Binary self-similar one-dimensional quasilattices: Mutual local-derivability classification and substitution rules

Self-similar binary one-dimensional (1D) quasilattices (QLs) are classified into mutual local-derivability (MLD) classes. It is shown that the MLD classification is closely related to the number-theoretical classification of parameters which specify the self-similar binary 1D QLs. An algorithm to derive an explicit substitution rule, which prescribes the transformation of a QL into another QL in the same MLD class, is presented. An explicit inflation rule, which prescribes the transformation of the self-similar 1D QL into itself, is obtained as a composition of the explicit substitution rules. Symmetric substitution rules and symmetric inflation rules are extensively discussed.Comment: 24 pages, 4 figures, submitted to PR

Minimizing energy below the glass thresholds

Focusing on the optimization version of the random K-satisfiability problem, the MAX-K-SAT problem, we study the performance of the finite energy version of the Survey Propagation (SP) algorithm. We show that a simple (linear time) backtrack decimation strategy is sufficient to reach configurations well below the lower bound for the dynamic threshold energy and very close to the analytic prediction for the optimal ground states. A comparative numerical study on one of the most efficient local search procedures is also given.Comment: 12 pages, submitted to Phys. Rev. E, accepted for publicatio

Trace and antitrace maps for aperiodic sequences, their extensions and applications

We study aperiodic systems based on substitution rules by means of a transfer-matrix approach. In addition to the well-known trace map, we investigate the so-called `antitrace' map, which is the corresponding map for the difference of the off-diagonal elements of the 2x2 transfer matrix. The antitrace maps are obtained for various binary, ternary and quaternary aperiodic sequences, such as the Fibonacci, Thue-Morse, period-doubling, Rudin-Shapiro sequences, and certain generalizations. For arbitrary substitution rules, we show that not only trace maps, but also antitrace maps exist. The dimension of the our antitrace map is r(r+1)/2, where r denotes the number of basic letters in the aperiodic sequence. Analogous maps for specific matrix elements of the transfer matrix can also be constructed, but the maps for the off-diagonal elements and for the difference of the diagonal elements coincide with the antitrace map. Thus, from the trace and antitrace map, we can determine any physical quantity related to the global transfer matrix of the system. As examples, we employ these dynamical maps to compute the transmission coefficients for optical multilayers, harmonic chains, and electronic systems.Comment: 13 pages, REVTeX, now also includes applications to electronic systems, some references adde

Recent growth coherence in long-term oak (Quercus spp.) ring width chronologies in the Czech Republic

Oak ring width measurements compiled from 44 sampling sites throughout the territory of the Czech Republic are analysed for the 1655-2013 period. Measurements taken at all these sites are sorted into 10 sub-chronologies on the basis of 5 environmental factors: soil moisture (dry/wet), elevation (low/high), age (young/old), species (Quercus robur or Q. petraea), and geographical position (east/west). Several statistical tests are applied to investigate existing significant differences between chronologies during 1920-2013. Further, the sensitivities of individual sub-chronologies to precipitation are compared. Three tests indicate 5 pairs of very similar sub-chronologies. Moreover, the growth-response to May-July precipitation totals is very much the same in these sub-chronologies. This analysis demonstrates that, even in the absence of certainty about age structure, species composition and some environmental factors in the earlier parts of oak ring width chronologies, the internal homogeneity of the chronology remains essentially unaffected, and the lack of such information does not preclude their use in dendroclimatology

Science with a small two-band UV-photometry mission II: Observations of stars and stellar systems

We outline the impact of a small two-band UV-photometry satellite mission on the field of stellar physics, magnetospheres of stars, binaries, stellar clusters, interstellar matter, and exoplanets. On specific examples of different types of stars and stellar systems, we discuss particular requirements for such satellite missions in terms of specific mission parameters such as bandpass, precision, cadence, and mission duration. We show that such a mission may provide crucial data not only for hot stars that emit most of their light in UV, but also for cool stars, where UV traces their activity. This is important, for instance, for exoplanetary studies, because the level of stellar activity influences habitability. While the main asset of the two-band UV mission rests in time-domain astronomy, an example of open clusters proves that such a mission would be important also for the study of stellar populations. Properties of the interstellar dust are best explored when combining optical and IR information with observations in UV. It is well known that dust absorbs UV radiation efficiently. Consequently, we outline how such a UV mission can be used to detect eclipses of sufficiently hot stars by various dusty objects and study disks, rings, clouds, disintegrating exoplanets or exoasteroids. Furthermore, UV radiation can be used to study the cooling of neutron stars providing information about the extreme states of matter in the interiors of neutron stars and used for mapping heated spots on their surfaces.Comment: Submitted to Space Science Review

A setting for higher order differential equations fields and higher order Lagrange and Finsler spaces

We use the Fr\"olicher-Nijenhuis formalism to reformulate the inverse problem of the calculus of variations for a system of differential equations of order 2k in terms of a semi-basic 1-form of order k. Within this general context, we use the homogeneity proposed by Crampin and Saunders in [14] to formulate and discuss the projective metrizability problem for higher order differential equation fields. We provide necessary and sufficient conditions for higher order projectivpre-e metrizability in terms of homogeneous semi-basic 1-forms. Such a semi-basic 1-form is the Poincar\'e-Cartan 1-form of a higher order Finsler function, while the potential of such semi-basic 1-form is a higher order Finsler function.Comment: final, pre-published versio

No systematic effects of sampling direction on climate-growth relationships in a large-scale, multi-species tree-ring data set

Ring-width series are important for diverse fields of research such as the study of past climate, forest ecology, forest genetics, and the determination of origin (dendro-provenancing) or dating of archaeological objects. Recent research suggests diverging climate-growth relationships in tree-rings due to the cardinal direction of extracting the tree cores (i.e. direction-specific effect). This presents an understudied source of bias that potentially affects many data sets in tree-ring research. In this study, we investigated possible direction-specific growth variability based on an international (10 countries), multi-species (8 species) tree-ring width network encompassing 22 sites. To estimate the effect of direction-specific growth variability on climate-growth relationships, we applied a combination of three methods: An analysis of signal strength differences, a Principal Component Gradient Analysis and a test on the direction-specific differences in correlations between indexed ring-widths series and climate variables. We found no evidence for systematic direction-specific effects on tree radial growth variability in high-pass filtered ring-width series. In addition, direction-specific growth showed only marginal effects on climate-growth correlations. These findings therefore indicate that there is no consistent bias caused by coring direction in data sets used for diverse dendrochronological applications on relatively mesic sites within forests in flat terrain, as were studied here. However, in extremely dry, warm or cold environments, or on steep slopes, and for different life-forms such as shrubs, further research is advisable.</p