Searching for a continuum limit in causal dynamical triangulation quantum gravity

We search for a continuum limit in the causal dynamical triangulation (CDT) approach to quantum gravity by determining the change in lattice spacing using two independent methods. The two methods yield similar results that may indicate how to tune the relevant couplings in the theory in order to take a continuum limit.Comment: 19 pages, 8 figures. Title change and journal reference adde

Signature Change of the Metric in CDT Quantum Gravity?

We study the effective transfer matrix within the semiclassical and bifurcation phases of CDT quantum gravity. We find that for sufficiently large lattice volumes the kinetic term of the effective transfer matrix has a different sign in each of the two phases. We argue that this sign change can be viewed as a Wick rotation of the metric. We discuss the likely microscopic mechanism responsible for the bifurcation phase transition, and propose an order parameter that can potentially be used to determine the precise location and order of the transition. Using the effective transfer matrix we approximately locate the position of the bifurcation transition in some region of coupling constant space, allowing us to present an updated version of the CDT phase diagram.Comment: 16 pages, 9 figure

Pseudo-Cartesian coordinates in a model of Causal Dynamical Triangulations

Causal Dynamical Triangulations is a non-perturbative quantum gravity model, defined with a lattice cut-off. The model can be viewed as defined with a proper time but with no reference to any three-dimensional spatial background geometry. It has four phases, depending on the parameters (the coupling constants) of the model. The particularly interesting behavior is observed in the so-called de Sitter phase, where the spatial three-volume distribution as a function of proper time has a semi-classical behavior which can be obtained from an effective mini-superspace action. In the case of the three-sphere spatial topology, it has been difficult to extend the effective semi-classical description in terms of proper time and spatial three-volume to include genuine spatial coordinates, partially because of the background independence inherent in the model. However, if the spatial topology is that of a three-torus, it is possible to define a number of new observables that might serve as spatial coordinates as well as new observables related to the winding numbers of the three-dimensional torus. The present paper outlines how to define the observables, and how they can be used in numerical simulations of the model.Comment: 26 pages, 15 figure

The phase structure of Causal Dynamical Triangulations with toroidal spatial topology

We investigate the impact of topology on the phase structure of four-dimensional Causal Dynamical Triangulations (CDT). Using numerical Monte Carlo simulations we study CDT with toroidal spatial topology. We confirm existence of all four distinct phases of quantum geometry earlier observed in CDT with spherical spatial topology. We plot the toroidal CDT phase diagram and find that it looks very similar to the case of the spherical spatial topology.Comment: 24 pages, 15 figure

Four-dimensional CDT with toroidal topology

3+1 dimensional Causal Dynamical Triangulations (CDT) describe a quantum theory of fluctuating geometries without the introduction of a background geometry. If the topology of space is constrained to be that of a three-dimensional torus we show that the system will fluctuate around a dynamically formed background geometry which can be understood from a simple minisuperspace action which contains both a classical part and a quantum part. We determine this action by integrating out degrees of freedom in the full model, as well as by transfer matrix methods.Comment: 28 pages, 15 figure

Building Benchmarks for Use Cases

This paper presents how the use-cases benchmark has been built and how it can be applied by researchers. Set of 16 industrial projects (with 524 use cases in total) has been analysed in order to obtain quantitative and qualitative profile of a typical use-case-based requirements specification. Based on the analysis, two types of referential use-case-based requirements specifications have been created, one taking only quantitative data into account and second considering qualitative data. Researchers who analyse use cases can utilise these specifications in order to validate their methods and tools before applying them to real projects. Moreover, such referential specification can be used as a benchmark and allows comparing accuracy and efficiency of tools for use-case analysis

The higher-order phase transition in toroidal CDT

We investigate the transition between the phases $B$ and $C_b$ observed in four-dimensional Causal Dynamical Triangulations (CDT). We find that the critical properties of CDT with toroidal spatial topology are the same as earlier observed in spherical spatial topology where the $B-C_b$ transition was found to be higher-order. This may have important consequences for the existence of the continuum limit of CDT, describing the perspective UV limit of quantum gravity, which potentially can be investigated in the toroidal model.Comment: 17 pages, 10 figure

The impact of data assimilation into the meteorological WRF model on birch pollen modelling

We analyse the impact of ground-based data assimilation to theWeather Research and Forecasting (WRF) meteorological model on parameters relevant for birch pollen emission calculations. Then, we use two different emission databases (BASE – no data assimilation, OBSNUD – data assimilation for the meteorological model) in the chemical transport model and evaluate birch pollen concentrations. Finally, we apply a scaling factor for the emissions (BASE and OBSNUD), based on the ratio between simulated and observed seasonal pollen integral (SPIn) to analyse its impact on birch concentrations over Central Europe. Assimilation of observational data significantly reducesmodel overestimation of air temperature,which is themain parameter responsible for the start of pollen emission and amount of released pollen. The results also show that a relatively small bias in air temperature from the model can lead to significant differences in heating degree days (HDD) value. This may cause the HDD threshold to be attained several days earlier/later than indicated from observational data which has further impact on the start of pollen emission. Even though the bias for air temperature was reduced for OBSNUD, the model indicates a start for the birch pollen season that is too early compared to observations. The start date of the seasonwas improved at two of the 11 stations in Poland. Data assimilation does not have a significant impact on the season's end or SPIn value. The application of the SPIn factor for the emissions results in a much closer birch pollen concentration level to observations even though the factor does not improve the start or end of the pollen season. The post-processing of modelled meteorological fields, such as the application of bias correction, can be considered as a way to further improve the pollen emission modelling