Deconstructing the glass transition through critical experiments on colloids

The glass transition is the most enduring grand-challenge problem in contemporary condensed matter physics. Here, we review the contribution of colloid experiments to our understanding of this problem. First, we briefly outline the success of colloidal systems in yielding microscopic insights into a wide range of condensed matter phenomena. In the context of the glass transition, we demonstrate their utility in revealing the nature of spatial and temporal dynamical heterogeneity. We then discuss the evidence from colloid experiments in favor of various theories of glass formation that has accumulated over the last two decades. In the next section, we expound on the recent paradigm shift in colloid experiments from an exploratory approach to a critical one aimed at distinguishing between predictions of competing frameworks. We demonstrate how this critical approach is aided by the discovery of novel dynamical crossovers within the range accessible to colloid experiments. We also highlight the impact of alternate routes to glass formation such as random pinning, trajectory space phase transitions and replica coupling on current and future research on the glass transition. We conclude our review by listing some key open challenges in glass physics such as the comparison of growing static lengthscales and the preparation of ultrastable glasses, that can be addressed using colloid experiments.Comment: 137 pages, 45 figure

Elastic scattering of e- and e+ from Rb and Cd

Differential cross section results are calculated for the elastic scattering of electrons and positrons from the ground state of Rb and Cd atoms. An optical model potential approach is used for the calculation. Results are compared with the available electron impact experimental results

The Other Side of the Tradeoff: The Impact of Risk on Executive Compensation

The principal-agent model of executive compensation is of central importance to the modern theory of the firm and corporate governance, yet the existing empirical evidence supporting it is quite weak. The key predication of the model is that the executive's pay-performance sensitivity is decreasing in the variance of the firm's performance. We demonstrate strong empirical confirmation of this prediction using a comprehensive sample of executives at large corporations. In general, the pay-performance sensitivity for executives at firms with the least volatile stock prices is an order of magnitude greater than the pay-performance sensitivity for executives at firms with the most volatile stock prices. This result holds for both chief executive officers and for other highly compensated executives. We further show that estimates of the pay-performance sensitivity that do not explicitly account for the effect of the variance of firm performance are biased toward zero. We also test for relative performance evaluation of executives against the performance of other firms. We find little support for the relative performance evaluation model. Our findings suggest that executive compensation contracts incorporate the benefits of risk-sharing but do not incorporate the potential informational advantages of relative performance evaluation.

Executive Compensation, Strategic Competition, and Relative Performance Evaluation: Theory and Evidence

We argue that strategic interactions between firms in an oligopoly can explain the puzzling lack of high-powered incentives in executive compensation contracts written by shareholders whose objective is to maximize the value of their shares. We derive the optimal compensation contracts for managers and demonstrate that the use of high-powered incentives will be limited by the need to soften product market competition. In particular, when managers can be compensated based on their own and their rivals' performance, we show that there will be an inverse relationship between the magnitude of high-powered incentives and the degree of competition in the industry. More competitive industries are characterized by weaker pay-performance incentives. Empirically, we find strong evidence of this inverse relationship in the compensation of executives in the United States. Our econometric results are not consistent with alternative theories of the effect of competition on executive compensation. We conclude that strategic considerations can preclude the use of high-powered incentives, in contrast to the predictions of the standard principal-agent model.

Preventing Unraveling in Social Networks Gets Harder

The behavior of users in social networks is often observed to be affected by the actions of their friends. Bhawalkar et al. \cite{bhawalkar-icalp} introduced a formal mathematical model for user engagement in social networks where each individual derives a benefit proportional to the number of its friends which are engaged. Given a threshold degree $k$ the equilibrium for this model is a maximal subgraph whose minimum degree is $\geq k$. However the dropping out of individuals with degrees less than $k$ might lead to a cascading effect of iterated withdrawals such that the size of equilibrium subgraph becomes very small. To overcome this some special vertices called "anchors" are introduced: these vertices need not have large degree. Bhawalkar et al. \cite{bhawalkar-icalp} considered the \textsc{Anchored $k$-Core} problem: Given a graph $G$ and integers $b, k$ and $p$ do there exist a set of vertices $B\subseteq H\subseteq V(G)$ such that $|B|\leq b, |H|\geq p$ and every vertex $v\in H\setminus B$ has degree at least $k$ is the induced subgraph $G[H]$. They showed that the problem is NP-hard for $k\geq 2$ and gave some inapproximability and fixed-parameter intractability results. In this paper we give improved hardness results for this problem. In particular we show that the \textsc{Anchored $k$-Core} problem is W[1]-hard parameterized by $p$, even for $k=3$. This improves the result of Bhawalkar et al. \cite{bhawalkar-icalp} (who show W[2]-hardness parameterized by $b$) as our parameter is always bigger since $p\geq b$. Then we answer a question of Bhawalkar et al. \cite{bhawalkar-icalp} by showing that the \textsc{Anchored $k$-Core} problem remains NP-hard on planar graphs for all $k\geq 3$, even if the maximum degree of the graph is $k+2$. Finally we show that the problem is FPT on planar graphs parameterized by $b$ for all $k\geq 7$.Comment: To appear in AAAI 201

Site-Specific Colloidal Crystal Nucleation by Template-enhanced Particle Transport

The monomer surface mobility is the single most important parameter that decides the nucleation density and morphology of islands during thin film growth. During template-assisted surface growth in particular, low surface mobilities can prevent monomers from reaching target sites and this results in a partial to complete loss of nucleation control. While in atomic systems a broad range of surface mobilities can be readily accessed, for colloids, owing to their large size, this window is substantially narrow and therefore imposes severe restrictions in extending template-assisted growth techniques to steer their self-assembly. Here, we circumvented this fundamental limitation by designing templates with spatially varying feature sizes, in this case moire patterns, which in the presence of short-range depletion attraction presented surface energy gradients for the diffusing colloids. The templates serve a dual purpose, first, directing the particles to target sites by enhancing their surface mean free paths and second, dictating the size and symmetry of the growing crystallites. Using optical microscopy, we directly followed the nucleation and growth kinetics of colloidal islands on these surfaces at the single-particle level. We demonstrate nucleation control, with high fidelity, in a regime that has remained unaccessed in theoretical, numerical and experimental studies on atoms and molecules as well. Our findings pave the way for fabricating non-trivial surface architectures composed of complex colloids and nanoparticles.Comment: 12 pages, 3 figure