Closed-form linear stability conditions for rotating RayleighBnard convection with rigid stress-free upper and lower boundaries

2003 ◽  
Vol 480 ◽  
pp. 25-42 ◽  
Author(s):  
R. C. KLOOSTERZIEL ◽  
G. F. CARNEVALE
Keyword(s):  
Closed Form ◽  
Linear Stability ◽  
Stability Conditions

Closed-form linear stability conditions for magneto-convection

2003 ◽  
Vol 490 ◽  
pp. 333-344 ◽  
Author(s):  
R. C. KLOOSTERZIEL ◽  
G. F. CARNEVALE
Keyword(s):  
Closed Form ◽  
Linear Stability ◽  
Stability Conditions

scholarly journals Analytical stability conditions for elastic composite materials with a non-positive-definite phase

2012 ◽  
Vol 468 (2144) ◽  
pp. 2230-2254 ◽  
Author(s):  
D. M. Kochmann ◽  
W. J. Drugan
Keyword(s):  
Stability Analysis ◽  
Composite Materials ◽  
Closed Form ◽  
Positive Definite ◽  
Stability Conditions ◽  
Two Phase ◽  
Analytical Stability ◽  
Sufficient Stability ◽  
Multi Phase ◽  
Sufficient Stability Conditions

Elastic multi-phase materials with a phase having appropriately tuned non-positive-definite elastic moduli have been shown theoretically to permit extreme increases in multiple desirable material properties. Stability analyses of such composites were only recently initiated. Here, we provide a thorough stability analysis for general composites when one phase violates positive-definiteness. We first investigate the dynamic deformation modes leading to instability in the fundamental two-phase solids of a coated cylinder (two dimensions) and a coated sphere (three dimensions), from which we derive closed-form analytical sufficient stability conditions for the full range of coating thicknesses. Next, we apply the energy method to derive a general correlation between composite stability limit and composite bulk modulus that enables determination of closed-form analytical sufficient stability conditions for arbitrary multi-phase materials by employing effective modulus formulas coupled with a numerical finite-element stability analysis. We demonstrate and confirm this new approach by applying it to (i) the two basic two-phase solids already analysed dynamically; and (ii) a more geometrically complex matrix/distributed-inclusions composite. The specific new analytical stability results, and new methods presented, provide a basis for creation of novel, stable composite materials.

Linear stability and stability of syzygy bundles

2018 ◽  
Vol 29 (11) ◽  
pp. 1850080 ◽  
Author(s):  
Abel Castorena ◽  
H. Torres-López
Keyword(s):  
Exact Sequence ◽  
Linear Stability ◽  
Commutative Diagram ◽  
Linear Series ◽  
Stability Conditions ◽  
Stable Bundle ◽  
Projective Curve ◽  
General Curve ◽  
The Stability ◽  
Natural Way

Let [Formula: see text] be a smooth irreducible projective curve and let [Formula: see text] be a complete and generated linear series on [Formula: see text]. Denote by [Formula: see text] the kernel of the evaluation map [Formula: see text]. The exact sequence [Formula: see text] fits into a commutative diagram that we call the Butler’s diagram. This diagram induces in a natural way a multiplication map on global sections [Formula: see text], where [Formula: see text] is a subspace and [Formula: see text] is the dual of a subbundle [Formula: see text]. When the subbundle [Formula: see text] is a stable bundle, we show that the map [Formula: see text] is surjective. When [Formula: see text] is a Brill–Noether general curve, we use the surjectivity of [Formula: see text] to give another proof of the semistability of [Formula: see text], moreover, we fill up a gap in some incomplete argument by Butler: With the surjectivity of [Formula: see text] we give conditions to determine the stability of [Formula: see text], and such conditions imply the well-known stability conditions for [Formula: see text] stated precisely by Butler. Finally we obtain the equivalence between the (semi)stability of [Formula: see text] and the linear (semi)stability of [Formula: see text] on [Formula: see text]-gonal curves.

Dynamical systems on networks

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Limit Cycles ◽  
Spectral Properties ◽  
Stability Conditions ◽  
Short Introduction ◽  
The Stability

An introduction to the theory of dynamical systems on networks. This chapter starts with a short introduction to classical (non-network) dynamical systems theory, including linear stability analysis, fixed points, and limit cycles. Dynamical systems on networks are introduced, focusing initially on systems with only one variable per node and progressing to multi-variable systems. Linear stability analysis is developed in detail, leading to master stability conditions and the connection between stability and the spectral properties of networks. The chapter ends with a discussion of synchronization phenomena, the stability of limit cycles, and master stability conditions for synchronization.

scholarly journals Stability Conditions for Affine Type A

2019 ◽  
Vol 23 (5) ◽  
pp. 2079-2111 ◽  
Author(s):  
P. J. Apruzzese ◽  
Kiyoshi Igusa
Keyword(s):  
Representation Theory ◽  
Linear Stability ◽  
Stability Condition ◽  
Central Charge ◽  
Type A ◽  
Maximal Length ◽  
Stability Conditions ◽  
Background Material ◽  
Affine Type

Abstract We construct maximal green sequences of maximal length for any affine quiver of type A. We determine which sets of modules (equivalently c-vectors) can occur in such sequences and, among these, which are given by a linear stability condition (also called a central charge). There is always at least one such maximal set which is linear. The proofs use representation theory and three kinds of diagrams shown in Fig. 1. Background material is reviewed with details presented in two separate papers Igusa (2017a, b).

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