Ultrahigh Enhancement of Electromagnetic Fields by Exciting Localized with Extended Surface Plasmons

Excitation of localized surface plasmons (LSPs) of metal nanoparticles (NPs) residing on a flat metal film has attracted great attentions recently due to the enhanced electromagnetic (EM) fields found to be higher than the case of NPs on a dielectric substrate. In the present work, it is shown that even much higher enhancement of EM fields is obtained by exciting the LSPs through extended surface plasmons (ESPs) generated at the metallic film surface using the Kretschmann-Raether configuration. We show that the largest EM field enhancement and the highest surface-enhanced fluorescence intensity are obtained when the incidence angle is the ESP resonance angle of the underlying metal film. The finite-difference time-domain simulations indicate that excitation of LSPs using ESPs can generate 1-3 orders higher EM field intensity than direct excitation of the LSPs using incidence from free space. The ultrahigh enhancement is attributed to the strong confinement of the ESP waves in the vertical direction. The drastically intensified EM fields are significant for highly-sensitive refractive index sensing, surface-enhanced spectroscopies, and enhancing the efficiency of optoelectronic devices.Comment: 25 pages, 5 figures and supplimentary informatio

Product Line Design, Pricing and Framing under General Choice Models

This thesis handles fundamental problems faced by retailers everyday: how do consumers make choices from an enormous variety of products? How to design a product portfolio to maximize the expected profit given consumers’ choice behavior? How to frame products if consumers’ choices are influenced by the display location? We solve those problems by first, constructing mathematical models to describe consumers’ choice behavior from a given offer set, i.e., consumer choice models; second, by designing efficient algorithms to optimally select the product portfolio to maximize the expected profit, i.e., assortment optimization. This thesis consists of three main parts: the first part solves assortment optimization problem under a consideration set based choice model proposed by Manzini and Mariotti (2014) [Manzini, Paola, Marco Mariotti. 2014. Stochastic choice and consideration sets. Econometrica 82(3) 1153-1176.]; the second part proposes an approximation algorithm to jointly optimize products’ selection and display; the third part works on optimally designing a product line under the Logit family choice models when a product’s utility depends on attribute-level configurations

Multiple solutions to elliptic equations on RN\mathbb{R}^N with combined nonlinearities

In this paper, we are concerned with the multiplicity of nontrivial radial solutions for the following elliptic equation \begin{equation*} \begin{cases} - \Delta u +V(x)u = -\lambda Q(x)|u|^{q-2}u+ Q(x)f(u),\quad x\in\mathbb{R}^N,\\ u(x)\rightarrow 0,\quad \hbox{as}\ |x|\rightarrow +\infty,\end{cases} \tag*{(P)$_\lambda$} \end{equation*} where $1<q<2,\ \lambda\in \mathbb{R}^+,\ N\geq 3$, $V$ and $Q$ are radial positive functions, which can be vanishing or coercive at infinity, $f$ is asymptotically linear or superlinear at infinity

Revenue Maximization and Learning in Products Ranking

We consider the revenue maximization problem for an online retailer who plans to display a set of products differing in their prices and qualities and rank them in order. The consumers have random attention spans and view the products sequentially before purchasing a ``satisficing'' product or leaving the platform empty-handed when the attention span gets exhausted. Our framework extends the cascade model in two directions: the consumers have random attention spans instead of fixed ones and the firm maximizes revenues instead of clicking probabilities. We show a nested structure of the optimal product ranking as a function of the attention span when the attention span is fixed and design a $1/e$-approximation algorithm accordingly for the random attention spans. When the conditional purchase probabilities are not known and may depend on consumer and product features, we devise an online learning algorithm that achieves $\tilde{\mathcal{O}}(\sqrt{T})$ regret relative to the approximation algorithm, despite of the censoring of information: the attention span of a customer who purchases an item is not observable. Numerical experiments demonstrate the outstanding performance of the approximation and online learning algorithms

Sewage Discharging in a Line: Global Optimization and Grand Cooperation

Players cooperating in a line is a special while essential phenomenon in real life collaborating activities such as assembly line production, pipeline supply chain management and other streamlining operational settings. In this paper, we study the scenario of cooperative sewage discharge with multiple participants positioning in a line along a river such that the optimization decision and cooperation strategy are mutually affected by both upstream and downstream players. We make three main contributions accordingly: Firstly, we formalize the sewage discharge problem (SDP) for different groups of players, and use greedy strategy and dynamic programming to design the optimal algorithms to solve the SDP in polynomial time. Secondly, we show that the cooperative game defined on sewage discharge problem, referred to as SDG, has a non-empty core due to its special line-positioning structure. Therefore, a grand stable cooperation is guaranteed. Furthermore, inspired by the fact that the SDG is core non-empty while non-convex, we successfully identify a relaxed concept of convexity -- directional-convexity, which can also serve as a sufficient condition for a cooperative game having a non-empty core

Approximation algorithms for product framing and pricing

We propose one of the first models of “product framing” and pricing. Product framing refers to the way consumer choice is influenced by how the products are framed or displayed. We present a model in which a set of products is displayed or framed into a set of virtual web pages. We assume that consumers consider only products in the top pages with different consumers willing to see different numbers of pages. Consumers select a product, if any, from these pages following a general choice model. We show that the product-framing problem is NP-hard. We derive algorithms with guaranteed performance relative to an optimal algorithm under reasonable assumptions. Our algorithms are fast and easy to implement. We also present structural results and design algorithms for pricing under framing effects for the multinomial logit model. We show that, for profit maximization problems, at optimality, products are displayed in descending order of their value gap and in ascending order of their markups

Experimental and numerical studies on indoor thermal comfort in fluid flow: a case study on primary school classrooms

Indoor thermal comfort in primary classrooms is important to students' learning and health. The studies focusing on it, especially under the subtropical plateau monsoon climate, are scarce. In this study, the indoor thermal comfort surveys and parameter measurements were made over the period from October 2018 to December 2018 in Kunming, China. A series of indoor thermal comfort and outdoor parameters were measured each 1 h and subjective questionnaire surveys were performed on the selected 20 students every week except on holidays. A series of three-dimensional numerical simulations were carried out using ANSYS Fluent