Recently, the theory of quasiregular mappings on Carnot groups has been developed intensively. Let ν stand for the homogeneous dimension of a Carnot group and let m be the index of the last vector space of the corresponding Lie algebra. We prove that the (ν −m− 1)-dimensional Hausdorff measure of the image of the branch set of a quasiregular mapping on the Carnot group is positive. Some estimat...

The Clausius-Clapeyron relation and its analogs in other first-order phase transitions, such as type-I superconductors, are derived using very elementary methods, without appealing to the more advanced concepts of entropy or Gibbs free energy. reasoning is based on Kelvin's formulation second law thermodynamics, should be accessible high school students. After recalling some basic facts about C...

In existing linear response theories for adiabatically driven cyclic heat engines, Onsager symmetry is identified only phenomenologically, and a relation between global local coefficients, defined over one cycle at any instant of cycle, respectively, not derived. To address this limitation, we develop theory the speed changing parameters temperature differences in generic Gaussian engines obeyi...

The Carnot cycle and its deduction of maximum conversion efficiency of heat inputted and outputted isothermally at different temperatures necessitated the construction of isothermal and adiabatic pathways within the cycle that were mechanically "reversible", leading eventually to the Kelvin-Clausius development of the entropy function S with differential dS = dq/T such that [symbol: see text]C ...

Let X and B be two Riemannian manifolds with π : X → B being a Riemannian submersion. Let H be the corresponding horizontal distribution, which is perpendicular to the tangent bundle of the fibres of π : X → B. Then X (just considered as a differentiable manifold), together with the distribution H, forms a so-called Carnot-Caratheodory space [1], when the Riemannian metric of X is restricted to...

The MCC InfoSleuth project [1] [2] is developing an architecture for and prototypes of an agent infrastructure for a variety of applications. The InfoSleuth research is building on the base technology developed in the recently completed MCC Carnot research project. The Carnot project [3] [4] was initiated in 1990 with the goal of addressing the problem of logically unifying physically-distribut...

In article number 2004717, Seok Woo Lee and co-workers present an efficient low-grade heat-harvesting system with a Carnot efficiency as high 50%. By tuning the hydration entropy during electrochemical reaction, temperature coefficient reaches value in thermally regenerative cycle. Moreover, harvesting of thermal energy various ranges, from 10 °C to 50 °C, is demonstrated for practical applicat...