Conformal or Walking? Monte Carlo renormalization group studies of SU(3) gauge models with fundamental fermions

Strongly coupled gauge systems with many fermions are important in many phenomenological models. I use the 2-lattice matching Monte Carlo renormalization group method to study the fixed point structure and critical indexes of SU(3) gauge models with 8 and 12 flavors of fundamental fermions. With an improved renormalization group block transformation I am able to connect the perturbative and confining regimes of the N_f=8 flavor system, thus verifying its QCD-like nature. With N_f=12 flavors the data favor the existence of an infrared fixed point and conformal phase, though the results are also consistent with very slow walking. I measure the anomalous mass dimension in both systems at several gauge couplings and find that they are barely different from the free field value.Comment: 26 pages, 11 figure

First-principles calculations of a high-pressure synthesized compound PtC

First-principles density-functional method is used to study the recently high-pressure synthesized compound PtC. It is confirmed by our calculations that the platinum carbide has a zinc-blende ground-state phase at zero pressure and the rock-salt structure is a high-pressure phase. The theoretical transition pressure from zinc-blende to rock-salt is determined to be 52GPa. Furthermore, our calculation shows the possibility that the experimentally synthesized PtC by Ono et al. under high pressure condition might undergo a transition from rock-salt structure to zinc-blende after the pressure quench to ambient condition.Comment: A revised versio

A New Model for Evaluating the Future Options of Integrating Ground Source Heat Pumps in Building Construction

Decision-making for effective infrastructure integration is challenging because the performances of long-lasting objects often depends on conditions which are either outside the control of the designer or difficult to foresee at the design stage. In this paper we examine a new approach to estimating the range of cost-effective solutions for integrating the construction/retrofit of two or more different types of infrastructure. Infrastructure integration has many perceived benefits, but also faces serious new challenges and doubts from practitioners, particularly in sectors with complex construction process, long asset lives, uncertain cost parameters, and slow and unwieldy decision-making, such as is common with civil engineering works. We test all main options in integrating a ground source heat pump (GSHP) system with the construction and retrofit of an archetypal, office building. A new simulation model is developed and parameterized using actual data in the UK. We incorporate unavoidable uncertainties and randomness in how the decisions are triggered, and test the effectiveness of proactive measures to embed future options. The model highlights how sensitive the range of cost-effective solutions is to the setting of renewable energy incentives, discount rates, technical performance and life-cycle asset management of interdependent infrastructure. This points to a clear need for establishing appropriate regulatory standards. We expect this model to find increasing applications in the planning and designing of integrated complexes of buildings, transport facilities, renewable energy supply, water supply and waste management in dense urban areas, which are an increasingly key part of sustainable urban development

The Abel-Zeilberger Algorithm

We use both Abel's lemma on summation by parts and Zeilberger's algorithm to find recurrence relations for definite summations. The role of Abel's lemma can be extended to the case of linear difference operators with polynomial coefficients. This approach can be used to verify and discover identities involving harmonic numbers and derangement numbers. As examples, we use the Abel-Zeilberger algorithm to prove the Paule-Schneider identities, the Apery-Schmidt-Strehl identity, Calkin's identity and some identities involving Fibonacci numbers.Comment: 18 page

Global Models of Planet Formation and Evolution

Despite the increase in observational data on exoplanets, the processes that lead to the formation of planets are still not well understood. But thanks to the high number of known exoplanets, it is now possible to look at them as a population that puts statistical constraints on theoretical models. A method that uses these constraints is planetary population synthesis. Its key element is a global model of planet formation and evolution that directly predicts observable planetary properties based on properties of the natal protoplanetary disk. To do so, global models build on many specialized models that address one specific physical process. We thoroughly review the physics of the sub-models included in global formation models. The sub-models can be classified as models describing the protoplanetary disk (gas and solids), the (proto)planet (solid core, gaseous envelope, and atmosphere), and finally the interactions (migration and N-body interaction). We compare the approaches in different global models and identify physical processes that require improved descriptions in future. We then address important results of population synthesis like the planetary mass function or the mass-radius relation. In these results, the global effects of physical mechanisms occurring during planet formation and evolution become apparent, and specialized models describing them can be put to the observational test. Due to their nature as meta models, global models depend on the development of the field of planet formation theory as a whole. Because there are important uncertainties in this theory, it is likely that global models will in future undergo significant modifications. Despite this, they can already now yield many testable predictions. With future global models addressing the geophysical characteristics, it should eventually become possible to make predictions about the habitability of planets.Comment: 30 pages, 16 figures. Accepted for publication in the International Journal of Astrobiology (Cambridge University Press