Gödel’s proof

In 1931, the great Austrian mathematician Kurt Gödel proved “all consistent axiomatic formulations of number theory include undecidable propositions”. This discovery of Gödel and its proof had enormous repercussions in mathematics and computer science. The proof hinged upon the writing of a self-referential mathematical statement, in the same way as the liar’s paradox — I am lying — is a self-referential statement. In this three-part article, we describe Gödel’s discovery and his famous proof.     

Transmission line realization of subwavelength resonator formed by a pair of conventional and LHM slabs

INTRODUCTION Left-handed materials (LHMs), first investigated theoretically by Veselago (1968), have received sub- stantial attention in the scientific and engineering communities. The unique properties of these meta- materials are promising for a diversity of microwave applications, such as new types of beam steerers, modulators, filters, superlens (Pendry, 2000), cou- plers and antenna radoms (Smith et al., 2004). Re- cently, a transmission line (TL) approach has been successfully in…     

The effect of acceleration signal processing for head impact numeric simulations

Brain injury research in sport employs a variety of physical models equipped with accelerometers. These acceleration signals are commonly processed using filters. The purpose of this research was to determine the effect of applying filters with different cutoff frequencies to the acceleration signals used as input for finite element modeling of the brain. Signals were generated from reconstructions of concussion events from American football and ice hockey in the laboratory using a Hybrid III headform. The resulting acceleration signals were used as input for the University College Dublin Brain Trauma Model after being processed with filters. The results indicated that using a filter with a cutoff of 300 Hz or higher had little effect on the resulting strain measures. In some cases there was some effect of the filters on the peak linear (8–30g) and rotational measures (1000–4000 rad/s²), but little effect on the finite element strain result (approximately 2–6 %). The short duration and high magnitude accelerations, such as the puck impact, were most affected by the cutoff frequency of different filters.     

Spannungsfeld Polyvalenz in der Lehrerbildung

The Bologna Process of higher education reform has led to a vast array of different programs of study in German teacher training. In this article, we firstly analyze the implementation of Bachelor programs in teacher training, comparing profession-oriented programs (i.e. those aiming to train students for the teaching profession from the beginning of studies) to polyvalent programs (i.e. those aiming at broad qualifications and including a late decision to become a teacher). Secondly, we investigate whether students enrolled in these study programs differ systematically in their subjective certainty about their career choice. To answer these questions, we analyze portfolios of documents related to teacher training programs from nine German universities that prepare students for teaching in the academic track. Additionally, we analyze data from N?=?2585 Bachelor and N?=?928 Master degree students. We found that most programs, even when they espouse polyvalence, require an early decision to become a teacher. Moreover, our data confirm findings from earlier studies indicating that student teachers are highly certain about their career choice from the very beginning, with students in polyvalent programs being slightly less certain than those in profession-oriented programs (d?=?0.32).     

Preliminary experimental study on solid-fuel rocket scramjet combustor

Liquid or gaseous fuel scramjet technology has made great progress, and there has been some research attention to solid-fuel scramjet. A new scramjet configuration using solid fuel as propellant, namely solid-fuel rocket scramjet, is tested experimentally. It consists of two combustors. One is a rocket combustor used as gas generator, and the other is a supersonic combustor used for secondary combustion. The experiment simulates a flight Mach number of 4 at high altitude (stagnation temperature and pressure are 1170 K and 1.16 MPa, respectively), and metalized solid fuel is used as propellant. The results reveal that fuel-rich gas from the gas generator can burn with air in the supersonic combustor. Preliminary evaluation results show that the combustion efficiency of the propellant is about 90%, and the total pressure recovery coefficient in the supersonic combustor is about 0.6. These results indicate that the configuration of solid-fuel rocket scramjet is feasible.     

Mode transition process in a typical strut-based scramjet combustor based on a parametric study

The combustion performance of hydrogen fuel in a scramjet combustor has been a popular focus for scholars all over the world. In this study, the influence of the jet-to-crossflow pressure ratio on combustion performance in a scramjet combustor was investigated numerically, and the influence of a wall-mounted cavity was evaluated. The simulations were conducted using the Reynolds-averaged Navier-Stokes (RANS) equations coupled with the renormalization group (RNG) k-ε turbulence model and the single-step chemical reaction mechanism. This numerical approach was validated by comparing predicted results with published experimental shadowgraphs and velocity and temperature measurements. When the pressure of the wall-injector increases, the performance of the combustor decreases. At the same inflow condition, this may lead to a scram-to-ram mode transition. The cavity adopted in this study would prevent pre-combustion shock waves from pushing out of the isolator and help to stabilize the flow field, but it would decrease the mixing and combustion efficiencies.