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Full-Text Articles in Applied Mathematics
An Optimal Principle In Fluid-Structure Interaction, Bong Jae Chung, Ashuwin Vaidya
An Optimal Principle In Fluid-Structure Interaction, Bong Jae Chung, Ashuwin Vaidya
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
We study the steady terminal orientation of a fore-aft symmetric body as it settles in a viscous fluid. An optimal principle for the settling behavior is discussed based upon entropy production in the system, both in the Stokes limit and the case of near equilibrium states when inertial effects emerge. We show that in the Stokes limit, the entropy production in the system is zero allowing any possible terminal orientation while in the presence of inertia, the particle assumes a horizontal position which coincides with the state of maximum entropy production. Our results are seen to agree well with experimental …
Topological Dynamics Of Two-Piece Eventually Expanding Maps, Youngna Choi
Topological Dynamics Of Two-Piece Eventually Expanding Maps, Youngna Choi
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
In this work we show that two-piece eventually expanding maps have the same topological dynamics as two-piece expanding maps. A two-piece eventually expanding map possesses an invariant set that is either a topological attractor or can be perturbed to become one.
Existence Of Multiple-Stable Equilibria For A Multi-Drug-Resistant Model Of Mycobacterium Tuberculosis, Abba B. Gumel, Baojun Song
Existence Of Multiple-Stable Equilibria For A Multi-Drug-Resistant Model Of Mycobacterium Tuberculosis, Abba B. Gumel, Baojun Song
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
The resurgence of multi-drug-resistant tuberculosis in some parts of Europe and North America calls for a mathematical study to assess the impact of the emergence and spread of such strain on the global effort to effectively control the burden of tuberculosis. This paper presents a deterministic compartmental model for the transmission dynamics of two strains of tuberculosis, a drug-sensitive (wild) one and a multi-drug-resistant strain. The model allows for the assessment of the treatment of people infected with the wild strain. The qualitative analysis of the model reveals the following. The model has a disease-free equilibrium, which is locally asymptotically …
Delay-Induced Instabilities In Self-Propelling Swarms, Eric Forgoston, Ira B. Schwartz
Delay-Induced Instabilities In Self-Propelling Swarms, Eric Forgoston, Ira B. Schwartz
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
We consider a general model of self-propelling particles interacting through a pairwise attractive force in the presence of noise and communication time delay. Previous work by Erdmann [Phys. Rev. E 71, 051904 (2005)] has shown that a large enough noise intensity will cause a translating swarm of individuals to transition to a rotating swarm with a stationary center of mass. We show that with the addition of a time delay, the model possesses a transition that depends on the size of the coupling amplitude. This transition is independent of the initial swarm state (traveling or rotating) and is characterized by …