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University of Texas Rio Grande Valley
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
- Keyword
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- 2d turbulence (1)
- Convective flow (1)
- Dendrite layer (1)
- Differential equations for Eisenstein series (1)
- Flow stability (1)
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- Hypergeometric differential equation (1)
- Hypergeometric functions (1)
- Local homogeneity (1)
- Mathematical model (1)
- Nonlinear flow (1)
- Parametric representations for Eisenstein series (1)
- QG turbulence (1)
- Quasi-Lagrangian (1)
- Ramanujan’s Eisenstein series (1)
- Sweeping interactions (1)
- Turbulence (1)
Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
On Mathematical Modeling, Nonlinear Properties And Stability Of Secondary Flow In A Dendrite Layer, Daniel N. Riahi
On Mathematical Modeling, Nonlinear Properties And Stability Of Secondary Flow In A Dendrite Layer, Daniel N. Riahi
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
This paper studies instabilities in the flow of melt within a horizontal dendrite layer with deformed upper boundary and in the presence or absence of rotation during the solidification of a binary alloy. In the presence of rotation, it is assumed that the layer is rotating about a vertical axis at a constant angular velocity. Linear and weakly nonlinear stability analyses provide results about various flow features such as the critical mode of convection, neutral stability curve, preferred flow pattern and the solid fraction distribution within the dendrite layer. The preferred shape of the deformed upper boundary of the layer, …
Is The Subdominant Part Of The Energy Spectrum Due To Downscale Energy Cascade Hidden In Quasi-Geostrophic Turbulence?, Eleftherios Gkioulekas, Ka Kit Tung
Is The Subdominant Part Of The Energy Spectrum Due To Downscale Energy Cascade Hidden In Quasi-Geostrophic Turbulence?, Eleftherios Gkioulekas, Ka Kit Tung
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In systems governing two-dimensional turbulence, surface quasi-geostrophic turbulence, (more generally $\alpha$-turbulence), two-layer quasi-geostrophic turbulence, etc., there often exist two conservative quadratic quantities, one "energy''-like and one "enstrophy''-like. In a finite inertial range there are in general two spectral fluxes, one associated with each conserved quantity. We derive here an inequality comparing the relative magnitudes of the "energy'' and "enstrophy'' fluxes for finite or infinitesimal dissipations, and for hyper or hypo viscosities. When this inequality is satisfied, as is the case of 2D turbulence,where the energy flux contribution to the energy spectrum is small, the subdominant part will be effectively hidden. …
New Integrable Hierarchy, Its Parametric Solutions, Cuspons, One-Peak Solitons, And M/W-Shape Peak Solitons, Zhijun Qiao
New Integrable Hierarchy, Its Parametric Solutions, Cuspons, One-Peak Solitons, And M/W-Shape Peak Solitons, Zhijun Qiao
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper, we propose a new completely integrable hierarchy. Particularly in the hierarchy we draw two new soliton equations: 1 mt= 1 2 1/m2xxx− 1 2 1/m2 x; 2 mt+mx u2−ux 2+2m2ux=0, m=u−uxx. The first one is the second positive member in the hierarchy while the second one is the second negative member in the hierarchy. Both equations can be derived from the two-dimensional Euler equation by using the approximation procedure. All equations in the hierarchy are proven to have bi-Hamiltonian operators and Lax pairs through solving a crucial matrix equation. Moreover, we develop parametric solutions of the entire …
On The Elimination Of The Sweeping Interactions From Theories Of Hydrodynamic Turbulence, Eleftherios Gkioulekas
On The Elimination Of The Sweeping Interactions From Theories Of Hydrodynamic Turbulence, Eleftherios Gkioulekas
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper, we revisit the claim that the Eulerian and quasi-Lagrangian same time correlation tensors are equal. This statement allows us to transform the results of an MSR quasi-Lagrangian statistical theory of hydrodynamic turbulence back to the Eulerian representation. We define a hierarchy of homogeneity symmetries between incremental homogeneity and global homogeneity. It is shown that both the elimination of the sweeping interactions and the derivation of the 4/5-law require a homogeneity assumption stronger than incremental homogeneity but weaker than global homogeneity. The quasi-Lagrangian transformation, on the other hand, requires an even stronger homogeneity assumption which is many-time rather …
Solving Ramanujan's Differential Equations For Eisenstein Series Via A First Order Riccati Equation, James M. Hill, Bruce C. Berndt, Timothy Huber
Solving Ramanujan's Differential Equations For Eisenstein Series Via A First Order Riccati Equation, James M. Hill, Bruce C. Berndt, Timothy Huber
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper we prove that Ramanujan's differential equations for the Eisenstein series P, Q, and R are invariant under a simple one-parameter stretching group of transformations. Using this, we show that the three differential equations may be reduced to a first order Riccati differential equation, the solution of which may be represented in terms of hypergeometric functions. The resulting formulas allow for the derivation of parametric representations of P, Q, and R, analogous to representations in Ramanujan's second notebook. In contrast, in the classical approach, one first needs to derive the fundamental formula connecting theta functions with elliptic integrals. …