Coloring intersection graphs of arc-connected sets in the plane

A family of sets in the plane is simple if the intersection of its any subfamily is arc-connected, and it is pierced by a line $L$ if the intersection of its any member with $L$ is a nonempty segment. It is proved that the intersection graphs of simple families of compact arc-connected sets in the plane pierced by a common line have chromatic number bounded by a function of their clique number.Comment: Minor changes + some additional references not included in the journal versio

Triangle-free geometric intersection graphs with large chromatic number

Several classical constructions illustrate the fact that the chromatic number of a graph can be arbitrarily large compared to its clique number. However, until very recently, no such construction was known for intersection graphs of geometric objects in the plane. We provide a general construction that for any arc-connected compact set $X$ in $\mathbb{R}^2$ that is not an axis-aligned rectangle and for any positive integer $k$ produces a family $\mathcal{F}$ of sets, each obtained by an independent horizontal and vertical scaling and translation of $X$, such that no three sets in $\mathcal{F}$ pairwise intersect and $\chi(\mathcal{F})>k$. This provides a negative answer to a question of Gyarfas and Lehel for L-shapes. With extra conditions, we also show how to construct a triangle-free family of homothetic (uniformly scaled) copies of a set with arbitrarily large chromatic number. This applies to many common shapes, like circles, square boundaries, and equilateral L-shapes. Additionally, we reveal a surprising connection between coloring geometric objects in the plane and on-line coloring of intervals on the line.Comment: Small corrections, bibliography updat

Many-Body Mobility Edge in Quantum Sun models

The 0-dimensional Quantum Sun model is an interacting model that exhibits sharp signatures of ergodicity breaking phase transition. Here, we show that the model exhibits a many-body mobility edge. We provide analytical arguments for its existence, complemented by the state-of-the-art numerical simulations. We also introduce the 0-dimensional Quantum Sun model with particle number conservation, and we argue that it shares many similarities with his unrestricted predecessor.Comment: 8pp.+ suppl 4pp. Commentas welcom

Triangle-free intersection graphs of line segments with large chromatic number

In the 1970s, Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is no. Specifically, for each positive integer $k$, we construct a triangle-free family of line segments in the plane with chromatic number greater than $k$. Our construction disproves a conjecture of Scott that graphs excluding induced subdivisions of any fixed graph have chromatic number bounded by a function of their clique number.Comment: Small corrections, bibliography updat

Spontaneous formation of liquid crystalline phases and phase transitions in highly concentrated plasmid DNA

The liquid crystalline (LC) properties of two supercoiled plasmid DNA samples, pBSK (2958 bp) and pGEM (3000 bp), have been studied using polarised light microscopy (PLM), circular dichroism (CD) and UV-Vis spectroscopy. The influence of methods of isolation on plasmid LC behaviour is described, and using PLM we have demonstrated the spontaneous formation of cholesteric fingerprint-like textures. Preliminary studies of LC phase transitions in pGEM show the irreversibility of LC phase formation, as a consequence of changes in the tertiary structure of supercoiled plasmids. Using UV-Vis spectroscopy a hyperchromic effect was observed with increasing temperature. The CD spectra clearly showed structural changes, and probably mismatching of DNA bases, during cooling. Finally, we have observed an irreversible phase transition in plasmid DNA which is very different from that previously reported in linear DNA

Deciphering the history of forest disturbance and its effects on landforms and soils : lessons from a pit-and-mound locality at Rogowa Kopa, Sudetes, SW Poland

The historical dimension of pit-and-mound topography has been studied at Mt Rogowa Kopa locality, Stołowe Mountains, SW Poland. This site represents one of the best developed regional examples of hummocky forest floor relief due to widespread tree uprooting and subsequent degradation of root plates. Through map analysis and dendrochronology the disturbance history was traced at least to the 1930s and most likely a strong wind episode from 1933 was the reason of forest calamity that resulted in nearly complete destruction of the original stand. However, the forest affected was a planted Norway spruce monoculture, introduced and managed at least till the beginning of 20th century, not a natural forest. The windthrow niche was then used by beech whose individuals preferentially chose mounds to grow, conserving hummocky microtopography. Changes in soil evolutionary pathways brought about by wind-driven disturbance include both homogenization (rejuvenation) and horizonation (differentiation). Evidence of soil rejuvenation includes decrease of organic carbon content and pH increase in the upper parts of soils developed on mounds in comparison with undisturbed references soils. Soil texture was relatively homogenized in pits and mounds. Dating of pit-and-mound microrelief by means of soil properties (organic carbon content, iron forms) was only partly successful. Although young age of pits and mounds is evident, the actual age inferred from soil properties was underestimated by a few tens of years. Evaluation of factors potentially controlling the propensity to widespread treethrow suggests that the type of forest is a far more important variable than local abiotic factors of bedrock geology, regolith characteristics, and slope inclination

Iron Doped SBA-15 Mesoporous Silica Studied by Mössbauer Spectroscopy

Mesoporous silica SBA-15 containing propyl-iron-phosphonate groups were considered to confirm their molecular structure. To detect the iron-containing group configuration the Mössbauer spectroscopy was used. Both mesoporous silica SBA-15 containing propyl-iron-phosphonate groups and pure doping agent (iron acetylacetate) were investigated using Mössbauer spectroscopy. The parameters such as isomer shift, quadrupole splitting, and asymmetry in 57Fe Mössbauer spectra were analyzed. The differences in Mössbauer spectra were explained assuming different local surroundings of Fe nuclei. On this base we were able to conclude about activation of phosphonate units by iron ions and determinate the oxidation state of the metal ion. To examine bonding between iron atoms and phosphonic units the resonance Raman spectroscopy was applied. The density functional theory (DFT) approach was used to make adequate calculations. The distribution of active units inside silica matrix was estimated by comparison of calculated vibrational spectra with the experimental ones. Analysis of both Mössbauer and resonance Raman spectra seems to confirm the correctness of the synthesis procedure. Also EDX elemental analysis confirms our conclusions

Coloring Intersection Graphs of Arc-Connected Sets in the Plane

A family of sets in the plane is simple if the intersection of any subfamily is arc-connected, and it is pierced by a line $$L$$ L if the intersection of any member with $$L$$ L is a nonempty segment. It is proved that the intersection graphs of simple families of compact arc-connected sets in the plane pierced by a common line have chromatic number bounded by a function of their clique number