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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
On The Hardness Of Counting And Sampling Center Strings, Christina Boucher, Mohamed Omar
On The Hardness Of Counting And Sampling Center Strings, Christina Boucher, Mohamed Omar
All HMC Faculty Publications and Research
Given a set S of n strings, each of length ℓ, and a nonnegative value d, we define a center string as a string of length ` that has Hamming distance at most d from each string in S. The #CLOSEST STRING problem aims to determine the number of center strings for a given set of strings S and input parameters n, ℓ, and d. We show #CLOSEST STRING is impossible to solve exactly or even approximately in polynomial time, and that restricting #CLOSEST STRING so that any one of the parameters n, ℓ, or d is fixed leads to …
Simulated Associating Polymer Networks, Joris Billen
Simulated Associating Polymer Networks, Joris Billen
CGU Theses & Dissertations
Telechelic associating polymer networks consist of polymer chains terminated by endgroups that have a different chemical composition than the polymer backbone. When dissolved in a solution, the endgroups cluster together to form aggregates. At low temperature, a strongly connected reversible network is formed and the system behaves like a gel. Telechelic networks are of interest since they are representative for biopolymer networks (e.g. F-actin) and are widely used in medical applications (e.g. hydrogels for tissue engineering, wound dressings) and consumer products (e.g. contact lenses, paint thickeners).
In this thesis such systems are studied by means of a molecular dynamics/Monte Carlo …
Study Of Vortex Ring Dynamics In The Nonlinear Schrödinger Equation Utilizing Gpu-Accelerated High-Order Compact Numerical Integrators, Ronald Meyer Caplan
Study Of Vortex Ring Dynamics In The Nonlinear Schrödinger Equation Utilizing Gpu-Accelerated High-Order Compact Numerical Integrators, Ronald Meyer Caplan
CGU Theses & Dissertations
We numerically study the dynamics and interactions of vortex rings in the nonlinear Schrödinger equation (NLSE). Single ring dynamics for both bright and dark vortex rings are explored including their traverse velocity, stability, and perturbations resulting in quadrupole oscillations. Multi-ring dynamics of dark vortex rings are investigated, including scattering and merging of two colliding rings, leapfrogging interactions of co-traveling rings, as well as co-moving steady-state multi-ring ensembles. Simulations of choreographed multi-ring setups are also performed, leading to intriguing interaction dynamics.
Due to the inherent lack of a close form solution for vortex rings and the dimensionality where they live, efficient …