Diffusive Geometries


Book Description

Architecture primarily serves as a way to create and control the environment around us. Unlike natural weather, climate conditions in architecture are often static and binary, with no diffusion in between. As a result, sensory experiences that are directly accessible outdoors, like atmospheric quality, diffusiveness, and flow, are completely excluded from the indoors. The climate is discretized in space into strict self-contained, functional units, where wetness is kept in wet spaces yet other areas are completely dry. Many of these weather experiences have certain architectural qualities. This project uses vapor as a medium to create the experience of micro-climates and weather conditions from the outside, and bring them back inside architecture as tectonic elements that modulate visibility, create cooling gradients, and produce spatial patterns in a controlled manner. The three main elements are: point – vapor vertex ring, line – vapor tornado, plane – vapor wall. The focused and diffused conditions of vapor enable both localized and global conditions with soft boundaries. Imagine a future where architects not only sculpt their ideal space but also control the weather inside: one corner feels like the Saharan Desert, while the other behaves like the Amazon rainforest. In one corner, an early morning mist greets the contemplative mind, and in the center space, a focused tornado vapor attracts a gathering crowd. The interior space no longer acts like static and binary units—with clear boundaries like rain for shower, snow for fridge, or sun for light—but like dynamic, diffused, and phenomenal experiences.




Analysis and Geometry of Markov Diffusion Operators


Book Description

The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.




Geometry-Driven Diffusion in Computer Vision


Book Description

Scale is a concept the antiquity of which can hardly be traced. Certainly the familiar phenomena that accompany sc ale changes in optical patterns are mentioned in the earliest written records. The most obvious topological changes such as the creation or annihilation of details have been a topic to philosophers, artists and later scientists. This appears to of fascination be the case for all cultures from which extensive written records exist. For th instance, chinese 17 c artist manuals remark that "distant faces have no eyes" . The merging of details is also obvious to many authors, e. g. , Lucretius mentions the fact that distant islands look like a single one. The one topo logical event that is (to the best of my knowledge) mentioned only late (by th John Ruskin in his "Elements of drawing" of the mid 19 c) is the splitting of a blob on blurring. The change of images on a gradual increase of resolu tion has been a recurring theme in the arts (e. g. , the poetic description of the distant armada in Calderon's The Constant Prince) and this "mystery" (as Ruskin calls it) is constantly exploited by painters.







Diffusion Models of Environmental Transport


Book Description

Fate and transport models are critical components in the determination of the exposure to and risk from hazardous contaminants. Analytical models are preferable because they are generally more accessible, more reliable, and require fewer computational resources. Surprisingly, until today, only a limited number of analytical models have been accessible in the literature. Now, there is Diffusion Models of Environmental Transport, which provides more than 40 analytical models of diffusion and advective-diffusion in one, two, and three layer systems, subject to a wide range of boundary and initial conditions. This text illustrates applications to contaminant transport in sediments and soils, including porewater and vapor transport, and also provides Mathcad spreadsheets to aid in the use of these models. The authors supply complete details of the solutions to the models for those who wish for a deeper understanding. For others, who do not have the time or the need, the solutions themselves are ready to be picked up and used. Reible and Choy use their 20-plus years of cumulative experience to create a thorough exploration of fate and transport models. This comprehensive text furnishes an invaluable reference for students and environmental professionals.







On the Geometry of Diffusion Operators and Stochastic Flows


Book Description

Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, especially those with interests in stochastic flows, infinite dimensional analysis, or geometric analysis, and also to researchers in sub-Riemannian geometry. A basic background in differential geometry is assumed, but the construction of the connections is very direct and itself gives an intuitive and concrete introduction. Knowledge of stochastic analysis is also assumed for later chapters.




Diffusion in Natural Porous Media


Book Description

Diffusion in Natural Porous Media: Contaminant Transport, Sorption/Desorption and Dissolution Kinetics introduces the general principles of diffusion in the subsurface environment and discusses the implications for the fate and transport of contaminants in soils and groundwater. Emphasis is placed on sorption/desorption and the dissolution kinetics of organic contaminants, both of which are limited by the slow speed of molecular diffusion. Diffusion in Natural Porous Media: Contaminant Transport, Sorption/Desorption and Dissolution Kinetics compiles methods for calculating the diffusion coefficients of organic compounds (in aqueous solution or vapor phase) in natural porous media. The author uses analytical solutions of Fick's 2nd law and some simple numerical models to model diffusive transport under various initial and boundary conditions. A number of these models may be solved using spreadsheets. The book examines sorption/desorption rates of organic compounds in various soils and aquifer materials, and also examines the dissolution kinetics of nonaqueous phase liquids in aquifers, in both the trapped residual phase and in pools. Diffusion in Natural Porous Media: Contaminant Transport, Sorption/Desorption and Dissolution Kinetics concludes with a discussion of the impact of slow diffusion processes on soil and groundwater decontamination and the implications of these processes for groundwater risk assessment.




The Roll-diffusion Bonding of Structural Shapes and Panels


Book Description

The report summarizes the progress in recent and current research and development programs to advance the state of the art of the roll-diffusion-bonding process as applied to the manufacture of structural panels and shapes. At the present time, there are seven such NASA and DOD programs in progress. These are reviewed in the report. (Author).