Measures of edge-uncolorability

The resistance $r(G)$ of a graph $G$ is the minimum number of edges that have to be removed from $G$ to obtain a graph which is $\Delta(G)$-edge-colorable. The paper relates the resistance to other parameters that measure how far is a graph from being $\Delta$-edge-colorable. The first part considers regular graphs and the relation of the resistance to structural properties in terms of 2-factors. The second part studies general (multi-) graphs $G$. Let $r_v(G)$ be the minimum number of vertices that have to be removed from $G$ to obtain a class 1 graph. We show that $\frac{r(G)}{r_v(G)} \leq \lfloor \frac{\Delta(G)}{2} \rfloor$, and that this bound is best possible.Comment: 9 page

Bis(diethyldithiocarbamato)(iodo)(4-methoxyphenyl)tellurium(IV), \u3cem\u3ep\u3c/em\u3e-MeOC\u3csub\u3e6\u3c/sub\u3eH\u3csub\u3e4\u3c/sub\u3eTe(Et\u3csub\u3e2\u3c/sub\u3eNCS\u3csub\u3e2\u3c/sub\u3e)\u3csub\u3e2\u3c/sub\u3eI, and its Isomorphous Partially Bromine-Replaced Analogue, \u3cem\u3ep\u3c/em\u3e-MeOC\u3csub\u3e6\u3c/sub\u3eH\u3csub\u3e4\u3c/sub\u3eTe(Et\u3csub\u3e2\u3c/sub\u3eNCS\u3csub\u3e2\u3c/sub\u3e)\u3csub\u3e2\u3c/sub\u3eBr\u3csub\u3e0.41\u3c/sub\u3eI\u3csub\u3e0.59\u3c/sub\u3e

The structure of the title TeIV complex, C13H19BrN2OS4Te.045(CH2Cl2), is pentagonal bipyramidal with four S atoms [Te-S 2.623 (1)-2.717 (1) Å] and the Br atom [Te-Br 2.890 (1) Å] in equatorial positions. The p-methoxyphenyl group is axial [Te-C 2.145 (3) Å] and the second axial position seems to be occupied by a dithiocarbamate group of a neighbouring molecule acting as a -ligand [TeC 3.751 (3) Å, C-TeC 170.2 (1)°], so that molecules are joined into centrosymmetric associations by this secondary coordination

\u3cem\u3ecis\u3c/em\u3e-(Diethyldithiocarbamato)diiodo(phenyl)tellurium(IV), PhTe(S\u3csub\u3e2\u3c/sub\u3eCNEt\u3csub\u3e2\u3c/sub\u3e)I\u3csub\u3e2\u3c/sub\u3e, and its Methoxy-Substituted Mixed Br/1 Analogue \u3cem\u3ecis\u3c/em\u3e-Bis(0.4-bromo/0.6-iodo)-(diethyldithiocarbamato)(4-methoxyphenyl) tellurium(IV), \u3cem\u3ep\u3c/em\u3e-MeOC\u3csub\u3e6\u3c/sub\u3eH\u3csub\u3e4\u3c/sub\u3eTe(S\u3csub\u3e2\u3c/sub\u3e CNEt\u3csub\u3e2\u3c/sub\u3e)(Br\u3csub\u3e0.4\u3c/sub\u3eI\u3csub\u3e0.6\u3c/sub\u3e)\u3csub\u3e2\u3c/sub\u3e

The TeIV complexes PhTe(S2CNEt2)I2, (1), and p-MeOC6H4Te(S2CNEt2)Br0.4/I0.6) 2, (2), have been synthesized by reacting PhTeI3 with NaS2CNEt2, and p-MeOC6H4Te(S2CNEt2)2I with Br2, respectively. In (2), both I atoms are partially replaced by Br atoms in a 3:2 ratio. The structures display distorted octahedral Te coordination with two symmetrically coordinated S atoms [Te—S 2.550 (2)—2.569 (2) Å in three independent molecules of (1) and 2.523 (1) Å in (2)] and with two cis-disposed halogen atoms [Te—I 2.941 (1)—2.986 (1) Å in (1) and 3.003 (4) and 3.049 (3) Å in (2); Te—Br 2.962(8) and 2.967 (8) Å in (2)] in equatorial positions. The aryl group is axial in both complexes [Te—C 2.137(6)—2.146(6) and 2.123(5) Å in (1) and (2) respectively] and the second axial position is occupied by a halogen atom of a neighbouring molecule [Te⋅⋅⋅I 3.898(1)—4233(1) Å in (1); Te⋅ ⋅ ⋅I3872(3) Å and Te⋅ ⋅ ⋅Br 3.676(6) Å in (2); trans angles C---Te⋅ ⋅ ⋅ (Br) 153.4(2)—177.7(2)°] so that the molecules are joined into (quasi)centrosymmetric pairs by these secondary interactions

Boltzmann Collision Term

We derive the Boltzmann equation for scalar fields using the Schwinger-Keldysh formalism. The focus lies on the derivation of the collision term. We show that the relevant self-energy diagrams have a factorization property. The collision term assumes the Boltzmann-like form of scattering probability times statistical factors for those self-energy diagrams which correspond to tree level scattering processes. Our proof covers scattering processes with any number of external particles, which come from self-energy diagrams with any number of loops.Comment: 17 pages, 4 figure

A statistical mechanics model for free-for-all airplane passenger boarding

I present and discuss a model for the free-for-all passenger boarding which is employed by some discount air carriers. The model is based on the principles of statistical mechanics where each seat in the aircraft has an associated energy which reflects the preferences of the population of air travelers. As each passenger enters the airplane they select their seats using Boltzmann statistics, proceed to that location, load their luggage, sit down, and the partition function seen by remaining passengers is modified to reflect this fact. I discuss the various model parameters and make qualitative comparisons of this passenger boarding model with models which involve assigned seats. This model can also be used to predict the probability that certain seats will be occupied at different times during the boarding process. These results may be of value to industry professionals as a useful description of this boarding method. However, it also has significant value as a pedagogical tool since it is a relatively unusual application of undergraduate level physics and it describes a situation with which many students and faculty may be familiar.Comment: version 1: 4 pages 2 figures version 2: 7 pages with 5 figure

Direct frequency-comb-driven Raman transitions in the terahertz range

We demonstrate the use of a femtosecond frequency comb to coherently drive stimulated Raman transitions between terahertz-spaced atomic energy levels. More specifically, we address the $3d~^2D_{3/2}$ and $3d~^2D_{5/2}$ fine structure levels of a single trapped $^{40}$Ca$^+$ ion and spectroscopically resolve the transition frequency to be $\nu_D = 1{,}819{,}599{,}021{,}534 \pm 8$ Hz. The achieved accuracy is nearly a factor of five better than the previous best Raman spectroscopy, and is currently limited by the stability of our atomic clock reference. Furthermore, the population dynamics of frequency-comb-driven Raman transitions can be fully predicted from the spectral properties of the frequency comb, and Rabi oscillations with a contrast of 99.3(6)\% and millisecond coherence time has been achieved. Importantly, the technique can be easily generalized to transitions in the sub-kHz to tens of THz range and should be applicable for driving, e.g., spin-resolved rovibrational transitions in molecules and hyperfine transitions in highly charged ions.Comment: 9 pages, 8 figure

Observation of asymmetric solitons in waveguide arrays with refractive index gradient

We study light propagation in waveguide arrays made in Kerr nonlinear media with a transverse refractive index gradient, and we find that the presence of the refractive index gradient leads to the appearance of a number of new soliton families. The effective coupling between the solitons and the localized linear eigenmodes of the lattice induces a drastic asymmetry in the soliton shapes and the appearance of long tails at the soliton wings. Such unusual solitons are found to be completely stable under propagation, and we report their experimental observation in fs-laser written waveguide arrays with focusing Kerr nonlinearity.Comment: 4 pages, 5 figures, to appear in Optics Letter

Global attractors and extinction dynamics of cyclically competing species

Transitions to absorbing states are of fundamental importance in nonequilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three cyclically interacting species. The interaction scheme comprises both direct competition between species as in the cyclic Lotka-Volterra model, and separated selection and reproduction processes as in the May-Leonard model. We show that the dynamic processes leading to the transient maintenance of biodiversity are closely linked to attractors of the nonlinear dynamics for the overall species' concentrations. The characteristics of these global attractors change qualitatively at certain threshold values of the mobility and depend on the relative strength of the different types of competition between species. They give information about the scaling of extinction times with the system size and thereby the stability of biodiversity. We define an effective free energy as the negative logarithm of the probability to find the system in a specific global state before reaching one of the absorbing states. The global attractors then correspond to minima of this effective energy landscape and determine the most probable values for the species' global concentrations. As in equilibrium thermodynamics, qualitative changes in the effective free energy landscape indicate and characterize the underlying nonequilibrium phase transitions. We provide the complete phase diagrams for the population dynamics and give a comprehensive analysis of the spatio-temporal dynamics and routes to extinction in the respective phases

The matter distribution in the local Universe as derived from galaxy groups in SDSS DR12 and 2MRS

Context. Friends-of-friends algorithms are a common tool to detect galaxy groups and clusters in large survey data. In order to be as precise as possible, they have to be carefully calibrated using mock catalogues. Aims. We create an accurate and robust description of the matter distribution in the local Universe using the most up-to-date available data. This will provide the input for a specific cosmological test planned as follow-up to this work, and will be useful for general extragalactic and cosmological research. Methods. We created a set of galaxy group catalogues based on the 2MRS and SDSS DR12 galaxy samples using a friends-of-friends based group finder algorithm. The algorithm was carefully calibrated and optimised on a new set of wide-angle mock catalogues from the Millennium simulation, in order to provide accurate total mass estimates of the galaxy groups taking into account the relevant observational biases in 2MRS and SDSS. Results. We provide four different catalogues (i) a 2MRS based group catalogue; (ii) an SDSS DR12 based group catalogue reaching out to a redshift z = 0.11 with stellar mass estimates for 70% of the galaxies; (iii) a catalogue providing additional fundamental plane distances for all groups of the SDSS catalogue that host elliptical galaxies; (iv) a catalogue of the mass distribution in the local Universe based on a combination of our 2MRS and SDSS catalogues. Conclusions. While motivated by a specific cosmological test, three of the four catalogues that we produced are well suited to act as reference databases for a variety of extragalactic and cosmological science cases. Our catalogue of fundamental plane distances for SDSS groups provides further added value to this paper.Comment: 31 pages, 25 figures, accepted for publication in A&