Cooling jug physics

We discuss the physics of the pot-in-pot cooler. By balancing temperature decrease due to evaporation and temperature increase due to heat exchange, we find the equilibrium temperature of the pot. In this simplified model, the cooling jug acts as a psychrometer, and the theoretical prediction of our model is in a good agreement with psychrometric tables. Next, we study dynamics of the jug cooling. The cooling rate is limited by water vapour diffusion through air, heat conduction through air, and heat conduction through the body of the jug. The derived rate of temperature decrease is in general agreement with the result of our experiment. In the end, we discuss some additional factors, such as capillary effects in the raw clay, water viscosity in the capillaries, and impact of complex shape of the jug.Comment: 10 page

A Constructive Proof of the Borel-Weil Theorem for Classical Groups

The Borel-Weil theorem is usually understood as a realization theorem for representations that have already been shown to exist by other means (``Theorem of the Highest Weight\u27\u27). In this thesis we turn the tables and show that, at least in the case of the classical groups $G = U(n)$, $SO(n)$ and $Sp(2n)$, the Borel-Weil construction can be used to quite explicitly prove existence of an irreducible representation having highest weight $\lambda$, for each dominant integral form $\lambda$ on the Lie algebra of a maximal torus of $G$

A Framework for anonymous background data delivery and feedback

The current state of the industry’s methods of collecting background data reflecting diagnostic and usage information are often opaque and require users to place a lot of trust in the entity receiving the data. For vendors, having a centralized database of potentially sensitive data is a privacy protection headache and a potential liability should a breach of that database occur. Unfortunately, high profile privacy failures are not uncommon, so many individuals and companies are understandably skeptical and choose not to contribute any information. It is a shame, since the data could be used for improving reliability, or getting stronger security, or for valuable academic research into real-world usage patterns. We propose, implement and evaluate a framework for non-realtime anonymous data collection, aggregation for analysis, and feedback. Departing from the usual “trusted core” approach, we aim to maintain reporters’ anonymity even if the centralized part of the system is compromised. We design a peer-to-peer mix network and its protocol that are tuned to the properties of background diagnostic traffic. Our system delivers data to a centralized repository while maintaining (i) source anonymity, (ii) privacy in transit, and (iii) the ability to provide analysis feedback back to the source. By removing the core’s ability to identify the source of data and to track users over time, we drastically reduce its attractiveness as a potential attack target and allow vendors to make concrete and verifiable privacy and anonymity claims

Audio to Architecture: House Music as a Form Generator

Contemporary music undergoes similar process of creation to that of the design process through computation and variation. House music as a representation of contemporary culture has a layered structure that allows specific characteristics to identify it as house music. Song components can vary and mix in different orders that form new dynamic compositions. I am going to explore the idea that every house music component can be translated into geometry with the use of parametric design techniques

Real-time dynamics for interactive environments

This thesis examines the design and implementation of an extensible objectoriented physics engine framework. The design and implementation consolidates concepts from the wide literature in the field and clearly documents the procedures and methods. Two primary dynamic behaviors are explored: rigid body dynamics and articulated dynamics. A generalized collision response model is built for rigid bodies and articulated structures which can be adapted to other types of behaviors. The framework is designed around the use of interfaces for modularity and easy extensibility. It supports both a standalone physics engine and a supplement to a distributed immersive rendering environment. We present our results as a number of scenarios that demonstrate the viability of the framework. These scenarios include rigid bodies and articulated structures in free-fall, collision with dynamic and static bodies, resting contact, and friction. We show that we can effectively combine different dynamics into one cohesive structure. We also explain how we can efficiently extend current behaviors to develop new ones, such as altering rigid bodies to produce different collision responses or flocking behavior. Additionally, we demonstrate these scenarios in both the standalone and the immersive environment