Length Dependent Thermal Conductivity Measurements Yield Phonon Mean Free Path Spectra in Nanostructures

Thermal conductivity measurements over variable lengths on nanostructures such as nanowires provide important information about the mean free paths (MFPs) of the phonons responsible for heat conduction. However, nearly all of these measurements have been interpreted using an average MFP even though phonons in many crystals possess a broad MFP spectrum. Here, we present a reconstruction method to obtain MFP spectra of nanostructures from variable-length thermal conductivity measurements. Using this method, we investigate recently reported length-dependent thermal conductivity measurements on SiGe alloy nanowires and suspended graphene ribbons. We find that the recent measurements on graphene imply that 70 % of the heat in graphene is carried by phonons with MFPs longer than 1 micron

Density-functional calculations of the electronic structure and lattice dynamics of superconducting LaO0.5_{0.5}F0.5_{0.5}BiS2_{2}: Evidence for an electron-phonon interaction near the charge-density-wave instability

We discuss the electronic structure, lattice dynamics and electron-phonon interaction of newly discovered superconductor LaO$_{0.5}$F$_{0.5}$BiS$_{2}$ using density functional based calculations. A strong Fermi surface nesting at $\mathbf{k}$=($\pi$,$\pi$,0) suggests a proximity to charge density wave instability and leads to imaginary harmonic phonons at this $\mathbf{k}$ point associated with in-plane displacements of S atoms. Total energy analysis resolves only a shallow double-well potential well preventing the appearance of static long-range order. Both harmonic and anharmonic contributions to electron-phonon coupling are evaluated and give a total coupling constant $\lambda \simeq 0.85$ prompting this material to be a conventional superconductor contrary to structurally similar FeAs materials.Comment: Supplementary Materials is adde

Sympathy and Punishment: Evolution of Cooperation in Public Goods Game

An important way to maintain human cooperation is punishing defection. However, since punishment is costly, how can it arise and evolve given that individuals who contribute but do not punish fare better than the punishers? This leads to a violation of causality, since the evolution of punishment is prior to the one of cooperation behaviour in evolutionary dynamics. Our public goods game computer simulations based on generalized Moran Process, show that, if there exists a \'behaviour-based sympathy\' that compensates those who punish at a personal cost, the way for the emergence and establishment of punishing behaviour is paved. In this way, the causality violation dissipates. Among humans sympathy can be expressed in many ways such as care, praise, solace, ethical support, admiration, and sometimes even adoration; in our computer simulations, we use a small amount of transfer payment to express \'behaviour-based sympathy\'. Our conclusions indicate that, there exists co-evolution of sympathy, punishment and cooperation. According to classical philosophy literature, sympathy is a key factor in morality and justice is embodied by punishment; in modern societies, both the moral norms and the judicial system, the representations of sympathy and punishment, play an essential role in stable social cooperation.Public Goods Game, Cooperation, Social Dilemma, Co-Evolution, Sympathy, Punishment

Inertial coalescence of droplets on a partially wetting substrate

We consider the growth rate of the height of the connecting bridge in rapid surface-tension-driven coalescence of two identical droplets attached on a partially wetting substrate. For a wide range of contact angle values, the height of the bridge grows with time following a power law with a universal exponent of 2/3, up to a threshold time, beyond which a 1/2 exponent results, that is known for coalescence of freely-suspended droplets. In a narrow range of contact angle values close to 90°, this threshold time rapidly vanishes and a 1/2 exponent results for a 90° contact angle. The argument is confirmed by three-dimensional numerical simulations based on a diffuse interface method with adaptive mesh refinement and a volume-of-fluid method

Low-Degree Hardness of Detection for Correlated Erd\H{o}s-R\'enyi Graphs

Given two Erd\H{o}s-R\'enyi graphs with $n$ vertices whose edges are correlated through a latent vertex correspondence, we study complexity lower bounds for the associated correlation detection problem for the class of low-degree polynomial algorithms. We provide evidence that any degree-$O(\rho^{-1})$ polynomial algorithm fails for detection, where $\rho$ is the edge correlation. Furthermore, in the sparse regime where the edge density $q=n^{-1+o(1)}$, we provide evidence that any degree-$d$ polynomial algorithm fails for detection, as long as $\log d=o\big( \frac{\log n}{\log nq} \wedge \sqrt{\log n} \big)$ and the correlation $\rho<\sqrt{\alpha}$ where $\alpha\approx 0.338$ is the Otter's constant. Our result suggests that several state-of-the-art algorithms on correlation detection and exact matching recovery may be essentially the best possible.Comment: 40 page