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Articles 1 - 8 of 8
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Entropy Production In A Fluid-Solid System Far From Thermodynamic Equilibrium, Bong Jae Chung, Blas Ortega, Ashuwin Vaidya
Entropy Production In A Fluid-Solid System Far From Thermodynamic Equilibrium, Bong Jae Chung, Blas Ortega, Ashuwin Vaidya
Department of Mathematics Facuty Scholarship and Creative Works
Abstract.: The terminal orientation of a rigid body in a moving fluid is an example of a dissipative system, out of thermodynamic equilibrium and therefore a perfect testing ground for the validity of the maximum entropy production principle (MaxEP). Thus far, dynamical equations alone have been employed in studying the equilibrium states in fluid-solid interactions, but these are far too complex and become analytically intractable when inertial effects come into play. At that stage, our only recourse is to rely on numerical techniques which can be computationally expensive. In our past work, we have shown that the MaxEP is a …
Connecting Advanced And Secondary Mathematics, Eileen Murray, Erin Baldinger, Nicholas Wasserman, Shawn Broderick, Diana White
Connecting Advanced And Secondary Mathematics, Eileen Murray, Erin Baldinger, Nicholas Wasserman, Shawn Broderick, Diana White
Department of Mathematics Facuty Scholarship and Creative Works
There is an ongoing debate among scholars in understanding what mathematical knowledge secondary teachers should have in order to provide effective instruction. We explore connections between advanced and secondary mathematics as an entry point into this debate. In many cases, advanced mathematics is considered relevant for secondary teachers simply because the content is inherently related. In this paper, we instead argue that there are connections between advanced mathematics and secondary mathematics that directly influence teaching. These are not discussions of the mathematical connections, per se, but rather discussions of specific ways in which knowing mathematical connections might influence secondary teachers’ …
Rainbow Perfect Matchings And Hamilton Cycles In The Random Geometric Graph, Deepak C. Bal, Patrick Bennett, Xavier Pérez‐Giménez, Paweł Prałat
Rainbow Perfect Matchings And Hamilton Cycles In The Random Geometric Graph, Deepak C. Bal, Patrick Bennett, Xavier Pérez‐Giménez, Paweł Prałat
Department of Mathematics Facuty Scholarship and Creative Works
Given a graph on n vertices and an assignment of colours to the edges, a rainbow Hamilton cycle is a cycle of length n visiting each vertex once and with pairwise different colours on the edges. Similarly (for even n) a rainbow perfect matching is a collection of independent edges with pairwise different colours. In this note we show that if we randomly colour the edges of a random geometric graph with sufficiently many colours, then a.a.s. the graph contains a rainbow perfect matching (rainbow Hamilton cycle) if and only if the minimum degree is at least 1 (respectively, …
Partitioning Random Graphs Into Monochromatic Components, Deepak Bal, Louis Debiasio
Partitioning Random Graphs Into Monochromatic Components, Deepak Bal, Louis Debiasio
Department of Mathematics Facuty Scholarship and Creative Works
Erdős, Gyàrfàs, and Pyber (1991) conjectured that every r-colored complete graph can be partitioned into at most r – 1 monochromatic components; this is a strengthening of a conjecture of Lovàsz (1975) and Ryser (1970) in which the components are only required to form a cover. An important partial result of Haxell and Kohayakawa (1995) shows that a partition into r monochromatic components is possible for sufficiently large r-colored complete graphs. We start by extending Haxell and Kohayakawa’s result to graphs with large minimum degree, then we provide some partial analogs of their result for random graphs. In particular, we …
Metastable States In Terminal Orientation Of Hinged Symmetric Bodies In A Flow, Doralia Castillo, Bong Jae Chung, Klaus Schnitzer, Karina Soriano, Haiyan Su, Ashuwin Vaidya
Metastable States In Terminal Orientation Of Hinged Symmetric Bodies In A Flow, Doralia Castillo, Bong Jae Chung, Klaus Schnitzer, Karina Soriano, Haiyan Su, Ashuwin Vaidya
Department of Mathematics Facuty Scholarship and Creative Works
Symmetric bodies such as cylinders and spheroidal bodies, in their terminal stable states, are long known to have their long axis align themselves perpendicular to the direction of the flow. This property has been confirmed in primarily sedimentation based theoretical, experimental and numerical techniques and the transition to a terminal stable state is believed to coincide with the onset of significant inertial effects in the flow. However, the threshold at which this transition occurs is yet unknown. We conduct modified experiments with hinged bodies and a CFD study to examine the nature of the transition of prolate spheroids and cylinders …
The Maximum Number Of Complete Subgraphs Of Fixed Size In A Graph With Given Maximum Degree, Jonathan Cutler, A. J. Radcliffe
The Maximum Number Of Complete Subgraphs Of Fixed Size In A Graph With Given Maximum Degree, Jonathan Cutler, A. J. Radcliffe
Department of Mathematics Facuty Scholarship and Creative Works
In this article, we make progress on a question related to one of Galvin that has attracted substantial attention recently. The question is that of determining among all graphs G with n vertices and Δ(G) ≤ r, which has the most complete subgraphs of size t, for t≥3. The conjectured extremal graph is aKr+1 ∪ Kb, where n = a(r + 1) + b with 0 ≤ b ≤ r. Gan et al. (Combin Probab Comput 24(3) (2015), 521–527) proved the conjecture when a ≤ 1, and also reduced the general conjecture to the case t = 3. We prove …
On The Three Dimensional Interaction Between Flexible Fibers And Fluid Flow, Bogdan Nita, Ryan Allaire
On The Three Dimensional Interaction Between Flexible Fibers And Fluid Flow, Bogdan Nita, Ryan Allaire
Department of Mathematics Facuty Scholarship and Creative Works
In this paper we discuss the deformation of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s by means of three dimensional numerical simulation developed in COMSOL . The effects of flow speed and initial configuration angle of the fiber relative to the flow are analyzed. A rigorous analysis of the numerical procedure is performed and our code is benchmarked against well established cases. The flow velocity and pressure are used to compute drag forces upon the fiber. Of particular interest is the behavior …
Freedericksz Transition In Nematic Liquid Crystal Couette Flow, Arup Mukherjee
Freedericksz Transition In Nematic Liquid Crystal Couette Flow, Arup Mukherjee
Department of Mathematics Facuty Scholarship and Creative Works
This article investigates the effects of an external magnetic field on the Freedericksz transition for an elastically anisotropic nematic liquid crystal sample occupying the annular region between two concentric cylinders in relative (slow) rotation. Assuming both azimuthal and radial magnetic fields and strong anchoring conditions for the liquid crystal director perpendicular to the surface of the cylinders, we investigate and characterize the differences in the director distortions and the critical field value for the onset of the transition.