Rare event sampling in applied stochastic dynamical systems

Predicting rare events is a challenging problem in many complex systems arising in physics, chemistry, biology, and materials science. Simulating rare events is often prohibitive in such systems due to their high dimensionality and the numerical cost of their simulation, yet analytical expressions for rare event probabilities are usually not available. This dissertation tackles the problem of approximation of the probability of rare catastrophic events in optical communication systems and spin-torque magnetic nanodevices. With the application of the geometric minimum action method, the probability of pulse position shifts or other parameter changes in a model of an actively mode-locked laser subject to noise from amplified spontaneous emission can be quantified. Similarly, by applying importance sampling with biasing functions motivated by optimal control, read and write soft error rates of macrospin and coupled-spin systems of spin-torque magnetic nanodevices can be efficiently estimated

Broadband Quantum Efficiency Enhancement in High Index Nanowires Resonators

Light trapping in sub-wavelength semiconductor nanowires (NWs) offers a promising approach to simultaneously reducing material consumption and enhancing photovoltaic performance. Nevertheless, the absorption efficiency of a NW, defined by the ratio of optical absorption cross section to the NW diameter, lingers around 1 in existing NW photonic devices, and the absorption enhancement suffers from a narrow spectral width. Here, we show that the absorption efficiency can be significantly improved in NWs with higher refractive indices, by an experimental observation of up to 350% external quantum efficiency (EQE) in lead sulfide (PbS) NW resonators, a 3-fold increase compared to Si NWs. Furthermore, broadband absorption enhancement is achieved in single tapered NWs, where light of various wavelengths is absorbed at segments with different diameters analogous to a tandem solar cell. Overall, the single NW Schottky junction solar cells benefit from optical resonance, near bandgap open circuit voltage, and long minority carrier diffusion length, demonstrating power conversion efficiency (PCE) comparable to single Si NW coaxial p-n junction cells11, but with much simpler fabrication processes

Consumer Asset Pricing Model Based on Heterogeneous Consumers and the Mystery of Equity Premium

As one of the core models of finance, the consumer capital asset pricing model (CCAPM) has produced the puzzle of equity premium. In order to explain this problem and get a more realistic pricing formula, this paper uses constant absolute risk aversion coefficient (Cara) utility function and introduces heterogeneous consumers to improve the original model, and finally gets a more effective form and there is no original puzzle in this form. At the end of the article, the American data are used to verify the results. The regression results support this model very well

OBMeshfree: An optimization-based meshfree solver for nonlocal diffusion and peridynamics models

We present OBMeshfree, an Optimization-Based Meshfree solver for compactly supported nonlocal integro-differential equations (IDEs) that can describe material heterogeneity and brittle fractures. OBMeshfree is developed based on a quadrature rule calculated via an equality constrained least square problem to reproduce exact integrals for polynomials. As such, a meshfree discretization method is obtained, whose solution possesses the asymptotically compatible convergence to the corresponding local solution. Moreover, when fracture occurs, this meshfree formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. As numerical examples, we consider the problem of modeling both homogeneous and heterogeneous materials with nonlocal diffusion and peridynamics models. Convergences to the analytical nonlocal solution and to the local theory are demonstrated. Finally, we verify the applicability of the approach to realistic problems by reproducing high-velocity impact results from the Kalthoff-Winkler experiments. Discussions on possible immediate extensions of the code to other nonlocal diffusion and peridynamics problems are provided. OBMeshfree is freely available on GitHub.Comment: For associated code, see https://github.com/youhq34/meshfree_quadrature_nonloca