Numerical analysis of 3D regimes of natural convection and surface radiation in a differentially heated enclosure

Numerical analysis of 3D regimes of convection-radiation heat transfer in cubic enclosure with two isothermal faces and adiabatic walls is performed. The mathematical model is constructed in dimensionless variables “vector potential-vorticity vector-temperature” in the Boussinesq approximation and with regard to diathermal medium filling the enclosure. 3D temperature and velocity fields, medium motion trajectories in a wide range of key parameters are obtained. Correlations for the integral heat exchange coefficient as a function of the key process characteristics are found

A non-standard analysis of a cultural icon: The case of Paul Halmos

We examine Paul Halmos' comments on category theory, Dedekind cuts, devil worship, logic, and Robinson's infinitesimals. Halmos' scepticism about category theory derives from his philosophical position of naive set-theoretic realism. In the words of an MAA biography, Halmos thought that mathematics is "certainty" and "architecture" yet 20th century logic teaches us is that mathematics is full of uncertainty or more precisely incompleteness. If the term architecture meant to imply that mathematics is one great solid castle, then modern logic tends to teach us the opposite lession, namely that the castle is floating in midair. Halmos' realism tends to color his judgment of purely scientific aspects of logic and the way it is practiced and applied. He often expressed distaste for nonstandard models, and made a sustained effort to eliminate first-order logic, the logicians' concept of interpretation, and the syntactic vs semantic distinction. He felt that these were vague, and sought to replace them all by his polyadic algebra. Halmos claimed that Robinson's framework is "unnecessary" but Henson and Keisler argue that Robinson's framework allows one to dig deeper into set-theoretic resources than is common in Archimedean mathematics. This can potentially prove theorems not accessible by standard methods, undermining Halmos' criticisms. Keywords: Archimedean axiom; bridge between discrete and continuous mathematics; hyperreals; incomparable quantities; indispensability; infinity; mathematical realism; Robinson.Comment: 15 pages, to appear in Logica Universali

Cutoff rigidity and particle trajectories online calculator

Over the years, many authors have developed unique software packages for calculating the geomagnetic cut- off rigidities and the asymptotic directions of particle arrival. Such programs are used for mass calculations and require some skill. However, it is often necessary to carry out single calculations with the same accu- racy. For this purpose, calculator programs have been created on the basis of already developed software packages. One of such programs, a calculator, is described in this work

Towards realisation of an efficient continuous wave terahertz source using quantum dot devices

A continuous wave (CW) terahertz source emitting in a broad frequency range (1-5THz) is promising towards achieving a compact, high power, finely tunable, room temperature terahertz generation system which will be of immense significance towards the realisation of terahertz applications in spectroscopy, communication, sensing, and imaging among others. We have demonstrated a tunable continuous-wave Quantum Dot external cavity laser emitting at two frequencies for continuous wave terahertz emission in a Quantum dot Photoconductive Antenna (PCA). The external cavity QD Laser has been characterised with tunability of 152nm and a tuning range from 1143nm -1295.8nm that lies within the THz difference frequency for the generation of THz radiation from QD based PCAs

Cauchy, infinitesimals and ghosts of departed quantifiers

Procedures relying on infinitesimals in Leibniz, Euler and Cauchy have been interpreted in both a Weierstrassian and Robinson's frameworks. The latter provides closer proxies for the procedures of the classical masters. Thus, Leibniz's distinction between assignable and inassignable numbers finds a proxy in the distinction between standard and nonstandard numbers in Robinson's framework, while Leibniz's law of homogeneity with the implied notion of equality up to negligible terms finds a mathematical formalisation in terms of standard part. It is hard to provide parallel formalisations in a Weierstrassian framework but scholars since Ishiguro have engaged in a quest for ghosts of departed quantifiers to provide a Weierstrassian account for Leibniz's infinitesimals. Euler similarly had notions of equality up to negligible terms, of which he distinguished two types: geometric and arithmetic. Euler routinely used product decompositions into a specific infinite number of factors, and used the binomial formula with an infinite exponent. Such procedures have immediate hyperfinite analogues in Robinson's framework, while in a Weierstrassian framework they can only be reinterpreted by means of paraphrases departing significantly from Euler's own presentation. Cauchy gives lucid definitions of continuity in terms of infinitesimals that find ready formalisations in Robinson's framework but scholars working in a Weierstrassian framework bend over backwards either to claim that Cauchy was vague or to engage in a quest for ghosts of departed quantifiers in his work. Cauchy's procedures in the context of his 1853 sum theorem (for series of continuous functions) are more readily understood from the viewpoint of Robinson's framework, where one can exploit tools such as the pointwise definition of the concept of uniform convergence. Keywords: historiography; infinitesimal; Latin model; butterfly modelComment: 45 pages, published in Mat. Stu