Heat flows to Riemannian manifolds of NPC

2008 ◽  
pp. 109-123
Keyword(s):  
Riemannian Manifolds ◽  
Heat Flows

scholarly journals Local Regularity for the Harmonic Map and Yang–Mills Heat Flows

2021 ◽  
Author(s):  
Ahmad Afuni
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Map ◽  
Local Regularity ◽  
Yang Mills ◽  
Heat Flows ◽  
Singular Sets ◽  
Regularity Results ◽  
Local Monotonicity ◽  
Partial Differ ◽  
Singular Time

AbstractWe establish new local regularity results for the harmonic map and Yang–Mills heat flows on Riemannian manifolds of dimension greater than 2 and 4, respectively, obtaining criteria for the smooth local extensibility of these flows. As a corollary, we obtain new characterisations of singularity formation and use this to obtain a local estimate on the Hausdorff measure of the singular sets of these flows at the first singular time. Finally, we show that smooth blow-ups at rapidly forming singularities of these flows are necessarily nontrivial and admit a positive lower bound on their heat ball energies. These results crucially depend on some local monotonicity formulæ for these flows recently established by Ecker (Calc Var Partial Differ Equ 23(1):67–81, 2005) and the Afuni (Calc Var 555(1):1–14, 2016; Adv Calc Var 12(2):135–156, 2019).

scholarly journals Sobolev-Kantorovich Inequalities

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Michel Ledoux
Keyword(s):  
Pattern Formation ◽  
Probability Density ◽  
Riemannian Manifolds ◽  
Wasserstein Distance ◽  
Sobolev Norm ◽  
Heat Flows ◽  
Interpolation Inequalities ◽  
Harnack Inequalities ◽  
Negatively Curved ◽  
Reference Measure

Abstract In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich-Wasserstein distance to μ. This article emphasizes this family of interpolation inequalities, called Sobolev-Kantorovich inequalities, which may be established in the rather large setting of non-negatively curved (weighted) Riemannian manifolds by means of heat flows and Harnack inequalities.

DYNAMIC AND THERMAL INTERFERENCE EFFECTS ON TWO NEIGHBOURING BUILDING MODELS

2019 ◽  
Vol 21 (5) ◽  
pp. 138-150
Author(s):  
S. V. Korobkov ◽  
A. I. Gnyrya ◽  
V. I. Terekhov
Keyword(s):  
Heat Exchange ◽  
Mutual Effect ◽  
Convective Heat Exchange ◽  
Physical Models ◽  
Interference Effects ◽  
Total Contribution ◽  
Heat Flows ◽  
Building Models ◽  
Number Of Factors ◽  
Thermal Interference

The paper considers the dynamic and thermal interference effects on two neighbouring building models in the form of square prisms arranged at a short distance from each other. It is shown how relative positions of the models affect the specific phenomena caused by the airflow interactions.The aim of this paper is to experimentally study the dynamic and thermal interference of a tandem of two building models in the form of square prisms depending on their relative position.The phenomenon of wind loads on buildings and structures has always attracted great interest among engineers and researchers. With the accumulation of knowledge and technical capabilities, the potential for likely ways to study wind flows and their impact on different objects increased. In recent years, the world science has accumulated an extensive knowledge base on wind impacts on objects of various shapes, such as prisms, pyramids, cylinders, etc. Studies are carried out for their mutual impact of several objects on changes in both the wind load and heat exchange. Their mutual effect on the air motion and turbulence is considered.There are two main areas in the field of the wind impact. The first impact is the force load on building, the second is the wind as a source of convective heat exchange. The object of this study is the interference parameters allowing to assess the influence on the field of pressure and heat recoil of disturbances evoked in front of the barriers.At the first stage, physical models help to study the pressure field on different facets and ratios of the local and medium heat exchange under the forced convection conditions. The next step is to jointly consider the wind (dynamic) load and heat flows, attempting to detect the total contribution to changes depending on the reciprocal model arrangement. All experiments are performed in the aerodynamic tube, at the TSUAB department. It is shown that the dynamic and thermal interference ratios vary greatly in two building models. At the same time, the thermal interference is very conservative compared to the dynamic. Using the interference parameters, it is easy to analyze the extreme pressure and the heat flow on the model surface depending on a large number of factors, including their arrangement.

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