Search results for "Eigenvalue"
showing 4 items of 344 documents
On Stability of a Concentrated Fiber Suspension Flow
2014
Linear stability analysis of a fiber suspension flow in a channel domain is performed using a modified Folgar-Tucker equation. Two kinds of potential instability are identified: one is associated with overcritical Reynolds number and another is associated with certain perturbations in fiber orientation field and is present for any Reynolds numbers. The second type of instability leads to initially growing transient perturbations in the microstructure. It is shown that both types of instability lead to instability of the bulk velocity field. As for the perturbed Orr-Sommerfeld eigenvalues, the presence of fibers increases the stability region; the stability region increases with growing C i …
Distribution of Large Eigenvalues for Elliptic Operators
2019
In this chapter we consider elliptic differential operators on a compact manifold and rather than taking the semi-classical limit (h →), we let h = 1 and study the distribution of large eigenvalues. Bordeaux Montrieux (Loi de Weyl presque sure et resolvante pour des operateurs differentiels non-autoadjoints, these, CMLS, Ecole Polytechnique, 2008. https://pastel.archives-ouvertes.fr/pastel-00005367, Ann Henri Poincare 12:173–204, 2011) studied elliptic systems of differential operators on S1 with random perturbations of the coefficients, and under some additional assumptions, he showed that the large eigenvalues obey the Weyl law almost surely. His analysis was based on a reduction to the s…
Computing the Trace
2001
So far we have been interested in the general expression for the WKB-propagation function. Now we turn our attention to the trace of that propagator, since we want to exhibit the energy eigenvalues of a given potential. From earlier discussions we know that the energy levels of a given Hamiltonian are provided by the poles of the Green’s function:
Game-Theoretic Approach to Hölder Regularity for PDEs Involving Eigenvalues of the Hessian
2021
AbstractWe prove a local Hölder estimate for any exponent $0<\delta <\frac {1}{2}$ 0 < δ < 1 2 for solutions of the dynamic programming principle $$ \begin{array}{@{}rcl@{}} u^{\varepsilon} (x) = \sum\limits_{j=1}^{n} \alpha_{j} \underset{\dim(S)=j}{\inf} \underset{|v|=1}{\underset{v\in S}{\sup}} \frac{u^{\varepsilon} (x + \varepsilon v) + u^{\varepsilon} (x - \varepsilon v)}{2} \end{array} $$ u ε ( x ) = ∑ j = 1 n α j inf dim ( S ) = j sup v ∈ S | v | = 1 u ε ( x + ε v ) + u ε ( x − ε v ) 2 with α1,αn > 0 and α2,⋯ ,αn− 1 ≥ 0. The proof is based on a new coupling idea from game theory. As an application, we get the same regularity estimate for viscosity solutions of the PDE $…