Stable transports between stationary random measures

We give an algorithm to construct a translation-invariant transport kernel between ergodic stationary random measures $\Phi$ and $\Psi$ on $\mathbb R^d$, given that they have equal intensities. As a result, this yields a construction of a shift-coupling of an ergodic stationary random measure and its Palm version. This algorithm constructs the transport kernel in a deterministic manner given realizations $\varphi$ and $\psi$ of the measures. The (non-constructive) existence of such a transport kernel was proved in [8]. Our algorithm is a generalization of the work of [3], in which a construction is provided for the Lebesgue measure and an ergodic simple point process. In the general case, we limit ourselves to what we call constrained densities and transport kernels. We give a definition of stability of constrained densities and introduce our construction algorithm inspired by the Gale-Shapley stable marriage algorithm. For stable constrained densities, we study existence, uniqueness, monotonicity w.r.t. the measures and boundedness.Comment: In the second version, we change the way of presentation of the main results in Section 4. The main results and their proofs are not changed significantly. We add Section 3 and Subsection 4.6. 25 pages and 2 figure

Point-Map-Probabilities of a Point Process and Mecke's Invariant Measure Equation

A compatible point-shift $F$ maps, in a translation invariant way, each point of a stationary point process $\Phi$ to some point of $\Phi$. It is fully determined by its associated point-map, $f$, which gives the image of the origin by $F$. It was proved by J. Mecke that if $F$ is bijective, then the Palm probability of $\Phi$ is left invariant by the translation of $-f$. The initial question motivating this paper is the following generalization of this invariance result: in the non-bijective case, what probability measures on the set of counting measures are left invariant by the translation of $-f$? The point-map probabilities of $\Phi$ are defined from the action of the semigroup of point-map translations on the space of Palm probabilities, and more precisely from the compactification of the orbits of this semigroup action. If the point-map probability exists, is uniquely defined, and if it satisfies certain continuity properties, it then provides a solution to this invariant measure problem. Point-map probabilities are objects of independent interest. They are shown to be a strict generalization of Palm probabilities: when $F$ is bijective, the point-map probability of $\Phi$ boils down to the Palm probability of $\Phi$. When it is not bijective, there exist cases where the point-map probability of $\Phi$ is singular with respect to its Palm probability. A tightness based criterion for the existence of the point-map probabilities of a stationary point process is given. An interpretation of the point-map probability as the conditional law of the point process given that the origin has $F$-pre-images of all orders is also provided. The results are illustrated by a few examples.Comment: 35 pages, 2 figure

Co-simulation of building energy simulation and computational fluid dynamics for whole-building heat, air and moisture engineering

Building performance simulation (BPS) is widely applied to analyse heat, air and moisture (HAM) related issues in the indoor environment such as energy consumption, thermal comfort, condensation and mould growth. The uncertainty associated with such simulations can be high, and incorrect simulation results can lead to a design with adverse effects on health, comfort and functionality of space. In recent years, the use of BPS tools to predict and analyse the HAM behaviour of the indoor environment has grown significantly. Among these tools, Building Energy Simulation (BES) and Computational Fluid Dynamics (CFD) are recognized as potential tools for assessing HAM behaviour of the indoor environment, such as interaction of the HVAC system with convective heat and mass transfer. These tools have strong capabilities, but also some particular deficiencies in terms of boundary conditions, physical models and resolution in space and time. BES is mainly used to assess the thermal performance of buildings throughout the entire year. It is a powerful tool, but when compared to CFD tools it includes simplified air flow, heat and moisture transfer modelling. Detailed HAM modelling of the building indoor environment is possible with CFD. In CFD, however, the implementation of meteorological boundary conditions, the whole HVAC system modelling etc. are significantly less advanced than in BES. In this thesis, it is hypothesized that if used correctly, the combination of BES and CFD tools will increase the accuracy of HAM simulations of the indoor environment. The thesis first presents approaches for domain integration, relevant physical phenomena, interface variables, and coupling requirements. Then, it introduces a newly developed prototype, which integrates BES and CFD for high resolution HAM simulation of the indoor environment. Next, it describes the verification of the prototype. This is followed by the validation study of the prototype, which shows that the accuracy of the HAM simulation is enhanced. Finally its usage potential is illustrated by discussion of the results of real applications in the building industry

Doeblin Trees

This paper is centered on the random graph generated by a Doeblin-type coupling of discrete time processes on a countable state space whereby when two paths meet, they merge. This random graph is studied through a novel subgraph, called a bridge graph, generated by paths started in a fixed state at any time. The bridge graph is made into a unimodular network by marking it and selecting a root in a specified fashion. The unimodularity of this network is leveraged to discern global properties of the larger Doeblin graph. Bi-recurrence, i.e., recurrence both forwards and backwards in time, is introduced and shown to be a key property in uniquely distinguishing paths in the Doeblin graph, and also a decisive property for Markov chains indexed by $\mathbb{Z}$. Properties related to simulating the bridge graph are also studied.Comment: 44 pages, 4 figure

Characteristics and Genesis of Some Soils of the Upper Terraces of Lake Bonneville

The genesis and characteristics of the Timpanogos, Hillfield, and Sterling soils and an unnamed Mollisol (soil formed on north- slope) on the east part of Cache Valley were studied in order to determine (1) why the soil morphology is not chronologically related to the geomorphic surface and (2} why different soils have developed on these surfaces , even though the soil forming factors appear similar. The particle size distribution of the upper horizons of the Timpanogos, Hillfield , and unnamed Mollisol pedons are relatively similar . These soils developed from stratified deposits with granulimetric composition in which 75 to 90 percent of the grains are less than 100 micrometers in diameter , characteristic of wind-blown material. Development of an incipient argillic horizon in Timpanogos pedon indicates this soil did not develop under the moist conditions of the Pleistocene and the geomorphic surface was not stable after deposition. The material was reworked by the wind. The Sterling soil formed on an alluvial fan which was deposited during Holocene time and its development is chronologically related to geomorphic surface. The development of an incipient argillic horizon in the Timpanogos soil and a weak cambic horizon in the Hillfield soil and the unnamed Mollisol is due to topographic condition of the landscapes. The thick and dark mollie epipedon in the unnamed Mollisol (north-slope) compared to the Hillfield soil (south- s lope) which has an epipedon with color light to be mollie and a less thick A horizon is related to effect of microclimate

Application of externally-coupled BES-CFD in HAM engineering of the indoor environment

The high importance of indoor environment performance aspects such as surface condensation, mold growth, thermal comfort, etc., is widely recognized. High-resolution simulation of heat, air and moisture (HAM) transfer can be used to enhance the prediction and analysis of these aspects. For this purpose, a coupling mechanism has been developed in order to perform run-time external coupling between Building Energy simulation (BES) and Computational Fluid Dynamics (CFD). This paper presents the results of indoor humidity calculation using the new coupled tool for the BESTEST case- 600. The results are compared with stand-alone BES results and the need and importance of coupled simulations is discussed