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Advanced Engineering Materials, EarlyView.Geometry‐driven thermal behavior in wire‐arc additive manufacturing (WAAM) influences microstructural evolution during nonequilibrium solidification of a chemically complex Fe–Cr–Nb–W–Mo–C nanocomposite system. By comparing different deposits configurations, distinct entropy–cooling rate correlations, segregation, and carbide evolution are revealed ...
Blanca Palacios +5 more
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Advanced Engineering Materials, EarlyView.Disordered (Fe50Co50)1−xPtx thin films exhibit a pronounced anomalous Nernst effect (ANE) with a strong composition dependence on both rigid and flexible substrates. The transverse thermoelectric response peaks near 22.5 at.% Pt, accompanied by enhanced αxy/σxy scaling, thermal transport, and ANE sensitivity.
Mojtaba Mohammadi +2 more
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Local Manifold Approximation of Dynamical System Based on Neural Ordinary Differential Equation
Xiao Ya +5 more
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Ordinary Differential Equations
Arch. Formal Proofs, 2012In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice.
Fabian Immler, Johannes Hölzl
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On Implicit Ordinary Differential Equations
IMA Journal of Numerical Analysis, 1984A geometric analysis of the problem \(f(x,y,y')=0\) is given which may be of value in developing numerical methods for solution near the singular points where \(fy'=0\). In particular, the approach here shows problems of switching branches when computing numerically a solution near an envelope, as noted by \textit{L. Fox} and \textit{D. F.
A. JEPSON, A. SPENCE
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Uniqueness for ordinary differential equations
Mathematical Systems Theory, 1975Various criteria are known for assuring uniqueness of the solution of a system ofn ordinary differential equations,x′ = f(t, x), with initial conditionx(t0) = x0. Most of these involve some sort of relaxed Lipschitz condition onf(t, x), with respect tox, valid on an open setD ⊂ R1+n which contains the point (t0, x0).
Stephen R. Bernfeld +2 more
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Reducible Ordinary Differential Equations
Journal of Nonlinear Science, 2006The class of reducible differential equations under consideration here includes the class of symmetric systems, and examples show that the inclusion is proper. We first discuss reducibility, as well as the stronger concept of complete reducibility, from the viewpoint of Lie algebras of vector fields and their invariants, and find Lie algebra conditions
Karl Peter Hadeler, Sebastian Walcher
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Multivalued Differential Equations and Ordinary Differential Equations
SIAM Journal on Applied Mathematics, 1970(E) e F(x, t), where F is upper semicontinuous, from known results in the theory of ordinary differential equations. This will be accomplished by showing that, for any F upper semicontinuous and convex, it is always possible to "approximate" the multivalued differential equation (E) by appropriately chosen ordinary differential equations. This would be
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Explicit Ordinary Differential Equations
1998In the last chapter we discussed the numerical treatment of explicit ordinary differential equations. Here, we will consider the more general case, implicit ordinary differential equations.
Edda Eich-Soellner, Claus Führer
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