dataset (CMB+baryon acoustic oscillations+supernovae) indicates that fully reconciling the tension solely within the framework of interacting DE remains challenging. Published by the American Physical Society 2024

A Kalman filter approach for state estimation in weakly monitored active distribution networks

Distribution networks are becoming active to improve security of operation under high net load volatility. Yet, the deployment of active devices creates new challenges to the operation of the weakly monitored distribution networks. One such challenge is to improve state estimation accuracy. This paper proposes to improve the estimation process of active distribution networks by embedding the active devices dynamics into the state dynamic equations, instead of translating them into the static measurement models. This is carried out with the Kalman filter (KF) by making use of the dynamic models and the static measurement models we have proposed earlier for active distribution networks. The paper provides the main steps to implement the estimation framework and illustrates its advantages under slow-responsive distribution network interactions. Results obtained show that the proposed KF approach has better performance than the static counterparts for networks subjected to multiple control decisions — the case where the relevance information on dynamics surpasses the relevance of setpoint information on static models alone.

Reconstruction of F(T,TG) gravity model with scalar fields

In this paper, we investigate the scalar field dark energy (DE) models within the context of [Formula: see text] gravity. Scalar field models are known for their dynamic nature. Parameters in the dynamical equation of state are responsible for the acceleration of the cosmos in recent epochs. We determined that the power-law cosmology fits the OHD and Pantheon data nicely. Using the Bayesian analysis and likelihood function in conjunction with the Markov Chain Monte Carlo (MCMC) method, we examine the three sets of the model parameters [Formula: see text] [Formula: see text] obtained by 57 points of the [Formula: see text] data, [Formula: see text] [Formula: see text] 1048 points of the Pantheon data and [Formula: see text] [Formula: see text] by using joint data ([Formula: see text]), respectively. We solved the modified Einstein’s field equations by taking the bulk-viscosity component [Formula: see text]. We also establish a correspondence between the [Formula: see text] gravity model and scalar field DE models such as quintessence, [Formula: see text]-essence, and DBI-essence. The nature of scalar fields and their corresponding potentials are being graphically analyzed. To check the validity of [Formula: see text] gravity model, we also analyze the behavior of energy conditions.

Research on unmanned navigation and PID control method for aircraft tractor

Unmanned navigation and control systems are gaining traction in various industries, including aviation. The related issues of control systems are also hot topics in research. This paper comprehensively studies the application of unmanned navigation and the implementation of proportional integral differential (PID) control methods for aircraft tractors. Aiming at the characteristics of large deviation of turning trajectory angle error and long lag time in the process of an unmanned tractor, the dynamic characteristics and state equation of the unmanned tractor are established by the PID method, and the motion equation is established by the Cartesian coordinate system. Finally, the simulation results show that the proposed method has good dynamic stability and rapidity. Compared with proportional control or integral control alone, the PID control system has better stability and a faster frequency response, which can be obtained that the PID control algorithm can effectively improve the work efficiency of the unmanned tractor and reduce its instability and slow response.

NONLINEAR EFFECTS IN CRYSTALLINE SOLIDS WITH SATURATION OF AMPLITUDE-DEPENDENT INTERNAL FRICTION, DECREASING WITH IN-CREASING FREQUENCY

As a result of modification of quasi-static elastic and inelastic hysteresis, dynamic hysteresis equations of state of crystalline solids with frequency-dependent saturation of amplitude-dependent internal friction decreasing with increasing frequency are proposed. The nonlinear propagation of initially harmonic longitudinal elastic waves in rods made of such materials is investigated by the perturbation method. Numerical, graphical and comparative analysis of the obtained solutions is carried out and characteristic amplitude-frequency dependenc-es of nonlinear wave effects are revealed. A method for determining the type of dynamic hysteresis for crystal-line solids with frequency-dependent saturation of amplitude-dependent internal friction is proposed.

Positioning of Tower Crane Trolley Based on D-S Evidence Theory and Kalman Filter

Due to the complex structure of the tower crane and the signal noise, it is difficult to estimate and predict the real position signal, which may lead to inaccurate positioning of the tower crane trolley. A tower crane positioning algorithm based on D-S evidence theory and unscented Kalman filter (DS-UKF) is established and developed. First, the nonlinear dynamic model, state equation, and detection equation of the tower crane are constructed based on the complex structure of the tower crane. Second, the arm angle is estimated, and the distance between the trolley and the root of the arm is positioned. Finally, in order to calculate the weight of a single sensor, the D-S evidence theory is used to process the measurement information of the sensor and the estimated value of the filter. The Kalman filter, which has good signal tracking and estimation ability, is used to predict and estimate the position of the trolley. The accurate positioning of the tower crane trolley is realized through the organic fusion of information. The simulation results show the effectiveness of the DS-UKF positioning algorithm.

The Mira–Titan Universe – IV. High-precision power spectrum emulation

ABSTRACT Modern cosmological surveys are delivering data sets characterized by unprecedented quality and statistical completeness; this trend is expected to continue in the future as new ground- and space-based surveys come online. In order to maximally extract cosmological information from these observations, matching theoretical predictions are needed. At low redshifts, the surveys probe the non-linear regime of structure formation where cosmological simulations are the primary means of obtaining the required information. The computational cost of sufficiently resolved large-volume simulations makes it prohibitive to run very large ensembles. Nevertheless, precision emulators built on a tractable number of high-quality simulations can be used to build very fast prediction schemes to enable a variety of cosmological inference studies. We have recently introduced the Mira–Titan Universe simulation suite designed to construct emulators for a range of cosmological probes. This gravity-only set of simulations covers the standard six cosmological parameters {ωm, ωb, σ8, h, ns, w0} and, in addition, includes massive neutrinos and a dynamical dark energy equation of state {ων, wa}. In this paper, we present the final emulator for the matter power spectrum based on 111 cosmological simulations, each covering a (2.1 Gpc)3 volume and evolving 32003 particles. An additional set of 1776 lower resolution simulations and TimeRG perturbation theory results for the power spectrum are used to cover scales straddling the linear to mildly non-linear regimes (maximum wavenumber k = 5 Mpc−1). The emulator provides predictions at the 2–3 per cent level of accuracy over a wide range of cosmological parameters and is publicly released as part of this paper.

Static and dynamic analyses of traditional Chinese timber columns under horizontal accelerations

Traditional Chinese timber columns are prone to rocking and sliding because the column feet are directly placed on foundation stones. Determining the motion of columns under horizontal accelerations is essential to preventing the collapse of traditional Chinese timber structures during earthquakes. This paper divides the states of motion of traditional Chinese timber columns into static and dynamic. For the static state, a coefficient describing the compression height is proposed based on the variation of the compressive zone at the column foot, and the moment-rotation relationship of the column foot is then established. For the dynamic state, the rocking and slide-rocking dynamic equations are proposed by considering the contribution of the column foot and the mortise-tenon joint to the lateral force of the timber columns. Finite element models of timber frames are constructed and validated through existing timber frame shaking table tests. Based on numerical simulation, this paper analyzed 125 groups of timber column models and 98 groups of timber frame models to validate the proposed static and dynamic equations. The results reveal that the proposed moment-rotation relationship of the column foot agreed with the simulated results at the initial stiffness and bearing capacity. Hence, the proposed dynamic equations reflect the timber columns' slide and rocking characteristics under horizontal acceleration. This investigation provides a theoretical base for the reinforcement and protection of traditional Chinese timber structures during earthquakes.

Euclid: Cosmological forecasts from the void size function

The Euclid mission – with its spectroscopic galaxy survey covering a sky area over 15 000 deg2 in the redshift range 0.9 < z < 1.8 – will provide a sample of tens of thousands of cosmic voids. This paper thoroughly explores for the first time the constraining power of the void size function on the properties of dark energy (DE) from a survey mock catalogue, the official Euclid Flagship simulation. We identified voids in the Flagship light-cone, which closely matches the features of the upcoming Euclid spectroscopic data set. We modelled the void size function considering a state-of-the art methodology: we relied on the volume-conserving (Vdn) model, a modification of the popular Sheth & van de Weygaert model for void number counts, extended by means of a linear function of the large-scale galaxy bias. We found an excellent agreement between model predictions and measured mock void number counts. We computed updated forecasts for the Euclid mission on DE from the void size function and provided reliable void number estimates to serve as a basis for further forecasts of cosmological applications using voids. We analysed two different cosmological models for DE: the first described by a constant DE equation of state parameter, w, and the second by a dynamic equation of state with coefficients w0 and wa. We forecast 1σ errors on w lower than 10% and we estimated an expected figure of merit (FoM) for the dynamical DE scenario FoMw0, wa = 17 when considering only the neutrino mass as additional free parameter of the model. The analysis is based on conservative assumptions to ensure full robustness, and is a pathfinder for future enhancements of the technique. Our results showcase the impressive constraining power of the void size function from the Euclid spectroscopic sample, both as a stand-alone probe, and to be combined with other Euclid cosmological probes.

New criterion for characterization of thermal-saline jets discharged from thermal desalination plants

• The hydrodynamic pattern of inclined thermal-saline jets was examined using LES. • Jets pattern depended only on the ratio of salinity to thermal Froude numbers ( R ρ ). • Jets with R ρ lower than 1.2 behaved similar to the negatively buoyant jet. • Jets with R ρ in a range of 1.2-1.3 achieved better mixing characteristics. • Geometrical characteristics of jets became asymptotic for R ρ less than 0.7. More than 80% of desalination plants use the multi-stage flash (MSF) technology in the Persian Gulf and hence may have a severe irreversible impact on the marine environment. In the present study, geometrical, mixing, and turbulence characteristics of thermal-saline jets, similar to MSF effluents, are numerically investigated using the dynamic Smagorinsky sub-grid scale (SGS) model and UNESCO equation of state. For this purpose, two affecting dimensionless parameters are considered: (1) density ratio, which is thermal flux to salinity flux ratio, and (2) salinity Froude number. Examining the effects of density ratio reveals that the jet flow pattern only depends on the density ratio with a separating range of 1.2-1.3. In addition, increasing the density ratio increases the geometrical values of descending jets, reduces the geometrical values of ascending ones, and increases the descending jet's dilution before returning to the bed. Furthermore, geometrical values of descending jets show asymptotic behavior for density ratios less than 0.7. Eventually, turbulence characteristics of different jet flow patterns show that large turbulence structures are more explicit for the quasi-neutral scenario. The current results recommend that thermal desalination discharges similar to quasi-neutral jets with density ratios in a range of 1.2-1.3 achieve better mixing characteristics.

Implications of an Extended Dark Energy Model with Massive Neutrinos

Recently there have been reports of finding a lower bound on the neutrino mass parameter (Σm ν ) when using the Atacama Cosmology Telescope (ACT) and SPTpol data; however, these bounds on the Σm ν are still weaker for most cases around the 1σ level. In this context, here in this work, we study the consequences of using an enlarged four parameter dynamical dark energy equation of state on the neutrino mass parameter as well as on the Hubble and S8 tensions. The four parameter dark energy equation of state incorporates a generic nonlinear monotonic evolution of the dark energy equation of state, where the four parameters are the early and the present value of the equation of state, the transition scale factor, and the sharpness of the transition. We report that with lensing-marginalized Planck + BAO + Pantheon and prior on absolute magnitude M B , and KIDS/Viking S 8 prior, the model favors a nonzero value for the neutrino mass parameter at most at the 1σ level ( eV). In this case this model also brings down the Hubble tension to a 2.5σ level and the S8 tension to a ∼1.5σ level. This model also provides tighter constraints on the value of the dark energy equation of state at present epoch w 0 () in comparison to the Chevalier-Polarski and Linder-like parameterization.

Dynamic characteristics of single-loop gear system based on bond graph method

The complexity of single-loop gear system transmission structure makes it difficult for traditional modeling methods to establish precise dynamic model, which greatly affects the accuracy of its dynamic characteristics research. Firstly, a structure diagram is established by adopting modularization idea according to the structural properties of single-loop gear system. On this basis, a precise bond graph model of the single-loop gear system is obtained combining the modeling principle of bond graph method and the advantages of rich graphics library. Secondly, the dynamic state equation of single-loop gear system is obtained from bond graph model. The simulation model of gear system is established by numerical simulation method. Eventually, the dynamic characteristics of a single-loop gear system are acquired by calculating two dynamic indexes of the system under linear and weakly nonlinear states. The simulation results show that the bond graph method can accurately describe the mathematical model of single-loop gear train and master the dynamic characteristics of complex gear train. This will provide a reference for the structural design and dynamic characteristics of the transmission system.

Model based investigation of reluctance force shunt damping—A numerical parameter study

An electromagnetic energy converter for vibration damping is studied. The device consists of a coil linked with a magnetic circuit with permanent magnetization and a variable air gap between the fixed magnet and a moving yoke. The reluctance force in the air gap causes magnet and yoke to attract each other. Passive shunts of the coil lead to a hysteresis between reluctance force and motion of the yoke causing damping. A numerical model is set up which describes the magnetic circuit by lumped elements. The nonlinear dynamic state equation of the magnetic flux is solved for harmonic air gap oscillation using the Harmonic Balance Method. Equivalent linear stiffness and damping of the flux-depending reluctance force are computed in order to study the mechanical behaviour of the system. Besides consideration of resistively shunted reluctance force dampers, deployment of a resonant shunt is proposed in order to amplify the damping effect. The influence of shunt parameters on the frequency-depending mechanical behaviour is investigated. Based on the frequency-depending equivalent damping, a suitable application for shunted reluctance force dampers is examined.

Dynamic Optimization Approach to Estimate Kinetic Parameters of Monod-Based Microalgae Growth Models.

The biomass concentration of microalgae growth in photobioreactor was predicted using the Monod-based growth models. Kinetic parameters such as maximum specific growth rate and saturation constant of light intensity were evaluated by nonlinear least squares methods that focused on minimizing the sum of squares error (SSE). The importance of good initial guess for the nonlinear least squares method was also discussed. The optimal control problem of the microalgae growth model was determined based on parameter sensitivity. Therefore, a dynamic optimization approach was used where an optimal input design method was formulated to obtain a control function of a problem. The dynamic state equations, additional state equations, cost function, and Hamiltonian function were used to establish a control function of microalgae growth in a photobioreactor. Hence, the biomass production of microalgae can be predicted using numerical methods such as the Taylor series method.

Grid-Based Bayesian Beam Tracking With Multiple Observations for Millimeter Wave Channels

In this paper, we study a beam tracking problem for millimeter wave (mmWave) channels in massive multiple-input and multiple-output communication systems. We formulate the beam tracking problem as a stochastic filtering problem by modeling the dynamic state equation and the observation equation. Then, given prior information of the channel, we propose an efficient grid-based Bayesian beam tracking algorithm by leveraging the sparsity of the mmWave channel. Our proposed algorithm examines neighboring transmit and receive beam pairs and exploits multiple observations on the angular domain representation in the sense of the Bayesian statistics. Numerical results show that the proposed Bayesian method with multiple observations outperforms conventional schemes in terms of both the beam tracking accuracy and computational complexity.

Almost-Pseudo-Ricci Symmetric FRW Universe with a Dynamic Cosmological Term and Equation of State

The objective of the present paper is to investigate an almost-pseudo-Ricci symmetric FRW spacetime with a constant Ricci scalar in a dynamic cosmological term Λ(t) and equation of state (EoS) ω(t) scenario. Several cosmological parameters are calculated in this setting and thoroughly studied, which shows that the model satisfies the late-time accelerating expansion of the universe. We also examine all of the energy conditions to check our model’s self-stability.

Dynamic hedging in incomplete markets using risk measures

Abstract In this paper, we consider the pricing of financial derivatives that involve dynamic hedging strategies and payments within the planning horizon. Equity-indexed annuities (EIAs), guaranteed investment certificates (GICs) and American and barrier options are typical examples of these products. Our exploration involves the use and comparison of alternative models that use risk measures. Although the hedging is done for each observation of the input stochastic process, the appropriate mix of risk measures and state dynamic equations helps the issuer to appropriately tailor the overall risk exercise. These different models are solved by a unified backward stochastic dynamic programming framework that we imbed with parametric techniques to shorten the running time and manage the curse of dimensionality in dynamic programming. To demonstrate the flexibility of this framework we present numerical examples featuring GICs and point-to-point EIAs. Finally, by using sampling techniques, optimal hedging strategies and specific indicators of the hedging performance, we make recommendations on how to fine tune the risk measure parameters.

Neural diffusivity and pre-emptive epileptic seizure intervention.

The propagation of epileptic seizure activity in the brain is a widespread pathophysiology that, in principle, should yield to intervention techniques guided by mathematical models of neuronal ensemble dynamics. During a seizure, neural activity will deviate from its current dynamical regime to one in which there are significant signal fluctuations. In silico treatments of neural activity are an important tool for the understanding of how the healthy brain can maintain stability, as well as of how pathology can lead to seizures. The hope is that, contained within the mathematical foundations of such treatments, there lie potential strategies for mitigating instabilities, e.g. via external stimulation. Here, we demonstrate that the dynamic causal modelling neuronal state equation generalises to a Fokker-Planck formalism if one extends the framework to model the ways in which activity propagates along the structural connections of neural systems. Using the Jacobian of this generalised state equation, we show that an initially unstable system can be rendered stable via a reduction in diffusivity–i.e., by lowering the rate at which neuronal fluctuations disperse to neighbouring regions. We show, for neural systems prone to epileptic seizures, that such a reduction in diffusivity can be achieved via external stimulation. Specifically, we show that this stimulation should be applied in such a way as to temporarily mirror the activity profile of a pathological region in its functionally connected areas. This counter-intuitive method is intended to be used pre-emptively–i.e., in order to mitigate the effects of the seizure, or ideally even prevent it from occurring in the first place. We offer proof of principle using simulations based on functional neuroimaging data collected from patients with idiopathic generalised epilepsy, in which we successfully suppress pathological activity in a distinct sub-network prior to seizure onset. Our hope is that this technique can form the basis for future real-time monitoring and intervention devices that are capable of treating epilepsy in a non-invasive manner.

Unconventional monetary policy in a nonlinear quadratic model

Abstract After the financial market meltdown and the Great Recession of the years 2007–9, the financial market-macro link has become an important issue in monetary policy modeling. We develop a dynamic model that contains a nonlinear Phillips curve, a dynamic output equation, and a nonlinear credit flow equation – capturing the importance of credit cycles, risk premia, and credit spreads. Our Nonlinear Quadratic Model (NLQ) model has three dynamic state equations and a quadratic objective function. It can be used to evaluate the response of central banks to the Great Recession in moving from conventional to unconventional monetary policy. We solve the model with a new numerical procedure using estimated parameters for the euro area. We conduct simulations to explore the (de)stabilizing effects of the nonlinearities in the model. We demonstrate that credit flows, risk premia, and credit spreads play an important role as an amplification mechanism and in affecting the transmission of monetary policy. We thereby highlight the importance of the natural rate of interest as an anchor for a central bank target and the weight it places on the credit flows for the effectiveness of unconventional monetary policy. Our model is similar in structure compared to larger scale macro-econometric models which many central banks employ.

Research on Meshing Characteristics of Shearer Walking Wheel Based on Rigid-Flexible Coupling

Frequent failure of the walking wheel seriously restricts the performance of the whole shearer. To reduce the failure rate and improve the working performance of the walking wheel, the meshing characteristics of the tooth pin are researched. The dynamic state equations of the walking wheel and the contact force model of tooth pin meshing are established. The rigid-flexible coupling simulation model of tooth pin meshing is built. The load distribution characteristics of the walking wheel are analyzed, as well as the effects of impact load amplitude and duration. Results show that the curve of the longitudinal load distribution coefficient (Kβ) of the contact area is W-shaped, with a maximum of 1.325 at the moment of a single tooth contact. The end of the transition curve is the most serious position of the longitudinal load imbalance at the tooth root. In addition, on the impact moment,Kβtends to decrease and maximum stress obviously increases with the increase in impact load under 40%; the material at the contact position will fail under an extra 39% instantaneous impact load. Furthermore, with the impact load of 30%, the influence of load impact duration under 0.5 s on the meshing characteristics of the walking wheel is relatively faint. The results provide some guidance for the design optimization of the walking wheel and provide a reference for improving the reliability of the shearer.