On the Extinction Probability for Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Hillslope Processes in Temperate Environments

In this chapter, we discuss the factors controlling the mechanisms and rates of hillslope failure in temperate environments with a major focus on the Swiss Alps. We frame this presentation by defining Alpine hillslopes as either strength- or transport-limited hillslopes. We organize this discussion into individual sections that outline how hillslope processes are related to (1) the mechanical strength and bedding orientation of bedrock, (2) the competition between channelized and hillslope processes, (3) hillslope–channel coupling relationships, and (4) fluvial erosion rates. We find that hillslope angles depend on bedrock strength along nonincised channels, but are not related to this parameter in inner gorges. We also find that valley flanks host deep-seated landslides where the bedrock dips parallel to the topographic slope. In the opposite case, the valley sides are dissected by a network of bedrock channels bordered by strength-limited hillslopes. In this chapter, we illustrate that a high ratio between sediment discharge on hillslopes and in channels explains the formation of smooth landscapes with low channel densities and long response times. This chapter considers the formation of strength-limited hillslopes as a consequence of an upslope-directed coupling between channels and hillslopes. The chapter also discusses that soil-mantled hillslopes occur where fluvial incision rates are less than weathering rates of bedrock, which are limited to 0.1–0.3 mm yr−1. We finally present evidence for a decreasing trend of hillslope-derived sediment discharge during the Holocene, but predict an opposite trend in the nearest future as winters are warmer and wetter.

Branching Processes in Autoregressive Random Environment

2000 Mathematics Subject Classification: 60J80, 60K05.

T. E. Harris and branching processes

T. E. Harris was a pioneer par excellence in many fields of probability theory. In this paper, we give a brief survey of the many fundamental contributions of Harris to the theory of branching processes, starting with his doctoral work at Princeton in the late forties and culminating in his fundamental book ``The Theory of Branching Processes,'' published in 1963.

Generalized Markov branching processes

A generalized Markov Brnching Process (GMBP) is a Markov branching model where the infinitesimal branching rates are modified with an interaction index. It is proved that there always exists only one GMBP. An associated differential-integral equation is derived. The extinction probalility and the mean and conditional mean extinction times are obtained. Ergodicity and stability of GMBP with resurrection are also considered. Easy checking criteria are established for ordinary and strong ergodicty. The equilibrium distribution is given in an elegant closed form. The probability meaning of our results is clear and thus explained.

Subcritical Randomly Indexed Branching Processes

2000 Mathematics Subject Classification: 60J80, 62P05.

Revisiting Offspring Maxima in Branching Processes

2000 Mathematics Subject Classification: 60J80; 60G70.

The Consequences of Phenotypic Plasticity in Cyclically Varying Environments: A Genetic Algorithm Study

By “phenotypic plasticity” we refer to the capacity of a genotype to exhibit different phenotypes, whether in the same or in different environments. We have previously demonstrated that phenotypic plasticity can improve the degree of adaptation achieved via natural selection (Behera & Nanjundiah, 1995). That result was obtained from a genetic algorithm model of haploid genotypes (idealized as one-dimensional strings of genes) evolving in a fixed environment. Here, the dynamics of evolution is examined under conditions of a cyclically varying environment. We find that the rate of evolution, as well as the extent of adaptation (as measured by mean population fitness) is lowered because of environmental cycling. The decrease is adaptation caused by a varying environment can, however, be partly or wholly compensated by an increase in the degree of plasticity that a genotype is capable of. Also, the reduction of population fitness caused by a variable environment can be partially offset by decreasing the total number of genetic loci. We conjecture that an increase in genome size may have been among the factors responsible for the evolution of phenotypic plasticity.

Thermodynamics of flow and vaporization processes in long-chain liquids

The flow and vaporization behaviors of long-chain esters of varying molecular weights (300-900) ana branching (linear, Y-shaped, and +-shaped molecules) have been studied. The flow behavior is found to depend on the structure as well as the molecular weight. Below a molecular weight of 600, the molecules flow wholly but above this, segmental motion occurs, and the flow becomes independent of the molecular weight which is explained from the blob model. The blob concept demonstrates that the hole of a size of about 11 angstrom is needed for the flow to occur and it is much less than the size of the molecule. The blob size is observed to slightly decrease along the series linear and Y- and +-branched esters. The heat of vaporization is found to be independent of the molecular structure since the molecules acquire a coiled spherical shape during vaporization and hence depends only on the molecular weight. A significant structural effect is observed for the esters on their glass transition temperature (T(g)). The T(g) vs molecular weight plot displays contrasting trend for linear and +-branched esters, with Y esters showing an intermediate behavior. It is explained from their molecular packing and entanglement as visualized by the blob model.

Probabilistic approach in weighted Markov branching processes

This note provides a new probabilistic approach in discussing the weighted Markov branching process (WMBP) which is a natural generalisation of the ordinary Markov branching process. Using this approach, some important characteristics regarding the hitting times of such processes can be easily obtained. In particular, the closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the process is investigated and the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained. The close link between these newly developed processes and the well-known compound Poisson processes is investigated. It is revealed that any weighted Markov branching process (WMBP) is a random time change of a compound Poisson process.

Branching ratios of x-ray photons from dielectronic recombination processes in H-like titanium ions

In dielectronic recombination of hydrogenlike ions an intermediate doubly excited heliumlike ion is formed. Since the K shell is empty, both excited electrons can decay sequentially to the ground state. In this paper we analyze the x-ray radiation emitted from doubly and singly excited heliumlike titanium ions produced inside the Tokyo electron beam ion trap. Theoretical population densities of the singly excited states after the first transition and the transition probabilities of these states into the ground state were also calculated. This allowed theoretical branching ratios to be determined for each manifold. These branching ratios are compared to the experimentally obtained x-ray distribution by fitting across the relevant peak using a convolution of the theoretically obtained resonance strengths and energies. By taking into account 2E1 transitions which are not observed in the experiment, the measured and calculated ratios agree well. This method provides a valuable insight into the transition dynamics of excited highly charged ions.

A geomatics-based approach for the derivation of the spatial distribution of sediment transport processes in periglacial mountain environments

Within this paper modern techniques such as satellite image analysis and tools provided by geographic information systems (GIS.) are exploited in order to extend and improve existing techniques for mapping the spatial distribution of sediment transport processes. The processes of interest comprise mass movements such as solifluction, slope wash, dirty avalanches and rock- and boulder falls. They differ considerably in nature and therefore different approaches for the derivation of their spatial extent are required. A major challenge is addressing the differences between the comparably coarse resolution of the available satellite data (Landsat TM/ETM+, 30 in x 30 m) and the actual scale of sediment transport in this environment. A three-stepped approach has been developed which is based on the concept of Geomorphic Process Units (GPUs): parameterization, process area delineation and combination. Parameters include land cover from satellite data and digital elevation model derivatives. Process areas are identified using a hierarchical classification scheme utilizing thresholds and definition of topology. The approach has been developed for the Karkevagge in Sweden and could be successfully transferred to the Rabotsbekken catchment at Okstindan, Norway using similar input data. Copyright (C) 2008 John Wiley & Sons, Ltd.

Quantifying sediment transport processes in periglacial mountain environments at a catchment scale using geomorphic process units

The research record on the quantification of sediment transport processes in periglacial mountain environments in Scandimvia dates back to the 1950s. A wide range of measurements is. available, especially from the Karkevagge region of northern Sweden. Within this paper satellite image analysis and tools provided by geographic information systems (GIS) are exploited in order to extend and improve this research and to complement geophysical methods. The processes of interest include mass movements such as solifluction, slope wash, dirty avalanches and rock-and boulder falls. Geomorphic process units have been derived in order to allow quantification via GIS techniques at a catchment scale. Mass movement rates based on existing Field measurements are employed in the budget calculation. In the Karkevagge catch ment. 80% of the area can be identified either as a source area for sediments or as a zone where sediments are deposited. The overall budget for the slopes beneath the rockwalls in the Karkevagge is approximately 680 t a(-1) whilst about 150 : a-1 are transported into the fluvial System.