Anabelian reconstruction of the Néron–Tate local height function

2021 ◽  
Author(s):  
Wojciech Porowski
Keyword(s):  
Height Function

scholarly journals On Sinaĭ Billiards on Flat Surfaces with Horns

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
Henk Bruin
Keyword(s):  
Exponential Decay ◽  
Height Function ◽  
Suspension Flow ◽  
Limit Laws ◽  
Suspension Flows ◽  
Flat Surfaces ◽  
Exponential Tails ◽  
Exponential Decay Of Correlations ◽  
Sinai Billiards ◽  
Young Towers

AbstractWe show that certain billiard flows on planar billiard tables with horns can be modeled as suspension flows over Young towers (Ann. Math. 147:585–650, 1998) with exponential tails. This implies exponential decay of correlations for the billiard map. Because the height function of the suspension flow itself is polynomial when the horns are Torricelli-like trumpets, one can derive Limit Laws for the billiard flow, including Stable Limits if the parameter of the Torricelli trumpet is chosen in (1, 2).

scholarly journals On the complex dynamics of birational surface maps defined over number fields

2016 ◽  
Vol 0 (0) ◽  
Author(s):  
Mattias Jonsson ◽  
Paul Reschke
Keyword(s):  
Number Field ◽  
Complex Dynamics ◽  
Energy Condition ◽  
Height Function ◽  
Number Fields ◽  
Projective Surface ◽  
Complex Projective Surface ◽  
Canonical Height ◽  
Dynamical Degree ◽  
Complex Projective

AbstractWe show that any birational selfmap of a complex projective surface that has dynamical degree greater than one and is defined over a number field automatically satisfies the Bedford–Diller energy condition after a suitable birational conjugacy. As a consequence, the complex dynamics of the map is well behaved. We also show that there is a well-defined canonical height function.

Simulation of Dendritic Growth Using a VOF Method

2009 ◽  
Author(s):  
Joaqui´n Lo´pez ◽  
Julio Herna´ndez ◽  
Claudio Zanzi ◽  
Fe´lix Faura ◽  
Pablo Go´mez
Keyword(s):  
Dendritic Growth ◽  
Piecewise Linear ◽  
Height Function ◽  
Vof Method ◽  
Three Dimensions ◽  
Advection Equation ◽  
Thermal Gradients ◽  
Interfacial Flows ◽  
Thermal Boundary Conditions ◽  
Interface Curvature

The volume of fluid (VOF) method is one of the most widely used methods to simulate interfacial flows using fixed grids. However, its application to phase change processes in solidification problems is relatively infrequent. In this work, preliminary results of the application of a new methodology to the simulation of dendritic growth of pure metals is presented. The proposed approach is based on a recent VOF method with PLIC (piecewise linear interface calculation) reconstruction of the interface. A diffused-interface method is used to solve the energy equation, which avoids the need of applying the thermal boundary conditions directly at the solid front. The thermal gradients at both sides of the interface, which are needed to accurately obtain the front velocity, are calculated with the aid of a distance function. The advection equation of a discretized solid fraction function is solved using the unsplit VOF advection method proposed by Lo´pez et al. [J. Comput. Phys. 195 (2004) 718–742] (extended to three dimensions by Herna´ndez et al. [Int. J. Numer. Methods Fluids 58 (2008) 897-921]). The interface curvature is computed using an improved height function (HF) technique, which provides second-order accuracy. The assessment of the proposed methodology is carried out by comparing the numerical results with analytical solutions and with results obtained by different authors for the formation of complex dendritic structures in two and three dimensions.

scholarly journals On number of moduli for gradient surface height function flows

2018 ◽  
Vol 20 (4) ◽  
pp. 419-428
Author(s):  
V. E. Kruglov
Keyword(s):  
Finite Number ◽  
Sufficient Conditions ◽  
Height Function ◽  
Orientable Surface ◽  
Topological Conjugacy ◽  
Topological Equivalence ◽  
Gradient Flows ◽  
A Chain ◽  
Gradient Surface ◽  
Equivalence Invariant

In 1978 J. Palis invented continuum topologically non-conjugate systems in a neighbourhood of a system with a heteroclinic contact; in other words, he invented so-called moduli. W. de Melo and С. van Strien in 1987 described a diffeomorphism class with a finite number of moduli. They discovered that a chain of saddles taking part in the heteroclinic contact of such diffeomorphism includes not more than three saddles. Surprisingly, such effect does not happen in flows. Here we consider gradient flows of the height function for an orientable surface of genus g>0. Such flows have a chain of 2g saddles. We found that the number of moduli for such flows is 2g−1 which is the straight consequence of the sufficient topological conjugacy conditions for such systems given in our paper. A complete topological equivalence invariant for such systems is four-colour graph carrying the information about its cells relative position. Equipping the graph's edges with the analytical parameters --- moduli, connected with the saddle connections, gives the sufficient conditions of the flows topological conjugacy.

Height function based Volume of Fluid code for simulations of multiphase magnetic fluids

2015 ◽  
Vol 113 ◽  
pp. 112-118 ◽  
Author(s):  
Holly Grant ◽  
Ruben Scardovelli ◽  
A. David Trubatch ◽  
Philip A. Yecko
Keyword(s):  
Height Function ◽  
Magnetic Fluids ◽  
Volume Of Fluid

Another Note on Sperner's Lemma

1971 ◽  
Vol 14 (2) ◽  
pp. 255-256 ◽  
Author(s):  
David A. Drake
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Height Function ◽  
Maximum Length ◽  
List Type ◽  
Type Number ◽  
Partially Ordered ◽  
A Chain ◽  
Universal Bounds ◽  
Positive Integers

Let Q be a finite partially ordered (by ≤) set with universal bounds O, I. The height function h of Q is defined by the rule: h(x) is the maximum length of a chain from O to x. Let h(I)=n. Suppose that for each k≥0, there exist positive integers a(k) and b(k) such that all elements of height k(i)are covered by a(k) elements of height k+1;(ii)cover b(k) elements of height k—1.Then we call Q a U-poset. Call a subset S of a partially ordered set an antichain if no two elements of S are comparable.

scholarly journals Spectra of overlapping Wishart matrices and the Gaussian free field

2018 ◽  
Vol 07 (02) ◽  
pp. 1850003 ◽  
Author(s):  
Ioana Dumitriu ◽  
Elliot Paquette
Keyword(s):  
Free Field ◽  
Covariance Structure ◽  
Height Function ◽  
Gaussian Free Field ◽  
Moment Conditions ◽  
Wishart Matrices ◽  
Wigner Random Matrices ◽  
Infinite Array ◽  
Univariate Polynomials ◽  
Upper Half Plane

Consider a doubly-infinite array of i.i.d. centered variables with moment conditions, from which one can extract a finite number of rectangular, overlapping submatrices, and form the corresponding Wishart matrices. We show that under basic smoothness assumptions, centered linear eigenstatistics of such matrices converge jointly to a Gaussian vector with an interesting covariance structure. This structure, which is similar to those appearing in [A. Borodin, Clt for spectra of submatrices of Wigner random matrices, Mosc. Math. J. 14(1) (2014) 29–38; A. Borodin and V. Gorin, General beta Jacobi corners process and the Gaussian free field, preprint (2013), arXiv:1305.3627; T. Johnson and S. Pal, Cycles and eigenvalues of sequentially growing random regular graphs, Ann. Probab. 42(4) (2014) 1396–1437], can be described in terms of the height function, and leads to a connection with the Gaussian Free Field on the upper half-plane. Finally, we generalize our results from univariate polynomials to a special class of planar functions.

Saturation Height Function in a Field Under Imbibition: A Case Study

2013 ◽  
Author(s):  
K. Seth ◽  
V. Beales ◽  
A. Kawasaki ◽  
T. Namba
Keyword(s):  
Height Function

scholarly journals River landscapes and optimal channel networks

2018 ◽  
Vol 115 (26) ◽  
pp. 6548-6553 ◽  
Author(s):  
Paul Balister ◽  
József Balogh ◽  
Enrico Bertuzzo ◽  
Béla Bollobás ◽  
Guido Caldarelli ◽  
...  
Keyword(s):  
Minimum Energy ◽  
Height Function ◽  
Gravitational Energy ◽  
Constant Factor ◽  
Channel Networks ◽  
Arbitrary Graph ◽  
Tree Structures ◽  
Dimensional Lattice ◽  
Natural Forms ◽  
Flow Directions

We study tree structures termed optimal channel networks (OCNs) that minimize the total gravitational energy loss in the system, an exact property of steady-state landscape configurations that prove dynamically accessible and strikingly similar to natural forms. Here, we show that every OCN is a so-called natural river tree, in the sense that there exists a height function such that the flow directions are always directed along steepest descent. We also study the natural river trees in an arbitrary graph in terms of forbidden substructures, which we call k-path obstacles, and OCNs on a d-dimensional lattice, improving earlier results by determining the minimum energy up to a constant factor for everyd≥2. Results extend our capabilities in environmental statistical mechanics.

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