Entropy-driven phase transition in a polydisperse hard-rods lattice system

We study a system of rods on the 2d square lattice, with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with orientational long-range order. This is in sharp contrast with the case N=2 (the monomer-dimer model), for which Heilmann and Lieb proved absence of phase transition at any fugacity. This is the first example of a pure hard-core system with phases displaying orientational order, but not translational order; this is a fundamental characteristic feature of liquid crystals

Sublinear-Time Algorithms for Monomer-Dimer Systems on Bounded Degree Graphs

For a graph $G$, let $Z(G,\lambda)$ be the partition function of the monomer-dimer system defined by $\sum_k m_k(G)\lambda^k$, where $m_k(G)$ is the number of matchings of size $k$ in $G$. We consider graphs of bounded degree and develop a sublinear-time algorithm for estimating $\log Z(G,\lambda)$ at an arbitrary value $\lambda>0$ within additive error $\epsilon n$ with high probability. The query complexity of our algorithm does not depend on the size of $G$ and is polynomial in $1/\epsilon$, and we also provide a lower bound quadratic in $1/\epsilon$ for this problem. This is the first analysis of a sublinear-time approximation algorithm for a # P-complete problem. Our approach is based on the correlation decay of the Gibbs distribution associated with $Z(G,\lambda)$. We show that our algorithm approximates the probability for a vertex to be covered by a matching, sampled according to this Gibbs distribution, in a near-optimal sublinear time. We extend our results to approximate the average size and the entropy of such a matching within an additive error with high probability, where again the query complexity is polynomial in $1/\epsilon$ and the lower bound is quadratic in $1/\epsilon$. Our algorithms are simple to implement and of practical use when dealing with massive datasets. Our results extend to other systems where the correlation decay is known to hold as for the independent set problem up to the critical activity

Soil and Vegetation Drive Sesquiterpene Lactone Content and Profile in Arnica montana L. Flower Heads From Apuseni-Mountains, Romania

Arnica montana L. (AM, Asteraceae) is a perennial, herbaceous vascular plant species of commercial importance. The flower heads’ pharmacological properties are attributed mainly to sesquiterpene lactones (SLs), with phenolic acids and flavonoids also considered of relevance. The botanical drug is still partly collected in different European mountain regions. The SL content can be influenced by genetic factors and environmental conditions (altitude, temperature and rainfall). Surprisingly, the influence of the soil on SL-content have rarely been investigated. However, the soil determines the occurrence, distribution and overall fitness of AM. Equally, environmental factors are crucial determinants for the biosynthesis and fluctuations in plant secondary metabolites. Therefore, different abiotic (pH, C/N ratio, base saturation, cation exchange capacity) and biotic (species richness, vegetation cover) parameters need to be assessed as potential drivers of the variable content of AM’s secondary metabolites. Consequently, we developed an in situ experimental design aiming to cover a wide range of soil pH conditions. We detected and investigated different AM populations growing in grassland on acidic soils, on siliceous as well as calcareous geologies within the same geographical region and altitudinal belt. The total SL content and most single SL contents of the AM flower heads differed significantly between the two geologies. AM flower heads of plants growing on loam on limestone showed a significant higher total SL content than the flower heads of plants growing in siliceous grasslands. Furthermore, the SL contents were significantly correlated with geobotanical species richness and vegetation cover pointing toward an effect of species interactions on the production of SLs. Moreover, the ratios of the main SLs helenalin to dihydrohelenalin esters were significantly correlated to environmental parameters indicating that SL composition might be a function of habitat conditions. The findings of this study shed light upon the often ignored, complex interactions between environmental conditions and plant secondary metabolites. We highlight the importance of both abiotic and biotic habitat parameters for SLs in AM

Scalable quantum tomography in a photonic chip

© 2017 IEEE. We formulate a method of quantum tomography that scales linearly with the number of photons and involves only one optical transformation. We demonstrate it experimentally for two-photon entangled states using a special photonic chip

Air quality impact of a decision support system for reducing pollutant emissions: CARBOTRAF

Traffic congestion with frequent “stop & go” situations causes substantial pollutant emissions. Black carbon (BC) is a good indicator of combustion-related air pollution and results in negative health effects. Both BC and CO2 emissions are also known to contribute significantly to global warming. Current traffic control systems are designed to improve traffic flow and reduce congestion. The CARBOTRAF system combines real-time monitoring of traffic and air pollution with simulation models for emission and local air quality prediction in order to deliver on-line recommendations for alternative adaptive traffic management. The aim of introducing a CARBOTRAF system is to reduce BC and CO2 emissions and improve air quality by optimizing the traffic flows. The system is implemented and evaluated in two pilot cities, Graz and Glasgow. Model simulations link traffic states to emission and air quality levels. A chain of models combines micro-scale traffic simulations, traffic volumes, emission models and air quality simulations. This process is completed for several ITS scenarios and a range of traffic boundary conditions. The real-time DSS system uses these off-line model simulations to select optimal traffic and air quality scenarios. Traffic and BC concentrations are simultaneously monitored. In this paper the effects of ITS measures on air quality are analysed with a focus on BC

An assessment of VMS-rerouting and traffic signal planning with emission objectives in an urban network — A case study for the city of Graz

This paper discusses a case study evaluating the potential impact of ITS traffic management on CO 2 and Black carbon tailpipe emissions. Results are based on extensive microsimulations performed using a calibrated VISSIM model in combination with the AIRE model for calculating the tailpipe emissions from simulated vehicle trajectories. The ITS traffic management options hereby consist of easily implementable actions such as the usage of a variable message sign (VMS) or the setting of fixed time signal plans. Our simulations show that in the current case shifting 5% of vehicles from one route to another one leads to an improvement in terms of emissions only if the VMS is complemented with an adaptation of the signal programs, while the VMS sign or the change of the signal plans alone do not yield benefits. This shows that it is not sufficient to evaluate single actions in a ceteris paribus analysis, but their joint network effects need to be taken into account

Matchings on infinite graphs

Elek and Lippner (2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting parameter via a local recursion defined directly on the limit of the graph sequence. Interestingly, the recursion may admit multiple solutions, implying non-trivial long-range dependencies between the covered vertices. We overcome this lack of correlation decay by introducing a perturbative parameter (temperature), which we let progressively go to zero. This allows us to uniquely identify the correct solution. In the important case where the graph limit is a unimodular Galton-Watson tree, the recursion simplifies into a distributional equation that can be solved explicitly, leading to a new asymptotic formula that considerably extends the well-known one by Karp and Sipser for Erd\"os-R\'enyi random graphs.Comment: 23 page

Algebraic Bethe ansatz approach for the one-dimensional Hubbard model

We formulate in terms of the quantum inverse scattering method the algebraic Bethe ansatz solution of the one-dimensional Hubbard model. The method developed is based on a new set of commutation relations which encodes a hidden symmetry of 6-vertex type.Comment: appendix additioned with Boltzmann weigths and R-matrix. Version to be published in J.Phys.A:math.Gen. (1997

Direct Observation of Field-Induced Incommensurate Fluctuations in a One-Dimensional S=1/2 Antiferromagnet

Neutron scattering from copper benzoate, Cu(C6D5COO)2 3D2O, provides the first direct experimental evidence for field-dependent incommensurate low energy modes in a one-dimensional spin S = 1/2 antiferromagnet. Soft modes occur for wavevectors q=\pi +- dq(H) where dq(H) ~ 2 \pi M(H)/g\mu_B as predicted by Bethe ansatz and spinon descriptions of the S = 1/2 chain. Unexpected was a field-induced energy gap $\Delta(H) \propto H^\alpha$, where $\alpha = 0.65(3)$ as determined from specific heat measurements. At H = 7 T (g\mu_B H/J = 0.52), the magnitude of the gap varies from 0.06 - 0.3 J depending on the orientation of the applied field.Comment: 11 pages, 5 postscript figures, LaTeX, Submitted to PRL 3/31/97, e-mail comments to [email protected]