Spectrophotometric measurements of the vibrational relaxation of CO in shock wave and nozzle expansion-flow environments

Spectrophotometric measurements of vibrational relaxation of CO in shock wave and nozzle expansion-flow environment

A unified IMEX Runge-Kutta approach for hyperbolic systems with multiscale relaxation

In this paper we consider the development of Implicit-Explicit (IMEX) Runge-Kutta schemes for hyperbolic systems with multiscale relaxation. In such systems the scaling depends on an additional parameter which modifies the nature of the asymptotic behavior which can be either hyperbolic or parabolic. Because of the multiple scalings, standard IMEX Runge-Kutta methods for hyperbolic systems with relaxation loose their efficiency and a different approach should be adopted to guarantee asymptotic preservation in stiff regimes. We show that the proposed approach is capable to capture the correct asymptotic limit of the system independently of the scaling used. Several numerical examples confirm our theoretical analysis

Parametric Surfaces for Augmented Architecture representation

Augmented Reality (AR) represents a growing communication channel, responding to the need to expand reality with additional information, offering easy and engaging access to digital data. AR for architectural representation allows a simple interaction with 3D models, facilitating spatial understanding of complex volumes and topological relationships between parts, overcoming some limitations related to Virtual Reality. In the last decade different developments in the pipeline process have seen a significant advancement in technological and algorithmic aspects, paying less attention to 3D modeling generation. For this, the article explores the construction of basic geometries for 3D model’s generation, highlighting the relationship between geometry and topology, basic for a consistent normal distribution. Moreover, a critical evaluation about corrective paths of existing 3D models is presented, analysing a complex architectural case study, the virtual model of Villa del Verginese, an emblematic example for topological emerged problems. The final aim of the paper is to refocus attention on 3D model construction, suggesting some "good practices" useful for preventing, minimizing or correcting topological problems, extending the accessibility of AR to people engaged in architectural representation

Implicit-Explicit Runge-Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit

We consider Implicit-Explicit (IMEX) Runge-Kutta (R-K) schemes for hyperbolic systems with stiff relaxation in the so-called diffusion limit. In such regime the system relaxes towards a convection-diffusion equation. The first objective of the paper is to show that traditional partitioned IMEX R-K schemes will relax to an explicit scheme for the limit equation with no need of modification of the original system. Of course the explicit scheme obtained in the limit suffers from the classical parabolic stability restriction on the time step. The main goal of the paper is to present an approach, based on IMEX R-K schemes, that in the diffusion limit relaxes to an IMEX R-K scheme for the convection-diffusion equation, in which the diffusion is treated implicitly. This is achieved by an original reformulation of the problem, and subsequent application of IMEX R-K schemes to it. An analysis on such schemes to the reformulated problem shows that the schemes reduce to IMEX R-K schemes for the limit equation, under the same conditions derived for hyperbolic relaxation. Several numerical examples including neutron transport equations confirm the theoretical analysis

Cosmological string models from Milne spaces and SL(2,Z) orbifold

The $n+1$-dimensional Milne Universe with extra free directions is used to construct simple FRW cosmological string models in four dimensions, describing expansion in the presence of matter with $p=k \rho$, $k=(4-n)/3n$. We then consider the n=2 case and make SL(2,Z) orbifold identifications. The model is surprisingly related to the null orbifold with an extra reflection generator. The study of the string spectrum involves the theory of harmonic functions in the fundamental domain of SL(2,Z). In particular, from this theory one can deduce a bound for the energy gap and the fact that there are an infinite number of excitations with a finite degeneracy. We discuss the structure of wave functions and give examples of physical winding states becoming light near the singularity.Comment: 14 pages, harvma

Basic principles of hp Virtual Elements on quasiuniform meshes

In the present paper we initiate the study of $hp$ Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimates that are explicit both in the mesh size $h$ and in the polynomial degree $p$ in the case of finite Sobolev regularity. Exponential convergence is proved in the case of analytic solutions. The theoretical convergence results are validated in numerical experiments. Finally, an initial study on the possible choice of local basis functions is included

Multi-loop open string amplitudes and their field theory limit

JHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.0This work was supported by STFC (Grant ST/J000469/1, ‘String theory, gauge theory & duality’) and by MIUR (Italy) under contracts 2006020509 004 and 2010YJ2NYW 00

The Virtual Element Method with curved edges

In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved interface. While an approximation of the domain with polygons leads, for degree of accuracy $k \geq 2$, to a sub-optimal rate of convergence, we show (both theoretically and numerically) that the proposed curved VEM lead to an optimal rate of convergence