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The radome of weather radars can be covered with a layer of water, degrading the quality of the radar products. Considering a simplified setup with a planar replica of the Swiss weather radars’ radome, we measure and model analytically its scattering parameters, with and without water. The measured reflectance of the dry radome replica agrees well with the one modeled according to the manufacturer specifications. Water forms droplets on the hydrophobic surface, but water films thicker than 1 mm can be created. Meteorologically more realistic thinner water films are expected on old radomes that have become hydrophilic with aging. Using hygroscopic silk and cotton tissues, we empirically imitate water films as thin as less than 0.1 mm. The measurements align with the simple analytical model of uniform plane wave incidence on the radome and water film but could be further improved by taking refraction and bending of the radome replica into account. Simulations with the General Reflector Antenna Software Package (GRASP) from TICRA complement the study for a representative setup with a spherical radome.
Heating, Ventilation, and Air Conditioning (HVAC) systems are major energy consumers in buildings, challenging the balance between efficiency and occupant comfort. While prior research explored generative AI for HVAC control in simulations, real-world validation remained scarce. This study addresses this gap by designing, deploying, and evaluating “Office-in-the-Loop,” a novel cyber-physical system leveraging generative AI within an operational office setting. Capitalizing on multimodal foundation models and Agentic AI, our system integrates real-time environmental sensor data (temperature, occupancy, etc.), occupants’ subjective thermal comfort feedback, and historical context as input prompts for the generative AI to dynamically predict optimal HVAC temperature setpoints. Extensive real-world experiments demonstrate significant energy savings (up to 47.92%) while simultaneously improving comfort (up to 26.36%) compared to baseline operation. Regression analysis confirmed the robustness of our approach against confounding variables like outdoor conditions and occupancy levels. Furthermore, we introduce Data-Driven Reasoning using Agentic AI, finding that prompting the AI for data-grounded rationales significantly enhances prediction stability and enables the inference of system dynamics and cost functions, bypassing the need for traditional reinforcement learning paradigms. This work bridges simulation and reality, showcasing generative AI’s potential for efficient, comfortable building environments and indicating future scalability to large systems like data centers.
Engineering mechanics is the branch of engineering that applies the laws of mechanics in design, and is at the core of every machine that is designed. This book offers a comprehensive discussion of the fundamental theories and principles of engineering mechanics. It begins by explaining the laws and idealization of mechanics, and then establishes the equation of equilibrium for a rigid body and free body diagram (FBD), along with their applications. Chapters on method of virtual work and mechanical vibration discuss in detail important topics such as principle of virtual work, potential energy and equilibrium and free vibration. The book also introduces the elastic spring method for finding deflection in beams and uses a simple integration method to calculate centroid and moment of inertia. This volume will serve as a useful textbook for undergraduates and engineering students studying engineering mechanics.
There are four forces in our universe. Two act only at the very smallest scales and one only at the very biggest. For everything inbetween, there is electromagnetism. The theory of electromagnetism is described by four gloriously simple and beautiful vector calculus equations known as the Maxwell equations. These are the first genuinely fundamental equations that we meet in our physics education and they survive, essentially unchanged, in our best modern theories of physics. They also serve as a blueprint for what subsequent laws of physics look like. This textbook takes us on a tour of the Maxwell equations and their many solutions. It starts with the basics of electric and magnetic phenomena and explains how their unification results in waves that we call light. It then describes more advanced topics such as superconductors, monopoles, radiation, and electromagnetism in matter. The book concludes with a detailed review of the mathematics of vector calculus.
In this chapter, we (a) introduce the notion of a convex problem in cone-constrained form, (b) present the Lagrange function of a cone-constrained convex problem, (c) prove the convex programming Duality Theorem in cone-constrained form, and (d) discuss conic programming and conic duality, and present the conic programming Duality Theorem.
In this chapter we present convex programming optimality conditions in both sadde point form and Karush--Kuhn--Tucker form for mathematical programming, and also optimality conditions for cone-constrained convex programs and for conic problems. We conclude the chapter by revisiting linear programming duality as a special case of conic duality and reproducing the classical results on the dual of a linearly constrained convex quadratic minimization problem.
We study the dispersion of bubble swarms rising in initially quiescent water using three-dimensional Lagrangian tracking of deformable bubbles and tracer particles in an octagonal bubble column. Two different bubble sizes (3.5 mm and 4.4 mm) and moderate gas volume fractions ($0.52\,\%{-}1.20\,\%$) are considered. First, we compare the dispersion inside bubble swarms with that for single-bubble cases, and find that the horizontal mean squared displacement (MSD) in the swarm cases exhibits oscillations around the asymptotic scaling predicted for a diffusive regime. This occurs due to wake-induced bubble motion; however, the oscillatory behaviour is heavily damped compared to the single-bubble cases due to the presence of bubble-induced turbulence (BIT) and bubble–bubble interactions in the swarm. The vertical MSD in bubble swarms is nearly an order of magnitude faster than in the single-bubble cases, due to the much higher vertical fluctuating bubble velocities in the swarms. We also investigate tracer dispersion in BIT, and find that concerning the time to transition away from the ballistic regime, larger bubbles with a higher gas void fraction transition earlier than tracers, consistent with Mathai et al. (2018, Phys. Rev. Lett., vol. 121, 054501). However, for bubble swarms with smaller bubbles and a lower gas void fraction, they transition at the same time. This differing behaviour is due to the turbulence being more well-mixed for the larger bubble case, whereas for the smaller bubble case, the tracer dispersion is highly dependent on the wake fluctuations generated by the oscillating motion of nearby bubbles.
In this chapter, we (a) outline operations preserving convexity of functions, (b) present differential criteria for convexity, (c) establish convexity of several important multivariate functioins, (d) present the gradient inequality, and (e) establish local boundedness and Lipschitz continuity of convex functions.
In this chapter, we (a) present the notion of a polyhedral representation and illustrate its importance, (b) demonstrate via Fourier--Motzkin eliminaton that every polyhedrally representable set is polyhedral, and (c) outline the calculus of polyhedral representations. As an immediate application, we demonstrate that a bounded and feasible LP problem is solvable.