Non-conservative Model Research Articles

ON PHASE–FIELD EQUATIONS OF PENROSE–FIFE TYPE WITH THE NON–CONSERVED ORDER PARAMETER UNDER FLUX BOUNDARY CONDITION. I: GLOBAL–IN–TIME SOLVABILITY

We study the initial-boundary value problem for the non-conserved phasefield model proposed by Penrose and Fife in 1990 [1] under the flux boundary condition for the temperature field in higher space dimensions, which is obliged to overcome additional difficulties in the mathematical treatment. In all the existing works concerning this problem, only one due to Horn et al. [2] was discussed under the correct form of the flux boundary condition. Here we prove that the same correctly formulated problem as theirs is well-posed globally-in-time in Sobolev–Slobodetski˘ı spaces. Moreover, it is shown that the temperature keeps positive through the time evolution.

Analisis Perpindahan Besar Akibat Gaya Non-Konservatif

Structural applications based on large displacement analysis are widespread in various fields, such as the application of aircraft structures, membranes, cables, pipelines and risers. In this study, the author reviews the structural responses based on large displacement theory and non-conservative load models, assuming linear sections and materials. The parameters reviewed are the variation of the load factor and the variation of the slope angle of the load P at the end of the span. Solving non-linear differential equations with non-conservative force, using numerical integration method. The simulation results with the variation of the load factor with the angle of inclination, vertical and horizontal displacements are obtained, where the final orientation of the acting force corresponds to the deformation of the structure, and the maximum deformation occurs at a load angle of 90o, the deformation decreases for the angle orientation is getting smaller.

Improving the Orbits of the BDS-2 IGSO and MEO Satellites with Compensating Thermal Radiation Pressure Parameters

The orbit accuracy of the navigation satellites relies on the accurate knowledge of the forces on the spacecraft, in particular the non-conservative perturbations. This study focuses on the Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites of the regional Chinese BeiDou Navigation Satellite System (BDS-2), for which apparent deficiencies of non-conservative models are identified and evidenced in the Satellite Laser Ranging (SLR) residuals. The orbit errors derived from the empirical 5-parameter Extended CODE Orbit Model (ECOM) as well as a semi-analytical adjustable box-wing model show prominent dependency on the Sun elongation angle, even in the yaw-steering attitude mode. Hence, a periodic acceleration in the normal direction of the +X surface, presumably generated by the mismodeled thermal radiation pressure, is introduced. The SLR validations reveal that the Sun elongation angle-dependent systematic errors were significantly reduced, and the orbit accuracy was improved by 10–30% to approximately 4.5 cm and 3.0 cm for the BDS-2 IGSO and MEO satellites, respectively.

Understanding and design of non-conservative optical matter systems using Markov state models

Non-conservative and permutationally-invariant Markov state models inform understanding and control of self-assembling optical matter systems.

Performance of conservative and non-conservative two-dimensional shallow water models in wavy river bed

Performance of conservative and non-conservative two-dimensional shallow water models in wavy river bed

Hyperelastic proportional damping for numerical non-conservative dynamic models of hard rubbers under large deformations

The paper deals with a new approach to modeling the non-conservative behavior of hard rubbers in damping structures operating under quasi-harmonic, low-frequency conditions and in the large deformation regime. In particular, a hyperelastic proportional damping (HPD) model is proposed based on experimental research of dynamic responses of cylindrical specimens to torsion excitation. The HPD model depends on two ingredients. First, it relies on the integration of the dissipated energy of an experimentally obtained steady hysteresis loop. And second, this hysteresis loop is employed to construct a so-called skeleton curve, which is utilized to obtain the parameters of a generalized Rivlin model of the hyperelastic material. In addition, attention is paid to the HPD model’s dependence on the frequency and amplitude of the torsional excitation. Finally, the problem of nonlinear transient vibration of a viscoelastic cylinder is formulated and numerically solved by the finite element method. The results obtained from finite element analyses are in accord with experimental data and validate the proposed HPD model for material damping evaluation.

Stability of planar rarefaction wave to a multi-dimensional non-conservative viscous compressible two-phase flow

We are concerned with the time-asymptotic stability of planar rarefaction wave to a non-conservative viscous compressible two-phase flow in two dimensions. In this paper, we show the planar rarefaction wave to a non-conservative viscous compressible two-phase model is asymptotically stable under small initial perturbation in H2. The stability result is proved by the energy method.

Josephson dynamics of superfluid Fermi gases in a double-well potential with dissipation or gain

We study the effects of dissipation or gain on Josephson dynamics of superfluid Fermi gases in a double-well potential. To this end, we phenomenologically introduce an imaginary term into the order-parameter equation, and derive a nonconservative and full two-mode (fTM) model under the two-mode approximation. The fTM model contains cross (high-order) interactions relevant to mixed products of wavefunctions at different sites, which are ignored by the two-mode (TM) model. It is because the cross interactions that the time-dependent equation for the total number of atoms is coupled to population imbalance and relative phase. Therefore, the derived nonconservative fTM model can lead to new Josephson behaviors that cannot be captured within the TM model. Specially, we find that the transitions of Josephson oscillations between the zero-phase and π-phase modes can be controlled by dissipation or gain, which may have applications in atomtronics devices serving as a switch or gate.

Zero-temperature coarsening in the two-dimensional long-range Ising model.

We investigate the nonequilibrium dynamics following a quench to zero temperature of the nonconserved Ising model with power-law decaying long-range interactions ∝1/r^{d+σ} in d=2 spatial dimensions. The zero-temperature coarsening is always of special interest among nonequilibrium processes, because often peculiar behavior is observed. We provide estimates of the nonequilibrium exponents, viz., the growth exponent α, the persistence exponent θ, and the fractal dimension d_{f}. It is found that the growth exponent α≈3/4 is independent of σ and different from α=1/2, as expected for nearest-neighbor models. In the large σ regime of the tunable interactions only the fractal dimension d_{f} of the nearest-neighbor Ising model is recovered, while the other exponents differ significantly. For the persistence exponents θ this is a direct consequence of the different growth exponents α as can be understood from the relation d-d_{f}=θ/α; they just differ by the ratio of the growth exponents ≈3/2. This relation has been proposed for annihilation processes and later numerically tested for the d=2 nearest-neighbor Ising model. We confirm this relation for all σ studied, reinforcing its general validity.

Fractional Birkhoffian Mechanics Based on Quasi-Fractional Dynamics Models and Its Noether Symmetry

This paper focuses on the exploration of fractional Birkhoffian mechanics and its fractional Noether theorems under quasi-fractional dynamics models. The quasi-fractional dynamics models under study are nonconservative dynamics models proposed by El-Nabulsi, including three cases: extended by Riemann–Liouville fractional integral (abbreviated as ERLFI), extended by exponential fractional integral (abbreviated as EEFI), and extended by periodic fractional integral (abbreviated as EPFI). First, the fractional Pfaff–Birkhoff principles based on quasi-fractional dynamics models are proposed, in which the Pfaff action contains the fractional-order derivative terms, and the corresponding fractional Birkhoff’s equations are obtained. Second, the Noether symmetries and conservation laws of the systems are studied. Finally, three concrete examples are given to demonstrate the validity of the results.

High order finite volume weighted essentially non-oscillatory scheme for solving the isentropic two-phase flow model

This article presents the fifth-order weighted essentially non-oscillatory numerical method for solving a five-equation two-pressure non-conservative model of isentropic two-phase flow. The presence of non-conservative terms, shock waves and contact discontinuities offers more challenging tasks for developing the high order robust numerical methods. The proposed numerical scheme suppresses the unwanted oscillations near the steep gradients and resolves the contact discontinuities in an efficient way. Further, different test problems are taken to validate the efficiency of the proposed numerical scheme. Moreover, the improved central upwind scheme (CUP) is extended to solve the same model for checking the accuracy of the proposed numerical method. The numerical solutions obtained by the suggested scheme are compared with the solution profiles obtained from modified central upwind scheme.

An energy-conserving dynamical model of GRB afterglows from magnetized forward and reverse shocks

ABSTRACT In the dynamical models of gamma-ray burst (GRB) afterglows, the uniform assumption of the shocked region is known as provoking total energy conservation problem. In this work, we consider shocks originating from magnetized ejecta and extend the energy-conserving hydrodynamical model of Yan, Wei & Fan to the MHD limit by applying the magnetized jump conditions from Zhang & Kobayashi. Compared with the non-conservative models, our Lorentz factor of the whole shocked region is larger by a factor ${\lesssim}\sqrt{2}$. The total pressure of the forward shocked region is higher than the reversed shocked region, in the relativistic regime with a factor of about 3 in our interstellar medium (ISM) cases while ejecta magnetization degree σ < 1, and a factor of about 2.4 in the wind cases. For σ ≤ 1, the non-conservative model loses 32–42 per cent of its total energy for ISM cases, and for wind cases 25–38 per cent, which happens specifically in the forward shocked region, making the shock synchrotron emission from the forward shock less luminous than expected. Once the energy conservation problem is fixed, the late-time light curves from the forward shock become nearly independent of the ejecta magnetization. The reverse shocked region does not suffer from the energy conservation problem since the changes of the Lorentz factor are recompensed by the changes of the shocked particle number density. The early light curves from the reverse shock are sensitive to the magnetization of the ejecta, thus are an important probe of the magnetization degree.

The Nature of the Eccentric Double-lined Eclipsing Binary System KIC 2306740 with Kepler Space Photometry

Abstract We present a detailed study of KIC 2306740, an eccentric double-lined eclipsing binary system. Kepler satellite data were combined with spectroscopic data obtained with the 4.2 m William Herschel Telescope (WHT). This allowed us to determine precise orbital and physical parameters of this relatively long period (P = 10.ͩ3) and slightly eccentric (e = 0.3) binary system. The physical parameters have been determined to be M 1 = 1.194 ± 0.008 M ⊙, M 2 = 1.078 ± 0.007 M ⊙, R 1 = 1.682 ± 0.004 R ⊙, R 2 = 1.226 ± 0.005 R ⊙, L 1 = 2.8 ± 0.4 L ⊙, L 2 = 1.8 ± 0.2 L ⊙, and orbital separation a = 26.20 ± 0.04 R ⊙ through simultaneous solutions of the Kepler light curves and WHT radial velocity data. Binarity effects were extracted from the light curve in order to study intrinsic variations in the residuals. Five significant and more than 100 combination frequencies were detected. We modeled the binary system assuming nonconservative evolution models with the Cambridge stars (twin) code, and we show the evolutionary tracks of the components in the log L – log T plane, the log R – log M plane, and the log P – age plane for both spin and orbital periods together with eccentricity e and log R 1 . The model of the nonconservative processes in the code led the system to evolve to the observed system parameters in roughly 5.1 Gyr.

A cautionary tale for machine learning generated configurations in presence of a conserved quantity

We investigate the performance of machine learning algorithms trained exclusively with configurations obtained from importance sampling Monte Carlo simulations of the two-dimensional Ising model with conserved magnetization. For supervised machine learning, we use convolutional neural networks and find that the corresponding output not only allows to locate the phase transition point with high precision, it also displays a finite-size scaling characterized by an Ising critical exponent. For unsupervised learning, restricted Boltzmann machines (RBM) are trained to generate new configurations that are then used to compute various quantities. We find that RBM generates configurations with magnetizations and energies forbidden in the original physical system. The RBM generated configurations result in energy density probability distributions with incorrect weights as well as in wrong spatial correlations. We show that shortcomings are also encountered when training RBM with configurations obtained from the non-conserved Ising model.

On a Non-conservative Compressible Two-Fluid Model in a Bounded Domain: Global Existence and Uniqueness

In this work, we consider the Dirichlet problem for a non-conservative compressible two-fluid model in three dimensions. In particular, capillary pressure is taken into account in the sense that $$P^+ - P^-=f\ne 0$$ where f is assumed to be a strictly decreasing function near the equilibrium. This work aims to prove that this assumption has an essential stabilization effect on the model in bounded domains.

Characterization of the internal state of NV center in diamond and second quantization formalism

In this paper a general study of NV center internal state in diamond is presented. This study is based on experimental and theoretical findingsfound in literature. First, a Hamiltonian model for center NV internal state is proposed in terms of a complete set of commuting observables(CSCO), which consist of angular momentum ^L, spin momentum ^ S, total angular momentum ^ J = ^L+ ^ S and spin momentum on z-direction^ Sz. The second quantization formalism –in steady-state (conservative model)– is used. The creation and annihilation operators are used todescribed the steady spin-levels structure and in dynamic-state (non-conservative model) and can also describe the system dynamic betweendifferent spin-levels transitions. Finally, a discussion is presented about the application of this study in the photochromism phenomenon andsolid-state quantum bit (qubit).

Non-conservative kinetic model of wealth exchange with saving of production

In this paper we propose a non-conservative kinetic model of wealth exchange with saving of production as an extension of the Chakraborti–Chakrabarti model of money exchange. Using microeconomic arguments, we achieve rules of interaction between economic agents that depend on two exogenous parameters, the exchange aversion of the agents (λ) and the saving of production (s), such that in the limit s = 0, these rules can be reduced to the ones of the Chakraborti–Chakrabarti model. The non-conservative dynamics are approached analytically through a mean field approximation and the Boltzmann kinetic equation. Both approximations allow us to compute a theoretical rate of exponential growth (g) and to fit the emergent distributions of wealth to a gamma probability density function, in such a way that g, the fit parameters and the Gini index can be expressed analytically in terms of λ and s. In general, the emergent distributions do not reach a stationary state, however it is possible to study the emergence of self-similar distributions that hold the gamma pattern and maximize the Shannon entropy. With the purpose of addressing labor income, we explore additionally the effect of salary income in the model by defining a two-class structure where population is separated into workers and producers. This assumption leads to an emergent rate of economic growth ge. The macroeconomic implications of this model are studied by means of the wealth/income ratio, which can be predicted as s∕ge, in accordance with the Solow model of economic growth. The results in this paper allow to tie some of the important facts of the modern economic speech, as well as the microeconomic theory, with some methods and ideas developed in the context of non-conservative exchange models.

Formation and Evolution of Ultraluminous X-Ray Pulsar Binaries to Pulsar–Neutron Star and Pulsar–White Dwarf Systems

Abstract Recent observational and theoretical results have suggested that some of ultraluminous X-ray (ULX) sources may contain neutron star (NS) accretors. However, the formation channel and properties of donor stars of NS ULXs remain uncertain. By adopting the nonconservative and rotation-dependent mass transfer model in the primordial binary evolution, we investigate the way to form pulsar ULXs like observed pulsar ULXs in a systematic way. Our simulation results indicate that pulsar ULXs with Be stars and intermediate or/and high-mass donors match observed apparent luminosities, orbital periods, and observationally indicated donor masses of known pulsar ULXs. ULXs with Be and intermediate donors are main contributors. The route of accretion-induced collapse of WDs has a 4.5% contribution to the NS ULXs, 4.0% of NSs in ULXs are formed through electron-capture supernovae (SNe), and 91.5% of NSs in ULXs are born with core-collapse SNe. We also studied the evolution of pulsar ULXs to double compact star systems. We do not find NS–black hole systems (merging in a Hubble time) that evolved from pulsar ULXs. Pulsar–white dwarf (WD) cases that evolve through pulsar ULXs have significant contributions to the whole NS–WD gravitational wave sources. Contributions of pulsar–WD and pulsar–NS cases that experienced pulsar ULXs are ∼40% and 11% among all LISA NS–WD and NS–NS sources, respectively. Monte Carlo simulation noise with different models give a nonnegligible uncertainty.

Stealth Entropy Production in Active Field Theories near Ising Critical Points.

We address the steady-state entropy production rate (EPR) of active scalar ϕ^{4} theories, which lack time-reversal symmetry, close to a phase-separation critical point. We consider both nonconserved (model A) and conserved (model B) dynamics at Gaussian level, and also address the former at leading order in ε=4-d. In each case, activity is irrelevant in the RG sense: the active model lies in the same (dynamic Ising) universality class as its time-reversible counterpart. Hence one might expect that activity brings no new critical behavior. Here we show instead that, on approach to criticality in these models, the singular part of the EPR per (diverging) spacetime correlation volume either remains finite or itself diverges. A nontrivial critical scaling for entropy production thus ranks among universal dynamic Ising-class properties.

Modeling invasive species risk from established populations: Insights for management and conservation

Ecologists commonly use ecological niche models (ENMs) to undertake invasive species risk assessments; however, knowledge shortfalls introduce bias in these models and increase uncertainty while addressing questions in biogeography. Therefore, our objective was to investigate how the lack of information related to population viability impairs invasive species risk assessments. We built ENMs for the invasive slider turtle (Trachemys scripta) and compared the native and invaded portions of its niches. Both analyses were generated based on two approaches: a conservative one, which excluded occurrence records where the establishment of invasive populations was not confirmed; and a non-conservative one, which encompassed all occurrence records. Under the conservative approach, the niche similarity test revealed that the similitude between native and invasive populations was not different than the expected by chance. Conversely, under the non-conservative approach, the test revealed that native and invasive populations use a similar ecological niche, despite that the occupied portion of the species’ niche during the invasion was quite larger than the native one. In fact, non-conservative models projected wider areas with high risk of invasion that were not detected by the conservative approach. While models’ outcomes were markedly different, both provide valuable information in terms of evolution and conservation. We found that information about population viability is really valuable and should be incorporated in risk assessment, invasive records without this information should not be discarded under any point of view. Finally, we discussed the best way to consider this kind of information to assess the management of invasive species.