Conditions For Structural Stability Research Articles

Nonrelativistic limit of the Euler‐HMPN approximation models arising in radiation hydrodynamics

In this paper, we are concerned with the nonrelativistic limit of a class of computable approximation models for radiation hydrodynamics. The models consist of the compressible Euler equations coupled with moment closure approximations to the radiative transfer equation. They are first‐order partial differential equations with source terms. As hyperbolic relaxation systems, they are showed to satisfy the structural stability condition proposed by the second author. Based on this, we verify the nonrelativistic limit by combining an energy method with a formal asymptotic analysis.

LMI-Based Stability Analysis of Continuous-Discrete Fractional-Order 2D Roesser Model

The manuscript investigates the problem of structural stability of continuous-discrete fractional-order 2D Roesser model. This model includes one continuous fractional-order dimension with fractional-order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \in (0,2)$ </tex-math></inline-formula> and one discrete dimension. By the equivalent transform and generalized Kalman–Yakubovič–Popov lemma, the necessary and sufficient stability conditions for structural stability of continuous-discrete fractional-order 2D Roesser model are established. Our results are all in the form of linear matrix inequalities. And compared with the existing results, our results have no conservativeness and can be applied in the cases with fractional-order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \in (0,2)$ </tex-math></inline-formula> in the continuous fractional-order dimension. Illustrated examples are provided to verify the effectiveness of our results.

Equilibrium stability analysis of hyperbolic shallow water moment equations

In this paper, we analyze the stability of equilibrium manifolds of hyperbolic shallow water moment equations. Shallow water moment equations describe shallow flows for complex velocity profiles which vary in vertical direction and the models can be seen as extensions of the standard shallow water equations. Equilibrium stability is an important property of balance laws that determines the linear stability of solutions in the vicinity of equilibrium manifolds, and it is seen as a necessary condition for stable numerical solutions. After an analysis of the hyperbolic structure of the models, we identify three different stability manifolds based on three different limits of the right‐hand side friction term, which physically correspond to water‐at‐rest, constant‐velocity, and bottom‐at‐rest velocity profiles. The stability analysis then shows that the structural stability conditions are fulfilled for the water‐at‐rest equilibrium and the constant‐velocity equilibrium. However, the bottom‐at‐rest equilibrium can lead to instable modes depending on the velocity profile. Relaxation toward the respective equilibrium manifolds is investigated numerically for different models.

Boundary conditions for hyperbolic relaxation systems with characteristic boundaries of type II

This paper is a continuation of our preceding work on hyperbolic relaxation systems with characteristic boundaries of type I. Here we focus on the characteristic boundaries of type II, where the boundary is characteristic for the equilibrium system and is non-characteristic for the relaxation system. For this kind of characteristic initial-boundary-value problems (IBVPs), we introduce a three-scale asymptotic expansion to analyze the boundary-layer behaviors of the general multi-dimensional linear relaxation systems. Moreover, we derive the reduced boundary condition under the Generalized Kreiss Condition by resorting to some subtle matrix transformations and the perturbation theory of linear operators. The reduced boundary condition is proved to satisfy the Uniform Kreiss Condition for characteristic IBVPs. Its validity is shown through an error estimate involving the Fourier-Laplace transformation and an energy method based on the structural stability condition.

Recent Advances on Boundary Conditions for Equations in Nonequilibrium Thermodynamics

This paper is concerned with modeling nonequilibrium phenomena in spatial domains with boundaries. The resultant models consist of hyperbolic systems of first-order partial differential equations with boundary conditions (BCs). Taking a linearized moment closure system as an example, we show that the structural stability condition and the uniform Kreiss condition do not automatically guarantee the compatibility of the models with the corresponding classical models. This motivated the generalized Kreiss condition (GKC)—a strengthened version of the uniform Kreiss condition. Under the GKC and the structural stability condition, we show how to derive the reduced BCs for the equilibrium systems as the classical models. For linearized problems, the validity of the reduced BCs can be rigorously verified. Furthermore, we use a simple example to show how thus far developed theory can be used to construct proper BCs for equations modeling nonequilibrium phenomena in spatial domains with boundaries.

Boundary conditions for hyperbolic relaxation systems with characteristic boundaries of type I

This work is concerned with boundary conditions for one-dimensional hyperbolic relaxation systems with characteristic boundaries. We assume that the relaxation system satisfies the structural stability condition proposed by the second author previously and the boundary is characteristic of type I (characteristic for the relaxation system but non-characteristic for the corresponding equilibrium system). For this kind of characteristic initial-boundary-value problems, we propose a modified Generalized Kreiss condition (GKC). This extends the GKC proposed by W.-A. Yong (1999) [28] for the non-characteristic boundaries to the present characteristic case. Under this modified GKC, we derive the reduced boundary condition and verify its validity by combining an energy estimate with the Laplace transform. Moreover, we show the existence of boundary-layers for nonlinear problems.

TPDH-graphene: A new two dimensional metallic carbon with NDR behaviour of its one dimensional derivatives

Abstract A new two dimensional carbon allotrope TPDH-graphene (Tetra-Penta-Deca-Hexagonal-graphene) belonging to the tetragonal-pentagonal carbon ring family is proposed in this work using density-functional method. The allotrope satisfies all the conditions of structural stability. This allotrope has lower cohesive energy than many existing planar carbon allotropes. It can withstand temperature as high as 1000 K without loosing its structural integrity. However, its electronic structure reflects metallic character due to delocalised pz orbital near the Fermi level. Further, this mechanically stable elastically anisotropic structure shows directional variation of In-plane Young's modulus and Poisson's ratio. It is stronger than graphene in a particular direction. Moreover, The material can be identified by four characteristic peaks in the electron energy loss spectra within 10 eV energy. It has optical reflectance peaks in the visible range at ∼600 nm yellow colour. Interestingly, some nanoribbons of this material show semimetallic, semiconducting and metallic behaviour. Non-equilibrium Green's function method along with density-functional theory is employed to study the nanodevices made of these nanoribbons. Strong current regulation property and robust negative differential resistance effect with a peak-to-valley ratio 3.3 are observed in two nanodevices making TPDH-graphene an attractive material for use in nanoelectronics.

New Tests for the Stability of 2-D Roesser Models

This article aims at broadening the panel of the existing conditions for structural stability of 2-D Roesser models. The models can be discrete, continuous, or mixed discrete/continuous. The conditions are necessary and sufficient. They are either expressed in terms of linear matrix inequalities or based on direct tests on eigenvalues of constant matrices. The effectiveness of these tests is highlighted.

Synergetic interpretation of bifurcations of open systems

Introduction . In order to establish the causes of unexpected bifurcations of open systems, this work is presented. It is based on the corporate interaction of unidirectional open systems, an assumption is made about the reasons for their self-improvement. Main part. The identification of bifurcations of closed and open systems is considered. The prerequisites for the occurrence of incorrect bifurcations of open systems are given. In studies of closed systems, it is imperative that the conditions of structural stability to relatively small perturbations, which cannot be satisfied when identifying open systems, are met. Self-improvement of open systems occurs due to the exchange of information with the external environment. Based on the assumption that the long-term memory of an open system can be considered as an external environment, the exchange of information can be considered through the cooperative interaction of an open single focus the most open system and its long-term memory. The latter leads to the formation of targeted actions that contribute to the self-improvement of an open system. An admissible regularization of a problem identified by an incorrect bifurcation of an open system is shown. The task is regularized in two stages. At the first stage, an operator is defined that regularizes the problem in the format of thinking corresponding to incorrect bifurcation. At the second stage, the solution obtained at the first stage is applied to the problem in the original format. Conclusions. It has been suggested that the occurrence of incorrect bifurcations of open systems is a result of the cooperation of the previously existing long-term memory with its present memory. These reasons indicate the incorrectness of such tasks. It is shown that the use of the logical operator allows partial regularization of such problems by identifying incorrect bifurcations. Due to the wide variety of open systems, the probability of an adequate identification of their bifurcations is obvious.

Hartman-Grobman theorem for iterated function systems

In this paper, for iterated function systems, we define the classic concept of the dynamical systems: topological conjugacy of diffeomorphisms. We generalize the Hartman-Grobman theorem for one-dimensional iterated function systems on $\mathbb {R}$ Also, we introduce the basic concept of structural stability for an iterated function system, and therefore, we investigate the necessary condition for structural stability of an iterated function system on $\mathbb {R}$

Boundary stabilization of hyperbolic balance laws with characteristic boundaries

This article is concerned with boundary stabilization of one-dimensional linear hyperbolic systems with characteristic boundaries. We assume that the systems satisfy a physically relevant structural stability condition for hyperbolic relaxation problems, which describe various non-equilibrium phenomena. By introducing new and simple Lyapunov functions, the structural stability condition is used to derive stabilization results for problems with characteristic boundaries. The result is illustrated with an application to the transport of neurofilaments in axons—a phenomenon studied in neuroscience.

О грубости и бифуркациях полиномиальных дифференциальных уравнений на окружности

A dynamical system defined by a differential equation on a manifold, the phase space of a system, is called structurally stable if the topological structure of the phase portrait does not change when passing to a close equation. The concept of structural stability emerged from the idea that the essential properties of a dynamical system describing a real process should not change with small changes in the parameters of the system. By now, natural necessary and sufficient conditions for structural stability of dynamical systems on closed manifolds of any dimension have been obtained. However, if we consider structural stability in narrower classes of dynamical systems, in particular, in the space of systems defined by differential equations with polynomial right-hand sides, the conditions of structural stability have not been studied even for small dimensions of the phase space. This paper considers the dynamic systems given by the d ifferential equations, the right-hand parts of which are trigonometric polynomials of the degree not exceeding the number n. The phase space of such systems is a circle. We describe equations that are structurally stable with respect to the space E ( n ) of all such equations . An equation is structurally stable if and only if its right-hand side has only simple zeros, that is, all singular points of which are hyperbolic. The set of all structurally stable equations is open and is dense everywhere in the space E ( n ). In the set of all non-structurally-stable equations, an open, everywhere-dense subset consisting of equations that are first order structurally unstable is distinguished. It is an analytic submanifold of codimension one in E ( n ) and consists of equations for which all the zeros of the right-hand side are simple, except for one double zero.

Structural Stability Conditions Soil Carbon Gains from Compost Management and Rotational Diversity

Structural Stability Conditions Soil Carbon Gains from Compost Management and Rotational Diversity

Structural Stability Conditions Soil Carbon Gains from Compost Management and Rotational Diversity

Core Ideas Soil structure and carbon pools were quantified in a 20‐year field crop trial. Compost management influenced soil aggregate size, labile carbon, and total carbon. An increased rotational diversity from one to five crops enhanced soil aggregate stability. Use of moderate compost increased soil carbon by 20% relative to fertilizer. Understanding processes that underlie soil carbon gains and enhance structural stability is key to sustainable production of intensively managed row crops. Long term consequences of crop diversity and interactions with compost management have rarely been tested with economically feasible, moderate rates of organic amendments. We investigated soil aggregation and carbon pools over twenty years on a field crop experiment that allowed quantification of the impact of rotational diversity within two integrated management regimes, one based on compost (3 Mg ha−1) and the other inorganic fertilizer, both at about 100 kg N ha−1 annually. The Living Field Laboratory (LFL) experimental study where the study was conducted is located at the W.K. Kellogg Biological Station in southwest Michigan. The rotational diversity treatments investigated included continuous corn (Zea mays L.) (CC), corn–soybean [Glycine max (L.) Merr.] rotation (CS), corn–soybean–wheat (Triticum aestivum L.) rotation (CSW), and corn–soybean–wheat rotation with a cover crop (CSWco). Soil C status in 1993 was 2584 g m−2 and by 2013 increased in integrated fertilizer and compost plots to 3026 and 3672 g kg−1, respectively. Compost management enhanced soil labile C, organic C and the proportion of large macroaggregates (&gt;2000 μm size fraction). Rotational diversity did not influence total soil C but was positively associated with soil aggregate stability and aggregate carbon pool size. The study findings were consistent with integrated organic and inorganic nutrient management as interacting positively with crop diversity, to support gains in soil structural stability and C accrual.

First-Principles Investigation of Structural Stability, Mechanical, Anisotropic, and Thermodynamic Properties of CeT2Al20 Intermetallics

Abstract First-principles calculations were carried out to explore the structural stability, elastic moduli, ductile or brittle behaviour, anisotropy, dynamical stability, and thermodynamic properties of pure Al and CeT2Al20 (T = Ti, V, Cr, Nb, and Ta) intermetallics. The calculated formation enthalpy and phonon frequencies confirm that these intermetallics satisfy the conditions for structural stability. The elastic constants Cij , elastic moduli B, G, and E, and the hardness Hv indicate these intermetallics have higher hardness and the better resistance against deformation than pure Al. The values of Poisson’s ratio (v) and B/G indicate that CeT2Al20 intermetallics are all brittle materials. The anisotropic constants and acoustic velocities confirm that CeT2Al20 intermetallics are all anisotropic, but CeV2Al20, CeNb2Al20, and CeTa2Al20 are nearly isotropic. Importantly, the calculated thermodynamic parameters show that CeT2Al20 intermetallics exhibit better thermodynamic properties than pure Al at high temperature.

Stability Analysis of Initially Curved Beams Mechanically Coupled in a Parallel Arrangement

This paper investigates the stability behavior of a mechanically coupled bi-stable mechanism made of two parallel and initially curved microbeams with focus on the influence of the coupled beams’ initial curvatures on the system. First, the nonlinear and coupled force–displacement equation is derived. Then, a parametric study of the coupled beams system is studied with the system categorized into different structural compartment types according to the initial curvature of the coupled beams. It is concluded that the snap-through of such a coupled bi-stable system is governed by the beams’ initial curvatures difference. The simulation results showed that these two parameters (the beams’ initial curvatures) essentially govern the structural behavior of the coupled system in satisfying the necessary structural stability condition. It is found that the smallest (critical) value of the minimum force amplitude occurs only when both initial beams’ mid-point elevations are equal to each other. Furthermore, it is shown that any probability to increase or decrease the curvature of any beam will alter the nonlinear behavior of the coupled beam system from a simple regular snap-through to a constrained-snap-through, and even to the disappearance of the snap-through. Finally, a finite element method is conducted to investigate the stability of the coupled mechanism, of which the results show a good agreement with the analytical results of this paper.

Structural Monostability of Activation-Inhibition Boolean Networks

Although any networked control system is specified by the combination of the network structure and the dynamics of the components , one often encounters a situation where the former is known but the latter is (almost) unknown . In such a case, we cannot apply any analysis and design method using the full information of the target system. So it is desirable to establish a framework of the structural analysis and design , that is, an analysis and design methodology based on the information only on the network structure. This paper addresses the structural stability , that is, the stability with unknown component dynamics, for a class of networked control systems. In particular, we consider here Boolean networks and present a series of (necessary and) sufficient conditions for structural stability.

Transmodal Fabry-Pérot Resonance: Theory and Realization with Elastic Metamaterials.

We discovered a new transmodal Fabry-Pérot resonance where one elastic-wave mode is maximally transmitted to another. It occurs when the phase difference of two dissimilar modes through an anisotropic layer becomes odd multiples of π under the reflection-free and weak mode-coupling assumptions. Unlike the well-established Fabry-Pérot resonance, the transmodal resonance must involve two coupled elastic waves between longitudinal and shear modes. The investigation into the origin of wiggly transmodal transmission spectra suggests that efficient broadband mode conversion can be achieved if the media satisfy the structural stability condition to some degree. The new resonance mechanism, also experimentally characterized, opens up new possibilities for manipulating elastic wave modes as an effective alternative to generating shear-mode ultrasound.

Incommensurate host-guest structures in compressed elements: Hume—Rothery effects as origin

Discovery of the incommensurate structure in the element Ba under pressure 15 years ago was followed by findings of a series of similar structures in other compressed elements. Incommensurately modulated structures of the host-guest type consist of a tetragonal host structure and a guest structure. The guest structure forms chains of atoms embedded in the channels of host atoms so that the axial ratio of these subcells along the c axis is not rational. Two types of the host-guest structures have been found so far: with the host cells containing 8 atoms and 16 atoms; in these both types the guest cells contain 2 atoms. These crystal structures contain a non-integer number of atoms in their unit cell: tI11* in Bi, Sb, As, Ba, Sr, Sc and tI19* in Na, K, Rb. We consider here a close structural relationship of these host-guest structures with the binary alloy phase Au3Cd5-tI32. This phase is related to the family of the Hume-Rothery phases that is stabilized by the Fermi sphere-Brillouin zone interaction. From similar considerations for alkali and alkaline-earth elements a necessary condition for structural stability emerges in which the valence electrons band overlaps with the upper core electrons and the valence electron count increases under compression.

Parabolic limit with differential constraints of first-order quasilinear hyperbolic systems

The goal of this work is to provide a general framework to study singular limits of initial-value problems for first-order quasilinear hyperbolic systems with stiff source terms in several space variables. We propose structural stability conditions of the problem and construct an approximate solution by a formal asymptotic expansion with initial layer corrections. In general, the equations defining the approximate solution may come together with differential constraints, and so far there are no results for the existence of solutions. Therefore, sufficient conditions are shown so that these equations are parabolic without differential constraint. We justify rigorously the validity of the asymptotic expansion on a time interval independent of the parameter, in the case of the existence of approximate solutions. Applications of the result include Euler equations with damping and an Euler–Maxwell system with relaxation. The latter system was considered in [27,9] which contain ideas used in the present paper.