Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation

By numerical calculation, the Planck spectrum with zero-point radiation is shown to satisfy a natural maximum-entropy principle whereas alternative choices of spectra do not. Specifically, if we consider a set of conducting-walled boxes, each with a partition placed at a different location in the box, so that across the collection of boxes the partitions are uniformly spaced across the volume, then the Planck spectrum correspond to that spectrum of random radiation (having constant energy kT per normal mode at low frequencies and zero-point energy (1/2)hw per normal mode at high frequencies) which gives maximum uniformity across the collection of boxes for the radiation energy per box. The analysis involves Casimir energies and zero-point radiation which do not usually appear in thermodynamic analyses. For simplicity, the analysis is presented for waves in one space dimension.Comment: 11 page

Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect

The formulae for Planck length, Hawking temperature and Unruh-Davies temperature are derived by using only laws of classical physics together with the Heisenberg principle. Besides, it is shown how the Hawking relation can be deduced from the Unruh relation by means of the principle of equivalence; the deep link between Hawking effect and Unruh effect is in this way clarified.Comment: LaTex file, 6 pages, no figure

Homogeneous heterotic supergravity solutions with linear dilaton

I construct solutions to the heterotic supergravity BPS-equations on products of Minkowski space with a non-symmetric coset. All of the bosonic fields are homogeneous and non-vanishing, the dilaton being a linear function on the non-compact part of spacetime.Comment: 36 pages; v2 conclusion updated and references adde

Randomizing world trade. II. A weighted network analysis

Based on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of the binary projections of the ITN by considering its weighted representations. We show that, unlike the binary case, all possible weighted representations of the ITN (directed/undirected, aggregated/disaggregated) cannot be traced back to local country-specific properties, which are therefore of limited informativeness. Our two papers show that traditional macroeconomic approaches systematically fail to capture the key properties of the ITN. In the binary case, they do not focus on the degree sequence and hence cannot characterize or replicate higher-order properties. In the weighted case, they generally focus on the strength sequence, but the knowledge of the latter is not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243 [physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011

Hydrodynamic reductions of the heavenly equation

We demonstrate that Pleba\'nski's first heavenly equation decouples in infinitely many ways into a triple of commuting (1+1)-dimensional systems of hydrodynamic type which satisfy the Egorov property. Solving these systems by the generalized hodograph method, one can construct exact solutions of the heavenly equation parametrized by arbitrary functions of a single variable. We discuss explicit examples of hydrodynamic reductions associated with the equations of one-dimensional nonlinear elasticity, linearly degenerate systems and the equations of associativity.Comment: 14 page

On Lagerstrom’s Model of Slow Incompressible Viscous Flow

The model discussed is a nonlinear boundary value problem which contains a parameter $\varepsilon$ that models the Reynolds number. The matched asymptotic expansions, an inner “Stokes” expansion valid near the inner boundary and an outer “Oseen” expansion valid away from it, that describe the solutions of the model problem for $\varepsilon$ small are extended. Numerical calculations show that these matched expansions have only a small range of usefulness, with the addition of further terms generally causing a worse, rather than better, approximation at moderate values of $\varepsilon$. Far better results are achieved when a single expansion, the outer expansion, is used throughout. The additional terms that have been calculated then consistently give improved approximations for all $\varepsilon$. It is also rigorously proved that an iterative method of solution of the model equation based on the outer “Oseen” approximation, converges for all $\varepsilon$ to a unique solution.\ud The results presented here for Lagerstrom’s model suggest that iterative improvement of the Oseen expansion may be an effective method of approximation of viscous flows at moderate Reynolds number

New non compact Calabi-Yau metrics in D=6

A method for constructing explicit Calabi-Yau metrics in six dimensions in terms of an initial hyperkahler structure is presented. The equations to solve are non linear in general, but become linear when the objects describing the metric depend on only one complex coordinate of the hyperkahler 4-dimensional space and its complex conjugated. This situation in particular gives a dual description of D6-branes wrapping a complex 1-cycle inside the hyperkahler space, which was studied by Fayyazuddin. The present work generalize the construction given by him. But the explicit solutions we present correspond to the non linear problem. This is a non linear equation with respect to two variables which, with the help of some specific anzatz, is reduced to a non linear equation with a single variable solvable in terms of elliptic functions. In these terms we construct an infinite family of non compact Calabi-Yau metrics.Comment: A numerical error has been corrected together with the corresponding analysis of the metri

Forum: Russia, Europe and the colonial present: the power of everyday geopolitics

This contribution to the debate on Russia, Europe and the colonial present brings together several closely linked events which – alongside the people participating in them – have unleashed enough kinetic energy to kill and maim hundreds of thousands of people in just 12 months. Being inspired and challenged, in equal measure, by Stefan Bouzarovski's intervention on the lasting power of energy colonialism, my aim here is to expose the key features of contemporary Russian imperialism as a concept and the Kremlin's professed lust for territorial expansion and colonial domination as a practice. The empirical vignettes described below are assembled to uncover this exemplar of imperialism and colonialism as a theory-to-practice dyad. They involve (a) a 2021 sketch of pseudoscientific “thermodynamic” theory of imperial geopolitics pencilled by the Kremlin's chief adviser on Ukrainian affairs, (b) a 2016 televised geography lesson from the chairperson of the Russian Geographical Society's board and (c) an original operational plan for achieving control over Ukraine drawn by Moscow in the run-up to its full-scale invasion on 24 February 2022