Single-Valued Hamiltonian via Legendre-Fenchel Transformation and Time Translation Symmetry

Under conventional Legendre transformation, systems with a non-convex Lagrangian will result in a multi-valued Hamiltonian as a function of conjugate momentum. This causes problems such as non-unitary time evolution of quantum state and non-determined motion of classical particles, and is physically unacceptable. In this work, we propose a new construction of single-valued Hamiltonian by applying Legendre-Fenchel transformation, which is a mathematically rigorous generalization of conventional Legendre transformation, valid for non-convex Lagrangian systems, but not yet widely known to the physics community. With the new single-valued Hamiltonian, we study spontaneous breaking of time translation symmetry and derive its vacuum state. Applications to theories of cosmology and gravitation are discussed.Comment: Journal Version, 16pp. All results + conclusions un-changed, only minor refinements to clarify the importance of our new LFT method and its physics applications; references adde

Wind pressure on a single building immersed in a low-jet wind profile

This paper for the first time discuss the wind pressure distribution on the building surface immersed in wind profile of low-level jet rather than a logarithmic boundary-layer profile. Two types of building models are considered, low-rise and high-rise building, relative to the low-level jet height. CFD simulation is carried out. The simulation results show that the wind pressure distribution immersed in a low-jet wine profile is very different from the typical uniform and boundary-layer flow. For the low-rise building, the stagnation point is located at the upper level of windward façade for the low-level jet wind case, and the separation zone above the roof top is not as obvious as the uniform case. For the high-rise building model, the height of stagnation point is almost as high as the low-level jet height

Reevaluation of the density dependence of nucleon radius and mass in the global color symmetry model of QCD

With the global color symmetry model (GCM) at finite chemical potential, the density dependence of the bag constant, the total energy and the radius of a nucleon in nuclear matter is investigated. A relation between the nuclear matter density and the chemical potential with the action of QCD being taken into account is obtained. A maximal nuclear matter density for the existence of the bag with three quarks confined within is given. The calculated results indicate that, before the maximal density is reached, the bag constant and the total energy of a nucleon decrease, and the radius of a nucleon increases slowly, with the increasing of the nuclear matter density. As the maximal nuclear matter density is reached, the mass of the nucleon vanishes and the radius becomes infinite suddenly. It manifests that a phase transition from nucleons to quarks takes place.Comment: 18 pages, 3 figure

Smart Pacing for Effective Online Ad Campaign Optimization

In targeted online advertising, advertisers look for maximizing campaign performance under delivery constraint within budget schedule. Most of the advertisers typically prefer to impose the delivery constraint to spend budget smoothly over the time in order to reach a wider range of audiences and have a sustainable impact. Since lots of impressions are traded through public auctions for online advertising today, the liquidity makes price elasticity and bid landscape between demand and supply change quite dynamically. Therefore, it is challenging to perform smooth pacing control and maximize campaign performance simultaneously. In this paper, we propose a smart pacing approach in which the delivery pace of each campaign is learned from both offline and online data to achieve smooth delivery and optimal performance goals. The implementation of the proposed approach in a real DSP system is also presented. Experimental evaluations on both real online ad campaigns and offline simulations show that our approach can effectively improve campaign performance and achieve delivery goals.Comment: KDD'15, August 10-13, 2015, Sydney, NSW, Australi

Natural ventilation assessment in typical open an semi-open urban environments under various wind directions

Semi-open street roofs protect pedestrians from intense sunshine and rains. Their effects on natural ventilation of urban canopy layers (UCL) are less understood. This paper investigates two idealized urban models consisting of 4(2×2) or 16(4×4) buildings under a neutral atmospheric condition with parallel (0°) or non-parallel (15°,30°,45°) approaching wind. The aspect ratio (building height (H) / street width (W)) is 1 and building width is B=3H. Computational fluid dynamic (CFD) simulations were first validated by experimental data, confirming that standard k-ε model predicted airflow velocity better than RNG k-ε model, realizable k–ε model and Reynolds stress model. Three ventilation indices were numerically analyzed for ventilation assessment, including flow rates across street roofs and openings to show the mechanisms of air exchange, age of air to display how long external air reaches a place after entering UCL, and purging flow rate to quantify the net UCL ventilation capacity induced by mean flows and turbulence. Five semi-open roof types are studied: Walls being hung above street roofs (coverage ratio λa=100%) at z=1.5H, 1.2H, 1.1H ('Hung1.5H', 'Hung1.2H', 'Hung1.1H' types); Walls partly covering street roofs (λa=80%) at z=H ('Partly-covered' type); Walls fully covering street roofs (λa=100%) at z=H ('Fully-covered' type).They basically obtain worse UCL ventilation than open street roof type due to the decreased roof ventilation. 'Hung1.1H', 'Hung1.2H', 'Hung1.5H' types are better designs than 'Fully-covered' and 'Partly-covered' types. Greater urban size contains larger UCL volume and requires longer time to ventilate. The methodologies and ventilation indices are confirmed effective to quantify UCL ventilation