Quantum fields in curved spacetime: renormalization

In this chapter, which forms the central chapter of Part II, the effective action of quantum matter fields in curved spacetime is formulated in terms of functional integrals. A qualitative, albeit incompletely conclusive, analysis of divergences and renormalization in curved space is given. Both non-covariant and covariant methods of calculations are discussed. Normal coordinates and local momentum representation are used to derive the effective potential. The basic elements of the Schwinger-DeWitt technique are elaborated in detail, resulting in the general formulas for one-loop divergences. The heat-kernel technique is also discussed.

Compact Local Structure-Preserving Algorithms for the Nonlinear Schrödinger Equation with Wave Operator

Combining the compact method with the structure-preserving algorithm, we propose a compact local energy-preserving scheme and a compact local momentum-preserving scheme for the nonlinear Schrödinger equation with wave operator (NSEW). The convergence rates of both schemes are Oh4+τ2. The discrete local conservative properties of the presented schemes are derived theoretically. Numerical experiments are carried out to demonstrate the convergence order and local conservation laws of the developed algorithms.

Charles Fulton: the regional reach of modernism in Australia

Charles Fulton (1905-1987) was an Australian architect who applied influences of European Modernism, particularly the civic architecture of Willem Dudok, into the design for several hospital projects in regional towns across Queensland, at the same time adapting a climatic responsive rationale to the projects. As with many remote contexts that have been overlooked by a European and American centric focus upon Modern architecture, the account of Australian Modernism has not been widely acknowledged outside its borders, despite a local momentum to effectively document and publish its achievements. Compounding this predicament, Queensland has suffered from its own exclusion relative to the southern states of New South Wales (Sydney) and Victoria (Melbourne), which have always been the dominant centers of the national profession, its conferences and publications. This paper seeks to address these schisms through the presentation of the work of Fulton, demonstrating how even in remote areas of Queensland, thousands of kilometers from major cities, the reach of Modern architecture found a place. Mobilized by the national federal body, the Office of Health and Home Affairs, drive to improve health services across the country post WWI, Fulton became a leading architect to modernize health facilities and brought about a cultural shift in the reception of Modern architecture across the regions.

Quantum aspects of Yukawa model with scalar and axial scalar fields in curved spacetime

We study the Yukawa model with one scalar and one axial scalar fields, coupled to N copies of Dirac fermions, in curved spacetime background. The theory possesses a reach set of coupling constants, including the scalar terms with odd powers of scalar fields in the potential, and constants of non-minimal coupling of the scalar fields to gravity. Using the heat-kernel technique and dimensional regularization, we derive the one-loop divergences, describe the renormalization of the theory under consideration and calculate the full set of beta- and gamma-functions for all coupling constants and fields. As a next step, we construct the renormalized one-loop effective potential of the scalar fields up to the terms linear in scalar curvature. This calculation includes only the contributions from quantum scalar fields, and is performed using covariant cut-off regularization and local momentum representation. Some difficulties of the renormalization group approach to the effective potential in the case under consideration are discussed.

TSUNAMI INUNDATION SIMULATIONS IN URBAN TOPOGRAPHY

The inundation of the 2011 Tohoku Earthquake Tsunami showed complex behavior over the land. According to the surveys of the Tohoku Earthquake Tsunami in 2011, the behavior of tsunami in urban areas was different from that in rural areas and the damage was not only dependent on the inundation heights but also the local momentum. The buildings are commonly excluded and smoothed off in the topography in the conventional inundation simulation but it’s important to understand the local characteristics of tsunami run-up in urban areas. The purpose of this study is to understand and validate numerical models of tsunami in the urban area.