Search

We study the role of anharmonicity at interfaces with an added intermediate layer designed to facilitate interfacial phonon transport. Our results demonstrate that while in the harmonic limit the bridge may lower the conductance due to fewer available channels, anharmonicity can strongly enhance the thermal conductance of the bridged structure due to added inelastic channels. Moreover, we show that the effect of anharmonicity on the conductance can be tuned by varying temperature or the bridge layer thickness, as both parameters change the total rate of occurrence of phonon-phonon scattering processes. Additionally, we show that the additive rule of thermal resistances(Ohms law) is valid for bridge layer thickness quite shorter than the average bulk MFP, beyond the regime it would be expected to fail.

A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in ArXiv: 1502.03998 and ArXiv: 1709.05181, which in this paper are called \emph{mild equilibrium} and \emph{weak equilibrium} respectively, a strong equilibrium captures the idea of subgame perfect Nash equilibrium more accurately. When the state process is a continuous-time Markov chain and the discount function is log sub-additive, we show that an optimal mild equilibrium is always a strong equilibrium. Moreover, we provide a new iteration method that can directly construct an optimal mild equilibrium and thus also prove its existence., Comment: Final version. To appear in Mathematical Finance. Keywords:Time-inconsistency, optimal stopping, strong equilibria, weak equilibria, mild equilibria, non-exponential discounting, subgame perfect Nash equilibrium

We numerically investigate thermal transport at solid-solid interfaces with graded intermediate layers whose masses vary exponentially from one side to the other. Using Non-Equilibrium Green's Function and Non-Equilibrium Molecular Dynamics simulations, we show that an exponentially mass-graded junction with a finite thickness can result in 68\% of enhancement in thermal conductance larger compared to a single bridging layer (29\%) and a linear mass-graded junction (64\%) of similar thickness. We examine how the thermal conductance at such interfaces is influenced by geometric qualities and strength of anharmonicity. For geometric properties, we tested the effects from number of layers and the junction thickness. In the absence of anharmonicity, increasing the number of layers results in better elastic phonon transmission at each individual boundary, countered by the decrease of available conducting channels. Consequently, in the harmonic regime, conductance initially increases with number of layers due to better bridging, but quickly saturates. The presence of slight anharmonic effects (at ultra-low temperature T = 2 K) turns the saturation into a monotonically increasing trend. Anharmonic effects can facilitate interfacial thermal transport through the thermalization of phonons. At high temperature, however, the role of anharmonicity as a facilitator of interfacial thermal transport reverses. Strong anharmonicity introduces significant intrinsic resistance, overruling the enhancement in thermal conduction at the boundaries. Our analysis shows that in our model Lennard-Jones system, the influence of a mass-graded junction on thermal conductance is dominated by the phonon thermalization through anharmonic effects, while elastic phonon transmission plays a secondary role.

Inspired by Strotz's consistent planning strategy, we formulate the infinite horizon mean-variance stopping problem as a subgame perfect Nash equilibrium in order to determine time consistent strategies with no regret. Equilibria among stopping times or randomized stopping times may not exist. This motivates us to consider the notion of liquidation strategies, which lets the stopping right to be divisible. We then argue that the mean-standard deviation variant of this problem makes more sense for this type of strategies in terms of time consistency. It turns out that an equilibrium liquidation strategy always exists. We then analyze whether optimal equilibrium liquidation strategies exist and whether they are unique and observe that neither may hold., Comment: Final version. To appear in the SIAM Journal on Financial Mathematics. Keywords: Time-inconsistency, optimal stopping, liquidation strategy, mean-variance problem, subgame perfect Nash equilibrium

We theoretically explore the influence of end-group chemistry (bond stiffness and mass) on the interfacial thermal conductance at a gold-alkane interface. We accomplish this using the Non-Equilibrium Green's Function (NEGF) coupled with first principle parameters in Density Functional Theory (DFT) within the harmonic approximation. Our results indicate that the interfacial thermal conductance is not a monotonic function of either chemical parameters, but instead maximizes at an optimal set of mass and bonding strength. This maximum is a result of the interplay between the overlap in local density of states of the device and that in the contacts, as well as the phonon group velocity. We also demonstrate the intrinsic relationship between the Diffusive Mismatch Model (DMM) and the properties from NEGF, and provide an approach to get DMM from first principles NEGF. By comparing the NEGF based DMM conductance and range of conductance while altering the mass and bonding strength, we show that DMM provides an upper bound for elastic transport in this dimensionally mismatched system. We thus have a prescription to enhance the thermal conductance of systems at low temperatures or at low dimensions where inelastic scattering is considerably suppressed.