Recent Results for Supercritical Controlled Branching Processes with Control Random Functions

2000 Mathematics Subject Classification: 60J80, 60F05

Estimation of the Offspring Mean in a General Single-Type Size-Dependent Branching Process

2000 Mathematics Subject Classification: 60J80, 62F12, 62P10

Branching Particle Representation of a Class of Semilinear Equations

2000 Mathematics Subject Classification: 60J80, 60J85

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Total Progeny in a Subcritical Branching Process with two Types of Immigration

2000 Mathematics Subject Classification: 60J80, 60F05

Simulation and Robust Modifications of Estimates in Branching Processes

This study is focused on the comparison and modification of different estimates arising in the branching processes. Simulations of models with or without migration are put through. Due to the complexity of the computations the algorithms are designed with the language of technical computing MATLAB. Using the simulations, estimates of the o spring mean of the generated processes are calculated. It is well known in the literature that under certain conditions the asymptotic distribution of the estimates is proved to be normal. Using the asymptotic normality a modified method of maximum likelihood is proposed. The aim is to obtain trimmed maximum likelihood estimates based on several sample paths with the same number of generations. Thus in a natural way the observations, inconsistent with the aprior information about the asymptotic normality are excluded from the model. The computation of the standard error allows the comparison of different types of estimates.

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

Lp Microlocal Supercritical Markov Branching Processes with Non-Homogeneous Poisson Immigration

2010 Mathematics Subject Classification: 60J80.

Time to Extinction in Branching Processes and its Application in Epidemiology

2010 Mathematics Subject Classification: Primary 60J80; Secondary 92D30.

Crump-Mode-Jagers Branching Process: Modelling and Application for Human Population

2010 Mathematics Subject Classification: 60J85, 92D25.

Limit Theorems for Non-Critical Branching Processes with Continuous State Space

2000 Mathematics Subject Classification: Primary 60J80, Secondary 60G99.

A study of branching fluid networks for enhancing the performance of thermal -fluid devices

Compact thermal-fluid systems are found in many industries from aerospace to microelectronics where a combination of small size, light weight, and high surface area to volume ratio fluid networks are necessary. These devices are typically designed with fluid networks consisting of many small parallel channels that effectively pack a large amount of heat transfer surface area in a very small volume but do so at the cost of increased pumping power requirements. ^ To offset this cost the use of a branching fluid network for the distribution of coolant within a heat sink is investigated. The goal of the branch design technique is to minimize the entropy generation associated with the combination of viscous dissipation and convection heat transfer experienced by the coolant in the heat sink while maintaining compact high heat transfer surface area to volume ratios. ^ The derivation of Murray's Law, originally developed to predict the geometry of physiological transport systems, is extended to heat sink designs which minimze entropy generation. Two heat sink designs at different scales are built, and tested experimentally and analytically. The first uses this new derivation of Murray's Law. The second uses a combination of Murray's Law and Constructal Theory. The results of the experiments were used to verify the analytical and numerical models. These models were then used to compare the performance of the heat sink with other compact high performance heat sink designs. The results showed that the techniques used to design branching fluid networks significantly improves the performance of active heat sinks. The design experience gained was then used to develop a set of geometric relations which optimize the heat transfer to pumping power ratio of a single cooling channel element. Each element can be connected together using a set of derived geometric guidelines which govern branch diameters and angles. The methodology can be used to design branching fluid networks which can fit any geometry. ^

Optimization of three-dimensional branching networks of microchannels for thermal management of microelectronics

The aim of this work is to present a methodology to develop cost-effective thermal management solutions for microelectronic devices, capable of removing maximum amount of heat and delivering maximally uniform temperature distributions. The topological and geometrical characteristics of multiple-story three-dimensional branching networks of microchannels were developed using multi-objective optimization. A conjugate heat transfer analysis software package and an automatic 3D microchannel network generator were developed and coupled with a modified version of a particle-swarm optimization algorithm with a goal of creating a design tool for 3D networks of optimized coolant flow passages. Numerical algorithms in the conjugate heat transfer solution package include a quasi-ID thermo-fluid solver and a steady heat diffusion solver, which were validated against results from high-fidelity Navier-Stokes equations solver and analytical solutions for basic fluid dynamics test cases. Pareto-optimal solutions demonstrate that thermal loads of up to 500 W/cm2 can be managed with 3D microchannel networks, with pumping power requirements up to 50% lower with respect to currently used high-performance cooling technologies.

Colony-specific calcification and mortality under ocean acidification in the branching coral Montipora digitata

Ocean acidification (OA) threatens calcifying marine organisms including reef-building corals. In this study, we examined the OA responses of individual colonies of the branching scleractinian coral Montipora digitata. We exposed nubbins of unique colonies (n = 15) to ambient or elevated pCO2 under natural light and temperature regimes for 110 days. Although elevated pCO2 exposure on average reduced calcification, individual colonies showed unique responses ranging from declines in positive calcification to negative calcification (decalcification) to no change. Similarly, mortality was greater on average in elevated pCO2, but also showed colony-specific patterns. High variation in colony responses suggests the possibility that ongoing OA may lead to natural selection of OA-tolerant colonies within a coral population.