Dynamic State Equations Research Articles

Neural network approach to computing outer inverses based on the full rank representation

The first intention of this paper is to emphasize equivalence between two well known general representations of outer inverses with prescribed range and null space of a given matrix. Two dynamical state equations, corresponding to particular expressions which are included in these representations, are defined within the second objective. In this way, two gradient based neural networks, initiated by introduced dynamical equations, are exploited in generating the class of outer inverses. The results corresponding to most common generalized inverses are obtained in particular cases. Numerical results are presented.

Aerodynamic resistance in upper atmosphere: case of the last stage Delta rocket fall in Argentina

On January 20th 2004, the engine of the third stage of a Delta-II launcher reached the Earth’s surface in the province of Corrientes, Argentina. As we were aware of the orbital data before entry as well as the location of the point of impact, we then refined a proper trajectory simulation 6D code to propagate the solutions of dynamic equations of state up to the encounter with the surface. During this propagation, the aerodynamic state is continuously adjusted to changes in the regimes of flight. When simulating the reentry, a possible trace of impact is obtained where it is estimated that the object will fall. The present work compared the effects of two atmospheric models: the static model USSA-76 versus the dynamic model NRLMSISE-00.

Cosmological constraints to dark matter with two- and many-body decays

We present a study of cosmological implications of generic dark matter decays. We consider two-body and many-body decaying scenarios. In the two-body case the massive particle has a possibly relativistic kick velocity and thus possesses a dynamical equation of state. This has implications to the expansion history of the universe. We use recent observational data from the cosmic microwave background, baryon acoustic oscillations and supernovae Type Ia to obtain constraints on the lifetime of the dark matter particle. We find that for an energy splitting where more than 40% of the dark matter particle energy is transferred to massless, relativistic particles in the two-body case, or more than 50% in the many-body case, lifetimes less than the age of the universe are excluded at more than 95% confidence. When the energy splitting falls to 10% the lifetime is constrained to be more than roughly half the age.

General polytropic magnetohydrodynamic cylinder under self-gravity

Abstract Based on general polytropic (GP) magnetohydrodynamics (MHD), we offer a self-similar dynamic formalism for a magnetized, infinitely long, axially uniform cylinder of axisymmetry under self-gravity with radial and axial flows and with helical magnetic field. We identify two major classes of solution domains and obtain a few valuable MHD integrals in general. We focus on one class that has the freedom of prescribing a GP dynamic equation of state including the isothermal limit and derive analytic asymptotic solutions for illustration. In particular, we re-visit the isothermal MHD problem of Tilley & Pudritz (TP) and find that TP's main conclusion regarding the MHD solution behaviour for a strong ring magnetic field of constant toroidal flux-to-mass ratio Γφ to be incorrect. As this is important for conceptual scenarios, MHD cylinder models, testing numerical codes and potential observational diagnostics of magnetized filaments in various astrophysical contexts, we show comprehensive theoretical analysis and reasons as well as extensive numerical results to clarify pertinent points in this Letter. In short, for any given Γφ value be it small or large, the asymptotic radial scaling of the reduced mass density α(x) at sufficiently large x should always be ∼x−4 instead of ∼x−2 contrary to the major claim of TP.

Background history and cosmic perturbations for a general system of self-conserved dynamical dark energy and matter

We determine the Hubble expansion and the general cosmic perturbation equations for a general system consisting of self-conserved matter, ρm, and self-conserved dark energy (DE), ρD. While at the background level the two components are non-interacting, they do interact at the perturbations level. We show that the coupled system of matter and DE perturbations can be transformed into a single, third order, matter perturbation equation, which reduces to the (derivative of the) standard one in the case that the DE is just a cosmological constant. As a nontrivial application we analyze a class of dynamical models whose DE density ρD(H) consists of a constant term, C0, and a series of powers of the Hubble rate. These models were previously analyzed from the point of view of dynamical vacuum models, but here we treat them as self-conserved DE models with a dynamical equation of state. We fit them to the wealth of expansion history and linear structure formation data and compare their fit quality with that of the concordance ΛCDM model. Those with C0=0 include the so-called ``entropic-force'' and ``QCD-ghost'' DE models, as well as the pure linear model ρD∼H, all of which appear strongly disfavored. The models with C0≠0 , in contrast, emerge as promising dynamical DE candidates whose phenomenological performance is highly competitive with the rigid Λ-term inherent to the ΛCDM.

Coupling dynamic analysis of spacecraft with multiple cylindrical tanks and flexible appendages

This paper is mainly concerned with the coupling dynamic analysis of a complex spacecraft consisting of one main rigid platform, multiple liquid-filled cylindrical tanks, and a number of flexible appendages. Firstly, the carrier potential function equations of liquid in the tanks are deduced according to the wall boundary conditions. Through employing the Fourier–Bessel series expansion method, the dynamic boundaries conditions on a curved free-surface under a low-gravity environment are transformed to general simple differential equations and the rigid-liquid coupled sloshing dynamic state equations of liquid in tanks are obtained. The state vectors of rigid-liquid coupled equations are composed with the modal coordinates of the relative potential function and the modal coordinates of wave height. Based on the Bernoulli–Euler beam theory and the D’Alembert’s principle, the rigid-flexible coupled dynamic state equations of flexible appendages are directly derived, and the coordinate transform matrixes of maneuvering flexible appendages are precisely computed as time-varying. Then, the coupling dynamics state equations of the overall system of the spacecraft are modularly built by means of the Lagrange’s equations in terms of quasi-coordinates. Lastly, the coupling dynamic performances of a typical complex spacecraft are studied. The availability and reliability of the presented method are also confirmed.

Hugoniot equation of state and dynamic strength of boron carbide

Boron carbide ceramics have been particularly problematic in attempts to develop adequate constitutive model descriptions for purposes of analysis of dynamic response in the shock and impact environment. Dynamic strength properties of boron carbide ceramic differ uniquely from comparable ceramics. Furthermore, boron carbide is suspected, but not definitely shown, to undergoing polymorphic phase transformation under shock compression. In the present paper, shock-wave compression measurements conducted over the past 40 years are assessed for the purpose of achieving improved understanding of the dynamic equation of state and strength of boron carbide. In particular, attention is focused on the often ignored Los Alamos National Laboratory (LANL) Hugoniot measurements performed on porous sintered boron carbide ceramic. The LANL data are shown to exhibit two compression anomalies on the shock Hugoniot within the range of 20–60 GPa that may relate to crystallographic structure transitions. More recent molecular...

Optical target tracking by scheduled range measurements

In this paper, optical target tracking, by regular target bearing measurements and target range in a lower and scheduled measurement rate is considered. Variance of the target range estimation error is used as scheduling criterion. For this purpose, target dynamic state vector in modified spherical coordinates is stated in such a way that all target states be decoupled from range-related target state. Target state dynamic equations in modified spherical coordinates for nearly constant velocity, nearly constant acceleration and coordinated turn rate kinematic models, are analytically derived. For resulted state dynamic equations, a UKF-IMM filter with range measurement scheduling is utilized as a tracking filter. It is shown that target states are estimated properly and applied filter has high performance in maneuvering target tracking.

Examples of cosmological rips in the scalar-tensor cosmology

Plenitude of models incorporating a dynamical dark energy equation of state are proposed and the scalar-tensor gravity is certainly one possible candidate. In this paper we examine whether a cosmological rip scenarios are possible in the scalar-tensor gravity by parametrizing the equation of state of dark energy Wde(z) in an appropriate way. The parameters of the model are constrained by the observational data of type Ia supernovas collected to Union 2.1 compilation.

Constraining recent oscillations in quintessence models with Euclid

Euclid is a future space-based mission that will constrain dark energy with unprecedented accuracy. Its photometric component is optimized for Weak Lensing studies, while the spectroscopic component is designed for Baryon Acoustic Oscillations (BAO) analysis. We use the Fisher matrix formalism to make forecasts on two quintessence dark energy models with a dynamical equation of state that leads to late-time oscillations in the expansion rate of the Universe. We find that Weak Lensing will place much stronger constraints than the BAO, being able to discriminate between oscillating models by measuring the relevant parameters to $1\sigma$ precisions of 5 to $20\%$. The tight constraints suggest that Euclid data could identify even quite small late-time oscillations in the expansion rate of the Universe.

Cosmological model of the interaction between dark matter and dark energy

In this paper, we test the dark matter-dark energy interacting cosmological model with a dynamic equation of state $w_{DE}(z)=w_{0}+w_{1}z/(1+z)$, using type Ia supernovae (SNe Ia), Hubble parameter data, baryonic acoustic oscillation (BAO) measurements, and the cosmic microwave background (CMB) observation. This interacting cosmological model has not been studied before. The best-fitted parameters with $1 \sigma$ uncertainties are $\delta=-0.022 \pm 0.006$, $\Omega_{DM}^{0}=0.213 \pm 0.008$, $w_0 =-1.210 \pm 0.033$ and $w_1=0.872 \pm 0.072$ with $\chi^2_{min}/dof = 0.990$. At the $1 \sigma$ confidence level, we find $\delta<0$, which means that the energy transfer prefers from dark matter to dark energy. We also find that the SNe Ia are in tension with the combination of CMB, BAO and Hubble parameter data. The evolution of $\rho_{DM}/\rho_{DE}$ indicates that this interacting model is a good approach to solve the coincidence problem, because the $\rho_{DE}$ decrease with scale factor $a$. The transition redshift is $z_{tr}=0.63 \pm 0.07$ in this model.

Chaotic Wave Solutions in a Nonlocal Model for Media With Vibrating Inclusions

The present paper is devoted to the investigation of wave solutions of a mathematical model of a complex medium that takes into account the nonlocal interaction of structural elements of the main medium and the vibration dynamics of an additional continuum (inclusions). By the methods of qualitative and numerical analysis, it is shown that an autonomous dynamic system with four-dimensional phase space has periodic, multiperiodic, quasiperiodic, and chaotic solutions. We construct bifurcation diagrams of the development of vibrations depending on the parameters of nonlocality of the dynamic equation of state of the medium

Dynamical Dipole and Equation of State in N/Z Asymmetric Fusion Reactions

In heavy ion reactions, in the case of N/Z asymmetry between projectile and target, the process leading to complete fusion is expected to produce pre-equilibrium dipole γ -ray emission. It is generated during the charge equilibration process and it is known as Dynamical Dipole. A new measurement of the dynamical dipole emission was performed by studying 16 O + 116 Sn at 12 MeV/u. These data, together with those measured at 8.1 MeV/u and 15.6 MeV/u for the same reaction, provide the dependence on the Dynamical Dipole total emission yield with beam energy and they can be compared with theoretical expectations. The experimental results show a weak increase of the Dynamical Dipole total yield with beam energies and are in agreement with the prediction of a theoretical model based on the Boltzmann–Nordheim–Vlasov (BNV) approach. The measured trend with beam energy does not confirm the rise and fall behavior previously reported for the same fused compound but with a much higher dipole moment.

Stability and dynamical features of solitary wave solutions for a hydrodynamic-type system taking into account nonlocal effects

We consider a hydrodynamic-type system of balance equations for mass and momentum closed by the dynamical equation of state taking into account the effects of spatial nonlocality. We study higher symmetry admitted by this system and establish its non-integrability for the generic values of parameters. A system of ODEs obtained from the system under study through the group theory reduction is investigated. The reduced system is shown to possess a family of the homoclinic solutions describing solitary waves of compression and rarefaction. The waves of compression are shown to be unstable. On the contrary, the waves of rarefaction are likely to be stable. Numerical simulations reveal some peculiarities of solitary waves of rarefaction, and, in particular, the recovery of their shape after the collisions.

A physical model of switching dynamics in tantalum oxide memristive devices

We present resistive switching model for TaOx memristors, which demonstrates that the radius of a tantalum rich conducting filament is the state variable controlling resistance. The model tracks the flux of individual oxygen ions and permits the derivation and solving of dynamical and static state equations. Model predictions for ON/OFF switching were tested experimentally with TaOx devices and shown to be in close quantitative agreement, including the experimentally observed transition from linear to non-linear conduction between RON and ROFF. This work presents a quantitative model of state variable dynamics in TaOx memristors, with direct comparison to high-speed resistive switching data.

Oscillatory Universe, dark energy and general relativity

The concept of oscillatory Universe appears to be realistic and buried in the dynamic dark energy equation of state. We explore its evolutionary history under the framework of general relativity. We observe that oscillations do not go unnoticed with such an equation of state and that their effects persist later on in cosmic evolution. The ‘classical’ general relativity seems to retain the past history of oscillatory Universe in the form of increasing scale factor as the classical thermodynamics retains this history in the form of increasing cosmological entropy.

Nonlinear wave processes in porous waterlike media containing a system of capillaries partially filled with a viscous liquid

A nonlinear dynamic state equation of waterlike porous material that contains a system of cylindrical capillaries partially filled with viscous liquid was received. It is shown that an acoustic nonlinearity of such media contains the relaxation elastic and inelastic components due to the nonlinear dependence of the capillary and viscous pressure in fluid on the capillary diameter. For the medium, theoretical study of such nonlinear phenomena as generation of the second harmonic and a difference frequency wave, self-demodulation of high-frequency pulses as well as the change in the propagation velocity and absorption coefficient of a test wave being under an action of static loading have been carried out. The frequency dependences of medium nonlinearity parameters for these processes were determined.

On the non-local hydrodynamic-type system and its soliton-like solutions

We consider a hydrodynamic system of balance equations for mass and momentum. This system is closed by the dynamic equation of state, taking into account the effects of spatio-temporal non-localities. Using group theory reduction, we obtain a system of ODEs, describing a set of approximate traveling wave solutions to the source system. The factorized system, containing a small parameter, proves to be Hamiltonian when the parameter is zero. Using Melnikov’s method, we show that the factorized system possesses, in general, a one-parameter family of homoclinic loops, corresponding to the approximate soliton-like solutions of the source system.

DARK ENERGY FROM SCALAR FIELD WITH GAUSS–BONNET AND NON-MINIMAL KINETIC COUPLING

We consider a model of scalar field with non-minimal kinetic couplings to the curvature, and additional coupling to the Gauss–Bonnet four-dimensional invariant. The model presents rich cosmological dynamics and some of its solutions are analyzed. A variety of scalar fields and potentials giving rise to power-law expansion have been found. Two solutions with dynamical equation of state are considered. The first solution unifies early time power-law behavior with late time cosmological constant dominance. The second solution is able to describe a universe in the phantom phase, and depending on the parameters may describe essentially dark energy behavior, or may contain the decelerated and accelerated phases.

Chaos Anticontrol Problems for a Nonlinear Circuit System

A third-order circuit system with nonlinear negative capacitance is studied. The dynamical equation and state equation of the system are established. By the phase portraits, the motions of the system are studied under the definite parameters. And by bifurcation diagram, the route from periodic motion to chaos is studied under the presented system parameters. Two anticontrol methods is used to control the periodic motion of the system to chaos. The phase plane portraits and bifurcation diagram of the anticontrolled system are obtained. The threshold values of the anticontrol values of the two control method are obtained. The advantages of the two anticontrolled methods are that the collect of the control signals are simple and can put on any time and the periodic system can be asymptotically chaotic with small control. The orbits of the system can be anticontrolled by these two methods according to our target