The Origin of the Boson Peak and the Thermal Conductivity Plateau in Low Temperature Glasses

We argue that the intrinsic glassy degrees of freedom in amorphous solids giving rise to the thermal conductivity plateau and the ``boson peak'' in the heat capacity at moderately low temperatures are directly connected to those motions giving rise to the two-level like excitations seen at still lower temperatures. These degrees of freedom can be thought of as strongly anharmonic transitions between the local minima of the glassy energy landscape that are accompanied by ripplon-like domain wall motions of the glassy mosaic structure predicted to occur at $T_g$ by the random first order transition theory. The energy spectrum of the vibrations of the mosaic depends on the glass transition temperature, the Debye frequency and the molecular length scale. The resulting spectrum reproduces the experimental low temperature Boson peak. The ``non-universality'' of the thermal conductivity plateau depends on $k_B T_g/\hbar \omega_D$ and arises from calculable interactions with the phonons.Comment: 4 pages, submitted to PR

Introduction to co-split Lie algebras

In this work, we introduce a new concept which is obtained by defining a new compatibility condition between Lie algebras and Lie coalgebras. With this terminology, we describe the interrelation between the Killing form and the adjoint representation in a new perspective

Robust semi-explicit model predictive control for hybrid automata

In this paper we propose an on-line design technique for the target control problem of hybrid automata. First, we compute on-line the shortest path, which has the minimum discrete cost, from an initial state to the given target set. Next, we derive a controller which successfully drives the system from the initial state to the target set while minimizing a cost function. The (robust) model predictive control (MPC) technique is used when the current state is not within a guard set, otherwise the (robust) mixed-integer predictive control (MIPC) technique is employed. An on-line, semi-explicit control algorithm is derived by combining the two techniques and applied on a high-speed and energy-saving control problem of the CPU processing

A Direct Elliptic Solver Based on Hierarchically Low-rank Schur Complements

A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with $O(N \log^2 N)$ arithmetic complexity and $O(N \log N)$ memory footprint. We provide a baseline for performance and applicability by comparing with well known implementations of the $\mathcal{H}$-LU factorization and algebraic multigrid with a parallel implementation that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $\mathcal{H}$-LU and that it can tackle problems where algebraic multigrid fails to converge