Microscopic Description of Coherent Transport by Thermal Phonons

We demonstrate the coherent transport of thermal energy in superlattices by introducing a microscopic definition of the phonon coherence length. We demonstrate how to distinguish a coherent transport regime from diffuse interface scattering and discuss how these can be specifically controlled by several physical parameters. Our approach provides a convenient framework for the interpretation of previous experiments and thermal conductivity calculations and paves the way for the design of a new class of thermal interface materials.Comment: 5 pages, 6 figures, 1 tables The method which is described is too sensitive to numerical noise. A new method has been developed and published in http://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.01430

Distinguishing between spatial coherence and temporal coherence of phonons

Coherent phonon transport is regarded as a promising strategy for controlling thermal properties in solids using the wave nature of phonons. However, no clear distinction between the spatial and temporal phonon coherence has been accounted for and a formalism that quantifies these two effects is still to be found. In this work, we propose a statistical approach for calculating the spatial and temporal coherence spectra using molecular dynamics simulations. We provide a microscopic assessment of these properties and we theoretically demonstrate that, while temporal and spatial coherence can be analytically related under specific conditions, they represent two characteristic lengths that set apart different physical effects. The former is associated with the phonon mean free path while the latter can be regarded as a measure of localization, representing the spatial extension of phonon wave packets. This provides a framework to engineer heat conduction in solids by quantitatively revealing the wave/particle nature of the vibrational modes

Isometric path complexity of graphs

A set $S$ of isometric paths of a graph $G$ is "$v$-rooted", where $v$ is a vertex of $G$, if $v$ is one of the end-vertices of all the isometric paths in $S$. The isometric path complexity of a graph $G$, denoted by $ipco(G)$, is the minimum integer $k$ such that there exists a vertex $v\in V(G)$ satisfying the following property: the vertices of any isometric path $P$ of $G$ can be covered by $k$ many $v$-rooted isometric paths. First, we provide an $O(n^2 m)$-time algorithm to compute the isometric path complexity of a graph with $n$ vertices and $m$ edges. Then we show that the isometric path complexity remains bounded for graphs in three seemingly unrelated graph classes, namely, hyperbolic graphs, (theta, prism, pyramid)-free graphs, and outerstring graphs. Hyperbolic graphs are extensively studied in Metric Graph Theory. The class of (theta, prism, pyramid)-free graphs are extensively studied in Structural Graph Theory, e.g. in the context of the Strong Perfect Graph Theorem. The class of outerstring graphs is studied in Geometric Graph Theory and Computational Geometry. Our results also show that the distance functions of these (structurally) different graph classes are more similar than previously thought. There is a direct algorithmic consequence of having small isometric path complexity. Specifically, we show that if the isometric path complexity of a graph $G$ is bounded by a constant, then there exists a polynomial-time constant-factor approximation algorithm for ISOMETRIC PATH COVER, whose objective is to cover all vertices of a graph with a minimum number of isometric paths. This applies to all the above graph classes.Comment: A preliminary version appeared in the proceedings of the MFCS 2023 conferenc

Cop and robber games when the robber can hide and ride

International audienceIn the classical cop and robber game, two players, the cop C and the robber R, move alternatively along edges of a finite graph G = (V , E). The cop captures the robber if both players are on the same vertex at the same moment of time. A graph G is called cop win if the cop always captures the robber after a finite number of steps. Nowakowski, Winkler (1983) and Quilliot (1983) characterized the cop-win graphs as dismantlable graphs. In this talk, we will characterize in a similar way the class CWFR(s, s′ ) of cop-win graphs in the game in which the cop and the robber move at different speeds s′ and s, s′ ≤ s. We also establish some connections between cop-win graphs for this game with s′ 1. We characterize the graphs which are k-winnable for any value of k

Medians in median graphs and their cube complexes in linear time

The median of a set of vertices $P$ of a graph $G$ is the set of all vertices $x$ of $G$ minimizing the sum of distances from $x$ to all vertices of $P$. In this paper, we present a linear time algorithm to compute medians in median graphs, improving over the existing quadratic time algorithm. We also present a linear time algorithm to compute medians in the $\ell_1$-cube complexes associated with median graphs. Median graphs constitute the principal class of graphs investigated in metric graph theory and have a rich geometric and combinatorial structure, due to their bijections with CAT(0) cube complexes and domains of event structures. Our algorithm is based on the majority rule characterization of medians in median graphs and on a fast computation of parallelism classes of edges ($\Theta$-classes or hyperplanes) via Lexicographic Breadth First Search (LexBFS). To prove the correctness of our algorithm, we show that any LexBFS ordering of the vertices of $G$ satisfies the following fellow traveler property of independent interest: the parents of any two adjacent vertices of $G$ are also adjacent. Using the fast computation of the $\Theta$-classes, we also compute the Wiener index (total distance) of $G$ in linear time and the distance matrix in optimal quadratic time

Mapping Simple Polygons: How Robots Benefit from Looking Back

We consider the problem of mapping an initially unknown polygon of size n with a simple robot that moves inside the polygon along straight lines between the vertices. The robot sees distant vertices in counter-clockwise order and is able to recognize the vertex among them which it came from in its last move, i.e.the robot can look back. Other than that the robot has no means of distinguishing distant vertices. We assume that an upper bound on n is known to the robot beforehand and show that it can always uniquely reconstruct the visibility graph of the polygon. Additionally, we show that multiple identical and deterministic robots can always solve the weak rendezvous problem in which the robots need to position themselves such that all of them are mutually visible to each other. Our results are tight in the sense that the strong rendezvous problem, where robots need to gather at a vertex, cannot be solved in general, and, without knowing a bound beforehand, not even n can be determined. In terms of mobile agents exploring a graph, our result implies that they can reconstruct any graph that is the visibility graph of a simple polygon. This is in contrast to the known result that the reconstruction of arbitrary graphs is impossible in general, even if n is know

Quantum thermal bath for molecular dynamics simulation

International audienceMolecular dynamics (MD) is a numerical simulation technique based on classical mechanics. It has been taken for granted that its use is limited to a large temperature regime where classical statistics is valid. To overcome this limitation, the authors introduce in a universal way a quantum thermal bath that accounts for quantum statistics while using standard MD. The efficiency of the new technique is illustrated by reproducing several experimental data at low temperatures in a regime where quantum statistical effects cannot be neglected

Radiative heat transfer from a black body to dielectric nanoparticles

International audienceHeating of dielectric nanoparticles by black-body radiation is investigated by using molecular-dynamics simulation. The thermal interaction with the radiation is modeled by coupling the ions with a random electric field and including a radiation reaction force. This approach shows that the heat is absorbed by the polariton mode. Its subsequent redistribution among other vibration modes strongly depends on the particle size and on temperature.We observe energy trapping in a finite subset of vibrational mode

Thermal Interface Conductance between Aluminum and Silicon by Molecular Dynamics Simulations

The thermal interface conductance between Al and Si was simulated by a non-equilibrium molecular dynamics method. In the simulations, the coupling between electrons and phonons in Al are considered by using a stochastic force. The results show the size dependence of the interface thermal conductance and the effect of electron-phonon coupling on the interface thermal conductance. To understand the mechanism of interface resistance, the vibration power spectra are calculated. We find that the atomic level disorder near the interface is an important aspect of interfacial phonon transport, which leads to a modification of the phonon states near the interface. There, the vibrational spectrum near the interface greatly differs from the bulk. This change in the vibrational spectrum affects the results predicted by AMM and DMM theories and indicates new physics is involved with phonon transport across interfaces. Keywords:Comment: Journal of Computational and Theoretical Nanoscience 201

Fast Approximation and Exact Computation of Negative Curvature Parameters of Graphs

In this paper, we study Gromov hyperbolicity and related parameters, that represent how close (locally) a metric space is to a tree from a metric point of view. The study of Gromov hyperbolicity for geodesic metric spaces can be reduced to the study of graph hyperbolicity. Our main contribution in this note is a new characterization of hyperbolicity for graphs (and for complete geodesic metric spaces). This characterization has algorithmic implications in the field of large-scale network analysis, which was one of our initial motivations. A sharp estimate of graph hyperbolicity is useful, {e.g.}, in embedding an undirected graph into hyperbolic space with minimum distortion [Verbeek and Suri, SoCG\u2714]. The hyperbolicity of a graph can be computed in polynomial-time, however it is unlikely that it can be done in subcubic time. This makes this parameter difficult to compute or to approximate on large graphs. Using our new characterization of graph hyperbolicity, we provide a simple factor 8 approximation algorithm for computing the hyperbolicity of an n-vertex graph G=(V,E) in optimal time O(n^2) (assuming that the input is the distance matrix of the graph). This algorithm leads to constant factor approximations of other graph-parameters related to hyperbolicity (thinness, slimness, and insize). We also present the first efficient algorithms for exact computation of these parameters. All of our algorithms can be used to approximate the hyperbolicity of a geodesic metric space