Results 31 to 40 of about 18,179 (207)
Nonlocal diffusion equations in Carnot groups
Rendiconti del Circolo Matematico di Palermo Series 2, 2022 Let $G$ be a Carnot group. We study nonlocal diffusion equations in a domain $ $ of $G$ of the form $$ u_t^ (x,t)=\int_{G}\frac{1}{ ^2}K_ (x,y)(u^ (y,t)-u^ (x,t))\,dy, \qquad x\in $$ with $u^ =g(x,t)$ for $x\notin $. For appropriate rescaled kernel $K_ $ we prove that solutions $u^ $, when $ \rightarrow0$, uniformly approximate the ...
Isolda E. Cardoso, Raúl E. Vidal
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Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group [PDF]
, 2016 We use a Riemannnian approximation scheme to define a notion of intrinsic Gaussian curvature for a Euclidean C2 -smooth surface in the Heisenberg group H away from characteristic points, and a notion of intrinsic signed geodesic curvature for Euclidean ...
Balogh, Zoltan M. +2 more
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Advanced Engineering Materials, EarlyView.A simulative evaluation of triply periodic minimal surface (TPMS) structures for an elastocaloric application under compressive load is performed. For the evaluation of the structure's performance, surface/volume ratio, generated heat and invested mechanical work are taken into account and are compared to a tube as a reference specimen.
Michael Fries +3 more
wiley +1 more source
Ricci curvatures in Carnot groups
Mathematical Control & Related Fields, 2013 29 pages, 1 ...
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The Traveling Salesman Theorem in Carnot groups [PDF]
Calculus of Variations and Partial Differential Equations, 2018 Let $\mathbb{G}$ be any Carnot group. We prove that, if a subset of $\mathbb{G}$ is contained in a rectifiable curve, then it satisfies Peter Jones' geometric lemma with some natural modifications. We thus prove one direction of the Traveling Salesman Theorem in $\mathbb{G}$.
Sean Li +2 more
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Thermionics in Topological Materials
Advanced Materials, EarlyView.Thermionics is one of the fundamental energy conversion mechanisms in solid state systems. Recent development in topological materials opens new avenues in developing thermionic systems and devices. Due to the linear energy dispersion and topological protection of charge transport, these new materials are promising candidates for high efficiency ...
Sunchao Huang +8 more
wiley +1 more source
Yamabe-Type Equations on Carnot Groups [PDF]
Potential Analysis, 2016 This article is concerned with a class of elliptic equations on Carnot groups depending of one real positive parameter and involving a critical nonlinearity. As a special case of our results we prove the existence of at least one nontrivial solution for a subelliptic critical equation defined on a smooth and bounded domain $D$ of the {Heisenberg group}
Molica Bisci G, Repovs D
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Privileged Coordinates and Nilpotent Approximation of Carnot Manifolds, I. General Results
, 2018 In this paper we attempt to give a systematic account on privileged coordinates and the nilpotent approximation of Carnot manifolds. By a Carnot manifold it is meant a manifold with a distinguished filtration of subbundles of the tangent bundle which is ...
Choi, Woocheol, Ponge, Raphael
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AI‐Driven Defect Engineering for Advanced Thermoelectric Materials
Advanced Materials, EarlyView.This review presents how AI accelerates the design of defect‐tuned thermoelectric materials. By integrating machine learning with high‐throughput data and physics‐informed representations, it enables efficient prediction of thermoelectric performance from complex defect landscapes.
Chu‐Liang Fu +9 more
wiley +1 more source
Interior HW^{1,p} estimates for divergence degenerate elliptic systems in Carnot groups
, 2012 Let X_1,...,X_q be the basis of the space of horizontal vector fields on a homogeneous Carnot group in R^n ...
Bramanti, Marco +2 more
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