Conditions For Structural Stability Research Articles

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 atom 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.

CFL condition, Boltzmann's H‐theorem, Onsager reciprocal relations and beyond

In this article, we show that the classical CFL condition from numerical analysis, Boltzmann's H‐theorem from kinetic theory and Onsager reciprocal relations from nonequilibrium thermodynamics are all related to some structural stability conditions for nonhomogeneous systems of first‐order partial differential equations. By doing this, we briefly review our previous works on first‐order partial differential equations. Copyright © 2013 John Wiley & Sons, Ltd.

Bifurcations of equilibrium sets in mechanical systems with dry friction

The presence of dry friction in mechanical systems induces the existence of an equilibrium set, consisting of infinitely many equilibrium points. The local dynamics of the trajectories near an equilibrium set is investigated for systems with one frictional interface. In this case, the equilibrium set will be an interval of a curve in phase space. It is shown in this paper that local bifurcations of equilibrium sets occur near the endpoints of this curve. Based on this result, sufficient conditions for structural stability of equilibrium sets in planar systems are given, and two new bifurcations are identified. The results are illustrated by application to a controlled mechanical system with friction.

On the Cauchy problem for macroscopic model of pedestrian flows

In this paper, we discuss the limit behavior of hyperbolic systems of conservation laws with stiff relaxation terms to the local systems as the relaxation time tends to zero. The prototype is crowd models derived from crowd dynamics according to macroscopic scaling when the flow of crowds is supposed to satisfy the paradigms of continuum mechanics. Under an appropriate structural stability condition, the asymptotic expansion is obtained when one assumes the existence of a smooth solution to the equilibrium system. In this case, the local existence of a classical solution is also shown.

Optimal shape analysis of a column structure under various loading conditions by using differential transform method (DTM)

The effects of loading on the optimal shape of an Euler–Bernoulli column is investigated by considering four loading conditions which are mainly classified as eccentric compressive and follower type. The governing equations obtained from the structural stability condition of the column are used as a constraint to determine the minimum value of the volume by applying Hamilton principle. In the preceding task, the analysis is presented in step-by-step manner. The calculations are carried out by using differential transform method (DTM) which is a seminumerical-analytical solution technique that can be applied to various types of differential equations. By using DTM, the non-linear constrained governing equations are reduced to recurrence relations and related boundary conditions are transformed into a set of algebraic equations. The optimal distribution of cross-sectional area along column-length is obtained. Then, the volume of such column is calculated and compared to that of the uniform column which is also stable under given loading. The results obtained revealed out that DTM is a quite powerful solution technique for optimal shape analysis of a column structure.

On models structurally stable in periodic motion

The results obtained for a class of models that are structurally stable in periodic motion were presented, and, in particular, the notion of structural stability was introduced. Feasibility of such structurally stable model was proved. For a model featuring space-time symmetry, the sufficient structural stability conditions were established, and examples were presented.

Symmetric array of off-axis singular beams: spiral beams and their critical points

We consider conditions of structural stability under which the array of singular beams preserves its topological structure and intensity distribution while slightly perturbing its intrinsic parameters. The orbital angular momentum of the array as a function of the array parameters is a characteristic function, and its extreme points correspond to stable and unstable array states.

Structural Stability of Planar Polynomial Foliations

We discuss natural notions of structural stability of planar polynomial foliations of fixed degree with respect to perturbation within the same restricted set, within the set of all polynomial vector fields of the same degree, and within the set of smooth vector fields. Characterization theorems for structural stability in the latter two settings are obtained as immediate corollaries of known results. We provide sufficient conditions and separate necessary conditions for structural stability of planar polynomial foliations with respect to perturbation within the set of planar polynomial foliations of the same degree.

Initial–Boundary Value Problem for a Class of Linear Relaxation Systems in Arbitrary Space Dimensions

In this paper, we consider the characteristic initial–boundary value problem (IBVP) for the multi-dimensional Jin–Xin relaxation model in a half-space with arbitrary space dimension n⩾2. As in the one-dimensional case ( n=1, see ( J. Differential Equations, 167 (2000), 388–437), our main interest is on the precise structural stability conditions on the relaxation system, particularly the formulation of boundary conditions, such that the relaxation IBVP is stiffly well posed, that is, uniformly well posed independent of the relaxation parameter ε>0, and the solution of the relaxation IBVP converges, as ε→0, to that of the corresponding limiting equilibrium system, except for a sharp transition layer near the boundary. Our main result can be roughly stated as Stiff Kreiss Condition= Uniform Kreiss Condition for the relaxation IBVP we consider in this paper, which is in sharp contrast to the one-dimensional case (Z. Xin and W.-Q. Xu, J. Differential Equations, 167 (2000), 388–437). More precisely, we show that the Uniform Kreiss Condition (which is necessary and sufficient for the well posedness of the relaxation IBVP for each fixed ε), together with the subcharacteristic condition (which is necessary and sufficient for the stiff well posedness of the corresponding Cauchy problem), also guarantees the stiff well posedness of our relaxation IBVP and the asymptotic convergence to the corresponding equilibrium system in the limit of small relaxation rate. Optimal convergence rates are obtained and various boundary layer behaviors are also rigorously justified.

Prediction of common secondary structures of RNAs: a genetic algorithm approach.

In this study we apply a genetic algorithm to a set of RNA sequences to find common RNA secondary structures. Our method is a three-step procedure. At the first stage of the procedure for each sequence, a genetic algorithm is used to optimize the structures in a population to a certain degree of stability. In this step, the free energy of a structure is the fitness criterion for the algorithm. Next, for each structure, we define a measure of structural conservation with respect to those in other sequences. We use this measure in a genetic algorithm to improve the structural similarity among sequences for the structures in the population of a sequence. Finally, we select those structures satisfying certain conditions of structural stability and similarity as predicted common structures for a set of RNA sequences. We have obtained satisfactory results from a set of tRNA, 5S rRNA, rev response elements (RRE) of HIV-1 and RRE of HIV-2/SIV, respectively.

Singular Perturbations of First-Order Hyperbolic Systems with Stiff Source Terms

This work develops a singular perturbation theory for initial-value problems of nonlinear first-order hyperbolic systems with stiff source terms in several space variables. It is observed that under reasonable assumptions, many equations of classical physics of that type admit a structural stability condition. This condition is equivalent to the well-known subcharacteristic condition for one-dimensional 2×2-systems and the well-known time-like condition for one-dimensional scalar second-order hyperbolic equations with a small positive parameter multiplying the highest derivatives. Under this stability condition, we construct formal asymptotic approximations of the initial-layer solution to the nonlinear problem. Furthermore, assuming some regularity of the solutions to the limiting inner problem and the reduced problem, we prove the existence of classical solutions in the uniform time interval where the reduced problem has a smooth solution and justify the validity of the formal approximations in any fixed compact subset of the uniform time interval. The stability condition seems to be a key to problems of this kind and can be easily verified. Moreover, this presentation unifies and improves earlier works for some specific equations.

Structural stability of least squares prediction methods

A structural stability condition is sought for least squares linear prediction methods in the given data case. Save the Toeplitz case, the structure of the normal equation matrix yields no acknowledged guarantee of stability. Here, a new sufficient condition is provided, and several least squares prediction methods are shown to be structurally stable.

Effect of lime (CaCO3) application on soil structural stability of a red earth

Changes in soil structural stability as a result of lime application (1·5 t/ha) were monitored over 3 years in a red earth with contrasting initial pH, organic carbon, and structural stability conditions at Wagga Wagga, NSW. The lime was applied to the surface of the direct drilled-soil without any incorporation, but in the case of the cultivated soils, the lime was incorporated into the top 10 cm by scarifying. After liming, an initial temporary reduction in macroaggregate (>2 µm) stability was detected in the immediate surface (0-2·5 cm) of the direct-drilled soil where the highest increases in pH, losses in soil organic carbon, and increases in microbial biomass were also observed. The decrease in structural stability was attributed to lime-induced increases in biological decomposition and the resulting soil organic carbon losses. Subsequent samplings did not detect any difference in either macro- or micro- (<50 µm) aggregate stability of this soil as a result of lime treatment. In contrast, for the 2 cultivated soils which had lower initial structural stability and organic carbon levels, a decline in stability was not observed. Instead, significant increases in macroaggregate and microaggregate stability were detected 1·5 years after lime application. By the end of 3 years, macroaggregate stability of the limed cultivated soils approached that of the direct-drilled soil. The improvement in structural stability extended to 7·5 cm depth 3 years after lime application. Wet-sieving experiments using prolonged periods of shaking indicated enhanced stability of the water-stable aggregates of the limed cultivated soils but not the direct-drilled soils.

Static and dynamic state feedback control model of basal ganglia-thalamocortical loops.

It is argued that a novel control architecture, the Static and Dynamic State (SDS) feedback scheme, which utilizes speed-field tracking, exhibits global stability, and allows on-line tuning by any adaptation mechanism without canceling stability if certain structural conditions are met, can be viewed as a model of basal ganglia-thalamocortical loops since (1) the SDS scheme predicts the neuronal groups that fit neuronal classification in the supplementary motor area, the motor cortex and the putamen, (2) the structural stability conditions require parallel channels, a feature that these loops provide, and (3) the SDS scheme predicts two major disorders that can be identified as Parkinson's and Huntington's diseases. Simulations suggests that the basal ganglia work outside the realm of the stability condition allowed by the robustness of the scheme and required for increased computation speeds.

Structural stability and selection of propagating fronts in semilinear parabolic partial differential equations.

An alternative viewpoint for the selection problem in propagating front systems is presented. We propose that the selected solution can be identified through analysis of the structural stability of the solutions in question. A solution to a given equation is considered structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. Applying the structural stability condition, we identify selected solutions for semilinear parabolic partial differential equations, single-mode equations of the Fisher type, and multiple-mode equations that assume something of a generalized Fisher form. The structural stability condition is confirmed for the subclass of single-mode equations to which the Aronson-Weinberger theorem applies [in Partial Differential Equations and Related Topics, edited by J. A. Goldstein (Springer, Heidelberg, 1975)]. For other single-mode equations and multiple-mode equations, the structural stability condition is confirmed numerically. Equations possessing multiple physically realizable solutions are also studied, and several causes for such behavior are identified. We describe what we believe to be the fundamental feature distinguishing physically realizable and physically unrealizable solutions.

Necessary Conditions for Stability of Nonsingular Endomorphisms of the Circle

In this article we prove that Axiom ${\rm {A}}$ is a necessary condition for structural stability of ${C^1}$ nonsingular endomorphisms of the circle.

Endomorphisms of Branche one-dimensional Manifolds

In this paper, in Part 4, we extend this result of Jakobson to the space lm~K) of all C ~ immersions of K preserving the branch set B: in Part 3, we extend the result of Shub for expanding endomorphisms of K preserving B. In Part 2 we give a necessary condition for structural stability of certain endomorphisms of K. We also prove that expanding endomorphisms on a branched l-manifold with non empty branch set are unstable. Using this fact we prove that structural stability is not generic. This paper contains parts of the author's thesis at the Instituto de Matemfitica Pura e Aplicada do C.N.Pq. of Brazil (t980). The author takes the opportunity to thank Professor Jorge Sotomayor, his thesis advisor, for his advice and constant encouragement.

Structural stability and hyperbolic attractors

A necessary condition for structural stability is presented that in the two dimensional case means that the system has a finite number of topological attractors.

The Methodological Basis of the Functional Theory of Social Change

There are at least two problems which should be solved by functionalism before it produces a fruitful theory of social change. One is to overcome its normative bias. The other is to introduce the category of causality. The methodological basis of the functional theory of social change will be established when it constructs “normism as a methodology” which is expected to solve the two problems presented above.The stress on the idea of integration does not necessarily lead to the negligence of the idea of change. The basic presupposition of the theory of social change of all kinds is a satisfactory analysis of the conditions of structural stability. The traditional functionalism has produced only an unsatisfactory theory of integration. The development of the sociological equilibrium theory may produce a satisfactory theory of integration. The specificatiom of the equilibrium postulate frees the functionalism from the unreasonable bias to integration. The specification might make alive the principle of causality in a new form. The functionalism will lead a scientific theory of social change only after it introduces the category of causality.The functional theory of social change is basically characterized as a theory which explains the stagnation and the change at the same time. The strategic policy of the functional theory of social change is to explain the present form and the change of social structure through the analysis of the conditions of stability. This policy has been realized especially in the functional requisite theory. But these requisites are necessarily the requisites for the system. How is it possible for the functional theory to grasp an independent demand of individual? It is the problem about the relation between man and institutionalization.Now let me introduce the concept of purposive causality. The purposive causality is defined as a causality in which individual motives and intentions can be the drive of change. The purposive causality is dependent on the structural causality in the framework of the traditional functionalism. The methodology of the functionalism has been unable to give a full explanation to a creative character of human action. The structural causality, on its last stage, appears as a true causality only when it is mediated by a concrete action of a real person.

Stability and Strength of an Undercarriage Radius Rod

An undercarriage radius rod arrangement frequently employed comprises articulated members having a retraction jack locked internally in the down position to stabilize the system. The loads from the ground cases induced in the members are dependent upon the geometry of the system and also the clastic properties of the members and their respective airframe pick‐up structure. The conditions for structural stability are analysed and a method is given for determining the nominal offset of the radius rod knuckle to achieve an efficient strength‐to‐weight ratio for the structure.