Acyclic orientations with path constraints

Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions of the vertex coloring and frequency assignment problems. In this paper we introduce a linear programming formulation of acyclic orientations with path constraints, and discuss its use in the solution of the vertex coloring problem and some versions of the frequency assignment problem. A study of the polytope associated with the formulation is presented, including proofs of which constraints of the formulation are facet-defining and the introduction of new classes of valid inequalities

Balanced cycles and circuit designs: even cases

International audienc

Traffic Grooming in Unidirectional WDM Rings with Bounded Degree Request Graph

Traffic grooming is a major issue in optical networks. It refers to grouping low rate signals into higher speed streams, in order to reduce the equipment cost. In SONET WDM networks, this cost is mostly given by the number of electronic terminations, namely ADMs. We consider the case when the topology is a unidirectional ring. In graph-theoretical terms, the traffic grooming problem in this case consists in partitioning the edges of a request graph into subgraphs with a maximum number of edges, while minimizing the total number of vertices of the decomposition. We consider the case when the request graph has bounded maximum degree $\Delta$, and our aim is to design a network being able to support any request graph satisfying the degree constraints. The existing theoretical models in the literature are much more rigid, and do not allow such adaptability. We formalize the problem, and solve the cases $\Delta=2$ (for all values of $C$) and $\Delta = 3$ (except the case C=4). We also provide lower and upper bounds for the general case

Equilibrium crystal shapes in the Potts model

The three-dimensional $q$-state Potts model, forced into coexistence by fixing the density of one state, is studied for $q=2$, 3, 4, and 6. As a function of temperature and number of states, we studied the resulting equilibrium droplet shapes. A theoretical discussion is given of the interface properties at large values of $q$. We found a roughening transition for each of the numbers of states we studied, at temperatures that decrease with increasing $q$, but increase when measured as a fraction of the melting temperature. We also found equilibrium shapes closely approaching a sphere near the melting point, even though the three-dimensional Potts model with three or more states does not have a phase transition with a diverging length scale at the melting point.Comment: 6 pages, 3 figures, submitted to PR

Intercomparison of Permittivity Measurement Techniques for Ferroelectric Thin Layers

International audienceThe dielectric properties of a KTa0.65Nb0.35O3 (KTN) ferroelectric composition for a submicronic thin layer were measured in the microwave domain using different electromagnetic characterization methods. Complementary experimental techniques (broadband methods versus resonant techniques, waveguide versus transmission line) and complementary data processing procedures (quasi-static theoretical approaches versus full-wave analysis) were selected to investigate the best way to characterize ferroelectric thin films. The measured data obtained from the cylindrical resonant cavity method, the experimental method that showed the least sources of uncertainty, were taken as reference values for comparisons with results obtained using broadband techniques. The error analysis on the methods used is discussed with regard to the respective domains of validity for each method; this enabled us to identify the best experimental approach for obtaining an accurate determination of the microwave dielectric properties of ferroelectric thin layers

Giant quantum oscillations in thermal transport in low-density metals via electron absorption of phonons

Oscillations of conductance observed in strong magnetic fields are a striking manifestation of the quantum dynamics of charge carriers in solids. The large charge carrier density in typical metals sets the scale of oscillations in both electrical and thermal conductivity, which characterize the Fermi surface. In semimetals, thermal transport at low-charge carrier density is expected to be phonon dominated, yet several experiments observe giant quantum oscillations in thermal transport. This raises the question of whether there is an overarching mechanism leading to sizable oscillations that survives in phonon-dominated semimetals. In this work, we show that such a mechanism exists. It relies on the peculiar phase-space allowed for phonon scattering by electrons when only a few Landau levels are filled. Our measurements on the Dirac semimetal ZrTe5 support this counter-intuitive mechanism through observation of pronounced thermal quantum oscillations, since they occur in similar magnitude and phase in directions parallel and transverse to the magnetic field. Our phase-space argument applies to all low-density semimetals, topological or not, including graphene and bismuth. Our work illustrates that phonon absorption can be leveraged to reveal degrees of freedom through their imprint on longitudinal thermal transport

Using the Wigner-Ibach Surmise to Analyze Terrace-Width Distributions: History, User's Guide, and Advances

A history is given of the applications of the simple expression generalized from the surmise by Wigner and also by Ibach to extract the strength of the interaction between steps on a vicinal surface, via the terrace width distribution (TWD). A concise guide for use with experiments and a summary of some recent extensions are provided.Comment: 11 pages, 4 figures, reformatted (with revtex) version of refereed paper for special issue of Applied Physics A entitled "From Surface Science to Device Physics", in honor of the retirements of Prof. H. Ibach and Prof. H. L\"ut