Search results for "Carnot cycle"
showing 9 items of 19 documents
Universal differentiability sets and maximal directional derivatives in Carnot groups
2019
We show that every Carnot group G of step 2 admits a Hausdorff dimension one `universal differentiability set' N such that every real-valued Lipschitz map on G is Pansu differentiable at some point of N. This relies on the fact that existence of a maximal directional derivative of f at a point x implies Pansu differentiability at the same point x. We show that such an implication holds in Carnot groups of step 2 but fails in the Engel group which has step 3.
A metric characterization of Carnot groups
2013
We give a short axiomatic introduction to Carnot groups and their subRiemannian and subFinsler geometry. We explain how such spaces can be metrically described as exactly those proper geodesic spaces that admit dilations and are isometrically homogeneous.
Remarks about the Besicovitch Covering Property in Carnot groups of step 3 and higher
2016
International audience
Nowhere differentiable intrinsic Lipschitz graphs
2021
We construct intrinsic Lipschitz graphs in Carnot groups with the property that, at every point, there exist infinitely many different blow-up limits, none of which is a homogeneous subgroup. This provides counterexamples to a Rademacher theorem for intrinsic Lipschitz graphs.
A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
2017
AbstractCarnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance. We present the basic theory of Carnot groups together with several remarks.We consider them as special cases of graded groups and as homogeneous metric spaces.We discuss the regularity of isometries in the general case of Carnot-Carathéodory spaces and of nilpotent metric Lie groups.
Space of signatures as inverse limits of Carnot groups
2021
We formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in ℝn, as introduced by Chen. Hambly-Lyons’s result on the uniqueness of signature implies that this space is a geodesic metric tree. As a particular consequence we deduce that every path in ℝn can be approximated by projections of some geodesics in some Carnot group of rank n, giving an evidence that the complexity of sub-Riemannian geodesics increases with the step.
Towards an AMTEC-like device based on non-alkali metal for efficient, safe and reliable direct conversion of thermal to electric power
2018
Alkali Metal ThermoElectric Converters directly convert heat into electric energy and have promising applicability in the field of sustainable and renewable energy. The high theoretical efficiency, close to Carnot's cycle, the lack of moving parts, and the interesting operating temperature range drive the search for new materials able to ensure safe and reliable operation at competitive costs.The present work focuses on the design of a non-alkali metal based cell and on the fabrication of a testing device to validate the design work. The selection of a new operating fluid for the cell improves durability, reliability and safety of the device. Finally, we discuss possible applications to alr…
Thermodynamics: Classical Framework
2016
This chapter starts with a summary of the thermodynamic potentials and the relationships between them which are obtained from Legendre transformation. This is followed by an excursion to some important global properties of materials such as specific heat, expansion coefficients and others. The thermodynamic relations provide the basis for a discussion of continuous changes of state which are illustrated by the Joule-Thomson effect and the Van der Waals gas. These are models which are more realistic than the ideal gas. The discussion of Carnot cycles leads to and illustrates the second and third laws of thermodynamics. The chapter closes with a discussion of entropy as a concave function of …
Characteristics of Mesozoic fluvio-lacustrine formations of the western Central African Republic (Carnot Sandstones) by means of mineralogical and ex…
1990
Abstract The so-called Carnot Sandstones, Mesozoic fluvio-lacustrine detrital formation, which stretch over an area of more than 40 000 km 2 in the western part of the Central African Republic, are made of a succession of conglomerates, sandstones and argilites which can reach 300 m in thickness. Heavy mineral analyses and quartz exoscopic studies of this detrital material allow to understand the geology of these formations. The detrital material origin: heavy mineral distribution in the lower levels indicates mostly a meridional origin with a quantitatively poor peripheral supply. The importance of the transport: quartz exoscopic observations show that the main part of the detrital materia…