Non-conservative Model Research Articles

Reduced-order model-inspired experimental identification of damped nonlinear structures

In this work, we address Nonlinear System Identification (NSI) of geometrically nonlinear structures using experimental response data. Specifically we consider nonlinear structures with large inertia effects. A laboratory scale cantilever-type beam structure is considered, which is chosen for its large inertial effects. Free decay data is gathered from the experimental cantilever-type beam system using an image-based measurement technique. A general mathematical model is derived for nonlinear systems with large inertia, by taking inspiration from model reduction methods. Specifically, a reduced-order modelling method, which accounts for the kinetic energy of the modes not included in the reduction basis, is utilised for experimental NSI. Experimental system identification using the ROM-inspired model shows superior accuracy compared to standard stiffness nonlinear models typically used for modelling such systems. We also identify the damping of the structure by projecting the effect of unmodelled modes onto non-conservative dissipative forces in the ROM-inspired model. We show that this addresses issues of poor fit associated with using a linear damping model. This results in a nonlinear damping force in the ROM-inspired model which accounts for the damping effect of the unmodelled modes. These nonconservative effects of unmodelled modes are often neglected, which results in an incorrect damping estimation. A crude Finite-Element (FE) model of the cantilever-type beam is used to generate the nonlinear mapping of nonlinear damping force. The free decay response of the identified nonconservative ROM-inspired model closely matches the measurement decay response. This further validates the accuracy of the ROM-inspired model in NSI.

Avalanche dynamics in nonconservative water droplet

The self-organized criticality (SOC) exhibits excellent performance in describing the dynamic features of multi-body systems in nature. It is usually considered that conservative law is a necessary condition for the existence of SOC. However, mass or energy dissipation typically exists in the process from self-organization to a critical state in natural systems such as earthquakes and air pollution, namely, non-conservation. At present, few physical experiments have systematically explored the SOC behavior in a non-conservative system, compared to numerical simulations. This study is the first to design a non-conservative sandpile experiment using water droplets. Based on this experiment, the dynamic evolution process of avalanches in a non-conservative system has been analyzed. The results show that the avalanche size of water droplets follows a power-law distribution, as the water mass decays with time. This phenomenon obeys the rules of scale-free distribution, which is consistent with SOC behavior. Moreover, the waiting time of water droplets avalanche follows a stretched exponential distribution. These results suggest that SOC behavior still exists in non-conservative multi-body systems, which is affected by the decay coefficient. We then explore the mechanism by which the decay coefficient affects the transition of the system to a critical state in the non-conservative sandpile model (NBTW). We find that only when the decay coefficient is small do the inequality measures, Gini coefficient g and Kolkata index k, exhibit nearly universal values, similar to the mechanism of the system transitioning to a critical state in the traditional BTW model. When the decay coefficient is large, the NBTW model shows scaling-limited effects and the scaling exponent of avalanche size increases with the decay coefficient. Furthermore, we use the NBTW model to study how the decay coefficient influences the scaling exponent of avalanche size. We find that the NBTW model can effectively explain the variability of scaling exponents observed in different SOC systems and establish a quantitative relationship between the mass decay coefficient and the avalanche size scaling exponent. This study provides new insight into SOC behavior in non-conservative systems in nature.

TRAA: a two-risk archive algorithm for expensive many-objective optimization

Many engineering problems are essentially expensive multi-/many-objective optimization problems, and surrogate-assisted evolutionary algorithms have gained widespread attention in dealing with them. As the objective dimension increases, the error of predicting solutions based on surrogate models accumulates. Existing algorithms do not have strong selection pressure in the candidate solution obtaining and adaptive sampling stages. These make the effectiveness and area of application of the algorithms unsatisfactory. Therefore, this paper proposes a two-risk archive algorithm, which contains a strategy for mining high-risk and low-risk archives and a four-state adaptive sampling criterion. In the candidate solution mining stage, two types of Kriging models are trained, then conservative optimization models and non-conservative optimization models are constructed for model searching, followed by archive selection to obtain more reliable two-risk archives. In the adaptive sampling stage, in order to improve the performance of the algorithms, the proposed criterion considers environmental assessment, demand assessment, and sampling, where the sampling approach involves the improvement of the comprehensive performance in reliable environments, convergence and diversity in controversial environments, and surrogate model uncertainty. Experimental results on numerous benchmark problems show that the proposed algorithm is far superior to seven state-of-the-art algorithms in terms of comprehensive performance.

Modelling the Dynamics of a Mobile Land Robot

The research focuses on a land-based robot consisting of a six-wheeled platform with independent suspension, onto which a short-range missile launcher is mounted. This study aims to analyse the dynamics of this mobile land robot equipped with weaponry. A model representing the dynamics of both the platform and the launcher, including the missiles, was developed. The model, formulated as a discrete system comprising solids and flexible elements, explores variability patterns in independent coordinates for both conservative and non-conservative models. The study reveals a need of modifying system parameters and structure to address the occurrence of the unfavourable phenomenon of rumble.

A nonconservative kinetic model under the action of an external force field for modeling the medical treatment of autoimmune response

In this paper, we develop a nonconservative kinetic framework to be applied to the study of immune system dysregulation. From the modeling viewpoint, the model regards a system composed of stochastically interacting agents, under the action of an eternal force field. According to the application perspectives of this paper, the external force field has a specific analytical shape. In this case, some analytical results are proved, i.e. existence, uniqueness, positivity, and boundedness of solution of the related Cauchy problem, at least locally in time. Then, the model is refined to be implemented for the study of treatment strategies in case of autoimmune response. Specifically, we distinguish the autonomous case from the nonautonomous one, representing the absence or delivery of drugs, respectively. The former allows us to gain some stability results. Whereas, the latter is qualitatively studied. Numerical simulations are provided for both schemes.

SLR Validation and Evaluation of BDS-3 MEO Satellite Precise Orbits

Starting from February 2023, the International Laser Ranging Service (ILRS) began releasing satellite laser ranging (SLR) data for all BeiDou global navigation satellite system (BDS-3) medium earth orbit (MEO) satellites. SLR data serve as the best external reference for validating satellite orbits, providing a basis for comprehensive evaluation of the BDS-3 satellite orbit. We utilized the SLR data from February to May 2023 to comprehensively evaluate the orbits of BDS-3 MEO satellites from different analysis centers (ACs). The results show that, whether during the eclipse season or the yaw maneuver season, the accuracy was not significantly decreased in the BDS-3 MEO orbit products released from the Center for Orbit Determination in Europe (CODE), Wuhan University (WHU), and the Deutsches GeoForschungsZentrum (GFZ) ACs, and the STD (Standard Deviation) of SLR residuals of those three ACs are all less than 5 cm. Among these, CODE had the smallest SLR residuals, with 9% and 12% improvement over WHU and GFZ, respectively. Moreover, the WHU precise orbits exhibit the smallest systematic biases, whether during non-eclipse seasons, eclipse seasons, or satellite yaw maneuver seasons. Additionally, we found some BDS-3 satellites (C32, C33, C34, C35, C45, and C46) exhibit orbit errors related to the Sun elongation angle, which indicates that continued effort for the refinement of the non-conservative force model further to improve the orbit accuracy of BDS-3 MEO satellites are in need.

Benchmark calculations for anisotropic scattering in kinetic models for low temperature plasma

Benchmark calculations are reported for anisotropic scattering in Boltzmann equation solvers and Monte Carlo collisional models of electron swarms in gases. The work focuses on isotropic, forward, and screened Coulomb models for angular scattering in electron-neutral collisions. The impact of scattering on electron swarm parameters is demonstrated in both conservative and non-conservative model atoms. The practical implementation of anisotropic scattering in the kinetic models is discussed.

The Cauchy Problem for a Non-conservative Compressible Two-Fluid Model with Far Field Vacuum in Three Dimensions

The Cauchy Problem for a Non-conservative Compressible Two-Fluid Model with Far Field Vacuum in Three Dimensions

Superdiffusion-like behavior in zero-temperature coarsening of the d=3 Ising model

One key aspect of coarsening following a quench below the critical temperature is domain growth. For the non-conserved Ising model a power-law growth of domains of like spins with exponent alpha = 1/2 is predicted. Including recent work, it was not possible to clearly observe this growth law in the special case of a zero-temperature quench in the three-dimensional model. Instead a slower growth with alpha <1/2 was reported. We attempt to clarify this discrepancy by running large-scale Monte Carlo simulations on simple-cubic lattices with linear lattice sizes up to L=2048 employing an efficient GPU implementation. Indeed, at late times we measure domain sizes compatible with the expected growth law—but surprisingly, at still later times domains even grow superdiffusively, i.e., with alpha > 1/2. We argue that this new problem is possibly caused by sponge-like structures emerging at early times.

The Global Solvability of the Non-conservative Viscous Compressible Two-Fluid Model with Capillarity Effects for Some Large Initial Data

The Global Solvability of the Non-conservative Viscous Compressible Two-Fluid Model with Capillarity Effects for Some Large Initial Data

Optimal decay rates of a nonconservative compressible two‐phase fluid model

AbstractWe are concerned with the time decay rates of strong solutions to a nonconservative compressible viscous two‐phase fluid model in the whole space . Compared to the previous related works, the main novelty of this paper lies in the fact that it provides a general framework that can be used to extract the optimal decay rates of the solution as well as its all‐order spatial derivatives from one‐order to the highest‐order, which are the same as those of the heat equation. Furthermore, for well‐chosen initial data, we also show the lower bounds on the decay rates. Our methods mainly consist of Hodge decomposition, low‐ and high‐frequency decomposition, delicate spectral analysis, and energy method based on finite induction.

Asymptotic stability of planar rarefaction wave to a multi-dimensional two-phase flow

&lt;p style='text-indent:20px;'&gt;We are concerned with the time-asymptotic stability of planar rarefaction wave to a non-conservative two-phase flow system described by two-dimentional compressible Euler and Navier-Stokes equations through drag force. In this paper, we show the planar rarefaction wave to a non-conservative compressible two-phase model is asymptotically stable under small initial perturbation in &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ H^3 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;. The main difficulties overcome in this paper come from the non-viscosity of one fluid and the interaction between two fluids caused by drag force. The stability result is proved by the energy method.&lt;/p&gt;

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

The conservativeness, stability, and robustness of the numerical models applied in braided river systems is primarily influenced by morphological complexities adverse, flow pattern and the channel roughness. Two-dimensional flow modelling over an undulating bed profile is critical on account of the existence of subsequent wet-dry regions in the flow domain. This work provides the applicability of the conservative and non-conservative form of two-dimensional unsteady flow equations in braided river system. Both models are solved by TVD McCormack predictor corrector finite difference method and applied in the Brahmaputra River near Majuli Island, Assam India. The computed outputs are compared with the field observed results for validation. Results indicate a satisfactory agreement between the computed and measured value. Two statistical indices are used in the model performance evaluation.

Optimal control of a nonconserved phase field model of Caginalp type with thermal memory and double obstacle potential

In this paper, we investigate optimal control problems for a nonlinear state system which constitutes a version of the Caginalp phase field system modeling nonisothermal phase transitions with a nonconserved order parameter that takes thermal memory into account. The state system, which is a first-order approximation of a thermodynamically consistent system, is inspired by the theories developed by Green and Naghdi. It consists of two nonlinearly coupled partial differential equations that govern the phase dynamics and the universal balance law for internal energy, written in terms of the phase variable and the so-called thermal displacement, i.e., a primitive with respect to time of temperature. We extend recent results obtained for optimal control problems in which the free energy governing the phase transition was differentiable (i.e., of regular or logarithmic type) to the nonsmooth case of a double obstacle potential. As is well known, in this nondifferentiable case standard methods to establish the existence of appropriate Lagrange multipliers fail. This difficulty is overcome utilizing of the so-called deep quench approach. Namely, the double obstacle potential is approximated by a family of (differentiable) logarithmic ones for which the existence of optimal controls and first-order necessary conditions of optimality in terms of the adjoint state variables and a variational inequality are known. By proving appropriate bounds for the adjoint states of the approximating systems, we can pass to the limit in the corresponding first-order necessary conditions, thereby establishing meaningful first-order necessary optimality conditions also for the case of the double obstacle potential.

A discontinuous Galerkin spectral element method for a nonconservative compressible multicomponent flow model

In this work, we propose an accurate, robust (the solution remains in the set of states), and stable discretization of a nonconservative model for the simulation of compressible multicomponent flows with shocks and material interfaces. We consider the gamma-based model by Shyue (1998) [58] where each component follows a stiffened gas equation of state (EOS). We here extend the framework proposed in Renac (2019) [53] and Coquel et al. (2021) [15] for the discretization of hyperbolic systems, with both fluxes and nonconservative products, to unstructured meshes with curved elements in multiple space dimensions. The framework relies on a high-order discontinuous Galerkin spectral element method (DGSEM) using collocation of quadrature and interpolation points as proposed by Gassner (2013) [27] in the case of hyperbolic conservation laws. We modify the integrals over discretization elements where we replace the physical fluxes and nonconservative products by two-point numerical fluctuations. The contributions of this work are threefold. First, we analyze the semi-discrete DGSEM discretization of general hyperbolic systems with conservative and nonconservative terms and derive the conditions to obtain a scheme that is high-order accurate, free-stream preserving, and entropy stable when excluding material interfaces. Second, we design a three-point scheme with a HLLC solver for the gamma-based model that does not require a root-finding algorithm for the approximation of the nonconservative products. The scheme is proved to be robust and entropy stable for convex entropies, to preserve uniform profiles of pressure and velocity across material interfaces (material interface preservation), and to satisfy a discrete minimum principle on the specific entropy and maximum principles on the parameters of the EOS. Third, the HLLC solver is applied at interfaces in the DGSEM, while we consider two kinds of fluctuations in the integrals over discretization elements: the former is entropy conservative (EC), while the latter preserves material interfaces (CP). Time integration is performed using high-order strong-stability preserving Runge-Kutta schemes. The fully discrete scheme is shown to preserve material interfaces with CP fluctuations. Under a given condition on the time step, both EC and CP fluctuations ensure that the cell-averaged solution remains in the set of states; satisfy a minimum principle on any convex entropy and maximum principles on the EOS parameters. These results have allowed us to use existing limiters in order to restore positivity, and discrete maximum principles of degrees-of-freedom within elements. Numerical experiments in one and two space dimensions on flows with discontinuous solutions support the conclusions of our analysis and highlight stability, robustness and accuracy of the proposed DGSEM with either CP, or EC fluctuations, while the scheme with CP fluctuations is shown to offer better resolution capabilities.

A non-homogenous model for the spring-block cellular automaton for earthquakes

Many complex systems exhibit self-organizing criticality (SOC). In fact, there is a consensus that the Earth’s crust is a SOC system. The Olami, Feder and Christensen (OFC) spring-block model is a non-conservative SOC model that is used successfully to simulate the dynamics of seismic faults. In this model the system of coupled differential equations representing the spring-block model is mapped to a cellular automaton. In this work we include the idea of asperity, which is an important concept in real seismicity, by varying the distribution in the spring-block network. Considering that in real life seismicity faults are composed of different elements, it is necessary to have a model with these characteristics. We were able of reproduce the Gutenberg-Richter behavior (previously obtained in the classic OFC model) in this non-homogenous distribution.

A comparative study of void characteristics on the mechanical response of unidirectional composites

Defects in composite structures, such as voids, cannot entirely be avoided during the manufacturing, and have detrimental effect on the damage behavior and mechanical properties. The main characteristics of voids in composites are void content, shape, size, location and distribution. To investigate the effect of void characteristics on the failure mechanisms and mechanical properties of unidirectional composites, a non-conservative modeling method based on separation axes is proposed to generate representative volume element with arbitrary local microstructures, then the effect of void characteristics on the mechanical responses of unidirectional composites is studied by computational mechanics. Four types of typical voids are investigated to reveal the effect of void shapes and locations on failure mechanism, the damage evolution processes and mechanical response under various loading cases are analyzed comprehensively. It was found that the presence of interfacial voids modified the trend of the stress–strain curve under shear loading and almost all voids led to a significant reduction in the failure strength under transverse and shear loadings. Besides, the influence of void characteristics in the onset and propagation of damage throughout the microstructure is obviously different. Finally, the predictions by present model are compared with analytical method and available experimental data, good overall agreement is found.

Information scrambling and redistribution of quantum correlations through dynamical evolution in spin chains

We investigate the propagation of local bipartite quantum correlations, along with the tripartite mutual information to characterize the information scrambling through dynamical evolution of spin chains. Starting from an initial state with the first pair of spins in a Bell state, we study how quantum correlations spread to other parts of the system, using different representative spin Hamiltonians, viz. the Heisenberg Model, a spin-conserving model, the transverse-field XY model, a non-conserving but integrable model, and the kicked Harper model, a spin conserving but nonintegrable model. We show that the local correlations spread consistently in the case of spin-conserving dynamics in both integrable and nonintegrable cases, with a strictly nonnegative tripartite mutual information. In contrast, in the case of non-conserving dynamics, tripartite mutual information is negative and local pair correlations do not propagate.

Curvature-driven growth and interfacial noise in the voter model with self-induced zealots.

We introduce a variant of the voter model in which agents may have different degrees of confidence in their opinions. Those with low confidence are normal voters whose state can change upon a single contact with a different neighboring opinion. However, confidence increases with opinion reinforcement, and above a certain threshold, these agents become zealots, irreducible agents who do not change their opinion. We show that both strategies, normal voters and zealots, may coexist (in the thermodynamical limit), leading to competition between two different kinetic mechanisms: curvature-driven growth and interfacial noise. The kinetically constrained zealots are formed well inside the clusters, away from the different opinions at the surfaces that help limit their confidence. Normal voters concentrate in a region around the interfaces, and their number, which is related to the distance between the surface and the zealotry bulk, depends on the rate at which the confidence changes. Despite this interface being rough and fragmented, typical of the voter model, the presence of zealots in the bulk of these domains induces a curvature-driven dynamics, similar to the low temperature coarsening behavior of the nonconserved Ising model after a temperature quench.

ON PHASE–FIELD EQUATIONS OF PENROSE–FIFE TYPE WITH NON–CONSERVED ORDER PARAMETER UNDER FLUX BOUNDARY CONDITION. II: UNIFORM BOUNDEDNESS

In [1] we showed the global-in-time solvability of the initial-boundary value problem for the non-conserved phase-field model proposed by Penrose and Fife [2, 3] under the correct form of flux boundary condition for the temperature field in higher space dimensions. In this paper we discuss the uniform boundedness up to the infinite time of its solution in Sobolev–Slobodetski spaces