S. Boukraa
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View article: Numerical and Experimental Investigation of a Confined Diffusion Flame of Heterogeneous Mixtures
Numerical and Experimental Investigation of a Confined Diffusion Flame of Heterogeneous Mixtures Open
It is generally assumed, sometimes implicitly, that the exploding gas cloud is uniform and homogeneous.However, in practice, the cloud often results from an accidental release of a chemical substance into the air, leading to a non-uniform …
View article: The lambda extensions of the Ising correlation functions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> <mml:mo>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo>,</mml:mo> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> </mml:math>
The lambda extensions of the Ising correlation functions Open
We revisit, with a pedagogical heuristic motivation, the lambda extension of the low-temperature row correlation functions of the two-dimensional Ising model. In particular, using these one-parameter series to understand the deforma…
View article: Symmetries of non-linear ODEs: lambda extensions of the Ising correlations
Symmetries of non-linear ODEs: lambda extensions of the Ising correlations Open
This paper provides several illustrations of the numerous remarkable properties of the lambda-extensions of the two-point correlation functions of the Ising model, sheding some light on the non-linear ODEs of the Painlevé type. We first sh…
View article: Symmetries of Non-Linear ODEs: Lambda Extensions of the Ising Correlations
Symmetries of Non-Linear ODEs: Lambda Extensions of the Ising Correlations Open
This paper provides several illustrations of the numerous remarkable properties of the lambda extensions of the two-point correlation functions of the Ising model, shedding some light on the non-linear ODEs of the Painlevé type they satisf…
View article: Diagonals of Rational Functions: From Differential Algebra to Effective Algebraic Geometry
Diagonals of Rational Functions: From Differential Algebra to Effective Algebraic Geometry Open
We show that the results we had previously obtained on diagonals of 9- and 10-parameter families of rational functions in three variables x, y, and z, using creative telescoping, yielding modular forms expressed as pullbacked 2F1 hypergeom…
View article: Factorization of Ising correlations C(M,N) for $ ν= \, -k$ and M+N odd, $M \le N$, $T < T_c$ and their lambda extensions
Factorization of Ising correlations C(M,N) for $ ν= \, -k$ and M+N odd, $M \le N$, $T < T_c$ and their lambda extensions Open
We study the factorizations of Ising low-temperature correlations C(M,N) for $ν=-k$ and M+N odd, $M \le N$, for both the cases $M\neq 0$ where there are two factors, and $M=0$ where there are four factors. We find that the two factors for …
View article: Diagonals of rational functions: from differential algebra to effective algebraic geometry (unabridged version)
Diagonals of rational functions: from differential algebra to effective algebraic geometry (unabridged version) Open
We show that the results we had obtained on diagonals of nine and ten parameters families of rational functions using creative telescoping, yielding modular forms expressed as pullbacked $ _2F_1$ hypergeometric functions, can be obtained, …
View article: Heun functions and diagonals of rational functions (unabridged version)
Heun functions and diagonals of rational functions (unabridged version) Open
We provide a set of diagonals of simple rational functions of three and four variables that are squares of Heun functions. These Heun functions obtained through creative telescoping, turn out to be either pullbacked $_2F_1$ hypergeometric …
View article: Diagonals of rational functions, pullbacked $\boldsymbol{_2F_1}$ hypergeometric functions and modular forms
Diagonals of rational functions, pullbacked $\boldsymbol{_2F_1}$ hypergeometric functions and modular forms Open
We recall that diagonals of rational functions naturally occur in lattice\nstatistical mechanics and enumerative combinatorics. We find that a\nseven-parameter rational function of three variables with a numerator equal to\none (reciprocal…
View article: Diagonals of rational functions, pullbacked 2F1 hypergeometric functions and modular forms (unabrigded version)
Diagonals of rational functions, pullbacked 2F1 hypergeometric functions and modular forms (unabrigded version) Open
We recall that diagonals of rational functions naturally occur in lattice statistical mechanics and enumerative combinatorics. We find that a seven-parameter rational function of three variables with a numerator equal to one (reciprocal of…
View article: Selected non-holonomic functions in lattice statistical mechanics and enumerative combinatorics
Selected non-holonomic functions in lattice statistical mechanics and enumerative combinatorics Open
We recall that the full susceptibility series of the Ising model, modulo\npowers of the prime 2, reduce to algebraic functions. We also recall the\nnon-linear polynomial differential equation obtained by Tutte for the\ngenerating function …