scholarly journals Scaling limit of the uniform infinite half-plane quadrangulation in the Gromov-Hausdorff-Prokhorov-uniform topology

2017 ◽  
Vol 22 (0) ◽  
Author(s):  
Ewain Gwynne ◽  
Jason Miller
Keyword(s):  
Half Plane ◽  
Scaling Limit ◽  
Uniform Topology

scholarly journals Planar random-cluster model: fractal properties of the critical phase

2021 ◽  
Author(s):  
Hugo Duminil-Copin ◽  
Ioan Manolescu ◽  
Vincent Tassion
Keyword(s):  
Half Plane ◽  
Cluster Model ◽  
Scaling Limit ◽  
Fractal Boundary ◽  
Random Cluster Model ◽  
Random Cluster ◽  
Fractal Properties ◽  
Critical Phase ◽  
Primal And Dual ◽  
The One

AbstractThis paper is studying the critical regime of the planar random-cluster model on $${\mathbb {Z}}^2$$ Z 2 with cluster-weight $$q\in [1,4)$$ q ∈ [ 1 , 4 ) . More precisely, we prove crossing estimates in quads which are uniform in their boundary conditions and depend only on their extremal lengths. They imply in particular that any fractal boundary is touched by macroscopic clusters, uniformly in its roughness or the configuration on the boundary. Additionally, they imply that any sub-sequential scaling limit of the collection of interfaces between primal and dual clusters is made of loops that are non-simple. We also obtain a number of properties of so-called arm-events: three universal critical exponents (two arms in the half-plane, three arms in the half-plane and five arms in the bulk), quasi-multiplicativity and well-separation properties (even when arms are not alternating between primal and dual), and the fact that the four-arm exponent is strictly smaller than 2. These results were previously known only for Bernoulli percolation ($$q = 1$$ q = 1 ) and the FK-Ising model ($$q = 2$$ q = 2 ). Finally, we prove new bounds on the one, two and four-arm exponents for $$q\in [1,2]$$ q ∈ [ 1 , 2 ] , as well as the one-arm exponent in the half-plane. These improve the previously known bounds, even for Bernoulli percolation.

scholarly journals The Navier–Stokes–Vlasov–Fokker–Planck System as a Scaling Limit of Particles in a Fluid

2021 ◽  
Vol 23 (2) ◽  
Author(s):  
Franco Flandoli ◽  
Marta Leocata ◽  
Cristiano Ricci
Keyword(s):  
Drag Force ◽  
Scaling Limit ◽  
Uniqueness Result ◽  
Navier Stokes ◽  
Empirical Measure ◽  
Stokes Component ◽  
Uniform Topology ◽  
Stokes Drag ◽  
System Of Particles ◽  
Fokker Planck

AbstractConvergence of a system of particles, interacting with a fluid, to Navier–Stokes–Vlasov–Fokker–Planck system is studied. The interaction between particles and fluid is described by Stokes drag force. The empirical measure of particles is proved to converge to the Vlasov–Fokker–Planck component of the system and the velocity of the fluid coupled with the particles converges in the uniform topology to the the Navier–Stokes component. A new uniqueness result for the PDE system is added.

Erdős distance problem in the hyperbolic half-plane

2009 ◽  
Author(s):  
Steven Senger
Keyword(s):  
Half Plane ◽  
Distance Problem

Improvement in Gate Dielectric Quality of Ultra Thin a: SiN:H MNS Capacitor by Hydrogen Etching of the Substrate

2002 ◽  
Vol 716 ◽  
Author(s):  
Parag C. Waghmare ◽  
Samadhan B. Patil ◽  
Rajiv O. Dusane ◽  
V.Ramgopal Rao
Keyword(s):  
Silicon Nitride ◽  
Gate Dielectric ◽  
Substrate Surface ◽  
Scaling Limit ◽  
Tunneling Current ◽  
Chemical Vapor ◽  
Poor Performance ◽  
State Density ◽  
Direct Tunneling Current

AbstractTo extend the scaling limit of thermal SiO2, in the ultra thin regime when the direct tunneling current becomes significant, members of our group embarked on a program to explore the potential of silicon nitride as an alternative gate dielectric. Silicon nitride can be deposited using several CVD methods and its properties significantly depend on the method of deposition. Although these CVD methods can give good physical properties, the electrical properties of devices made with CVD silicon nitride show very poor performance related to very poor interface, poor stability, presence of large quantity of bulk traps and high gate leakage current. We have employed the rather newly developed Hot Wire Chemical Vapor Deposition (HWCVD) technique to develop the a:SiN:H material. From the results of large number of optimization experiments we propose the atomic hydrogen of the substrate surface prior to deposition to improve the quality of gate dielectric. Our preliminary results of these efforts show a five times improvement in the fixed charges and interface state density.

Approximate Solution Of A Singular Integral Equation With A Multiplicative Cauchy Kernel In The Half-Plane

2008 ◽  
Vol 8 (2) ◽  
pp. 143-154 ◽  
Author(s):  
P. KARCZMAREK
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Half Plane ◽  
Singular Integral ◽  
Trigonometric Polynomials ◽  
Cauchy Kernel

AbstractIn this paper, Jacobi and trigonometric polynomials are used to con-struct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

Rayleigh Wave in a Rotating Magneto-Thermo-Elastic Half-Plane

2012 ◽  
Vol 42 (4) ◽  
Author(s):  
Baljeet Singh ◽  
Sangeeta Kumari ◽  
Jagdish Singh
Keyword(s):  
Rayleigh Wave ◽  
Half Plane

Analytical solution of half-plane with multi-cracks

2014 ◽  
Author(s):  
Y. Ding ◽  
X.C. Yang ◽  
S. Yang ◽  
T. Li
Keyword(s):  
Analytical Solution ◽  
Half Plane

The Crack Problem for an Orthotropic Half Plane Stiffened by Elastic Films

1992 ◽  
Author(s):  
R. Mahajan ◽  
F. Erdogan ◽  
Y. T. Chou
Keyword(s):  
Half Plane ◽  
Crack Problem

Cracking of a Graded Half Plane Due to Sliding Contact

2001 ◽  
Author(s):  
Frazil Erdogan ◽  
Serkan Dag
Keyword(s):  
Half Plane ◽  
Sliding Contact
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