Reduced order modeling plays an indispensible role in most real-world complex models. A hybrid application of order reduction methods, introduced previously, has been shown to effectively reduce the computational cost required to find a reduced order model with quantifiable bounds on the reduction errors, which is achieved by hybridizing the application of local variational and global sampling ...

We derive a phase field model which approximates a sharp interface model for solidification of a multicomponent alloy to second order in the interfacial thickness ε. Since in numerical computations for phase field models the spatial grid size has to be smaller than ε the new approach allows for considerably more accurate phase field computations than have been possible so far. In the classical ...

The traditional parameter used as a measure of vulnerability of a network modeled by a graph with perfect nodes and edges that may fail is the edge connectivity λ. Of course , () p q K p λ = where p q ≤. In that case, failure of the network simply means that the surviving subgraph becomes disconnected upon the failure of individual edges. If, instead, failure of the network is defined to mean t...

The line density of line defects in terms of a two-component vector order parameter are obtained from the definition of topological charges of line defects. The spatial structure and bifurcation of line defects in three-dimensional space are also studied from the topological properties of the two-component vector order parameter. The branch conditions for generating, annihilating, colliding, sp...

We derive a structural model of the amount of private information that is conveyed to the market via order flows. The model is a continuous-time Kyle model in which there is public information arrival and in which the strategic trader may or may not have private information. For empirical implementation, we treat each trading day as a separate instance of the model. Monte Carlo analysis shows t...

The low-order modes of spheroidal, pure electron plasmas have been studied experimentally, both in a cylindrical eiectrode structure and in a quadrupole trap. Comparison is made between measurements of mode frequencies, recent analytical theories, and numerical simulations. Effects considered include trap anharmonicity, image charges, and temperature. Quantitative agreement is obtained between ...

We investigate the nematic and loop-current-type orders that may arise as vestigial precursor phases in a model with an underlying pair-density wave (PDW) instability. discuss how such phase gives rise to highly anisotropic stiffness for coexisting single-component superconductor low intrinsic stiffness, is case underdoped cuprate superconductors. Next, focusing on regime mean-field PDW ground ...