37 citations · 92 across the 19 of their papers we have counts for
19 papers
A solid-state theory for dense cylindrical packings of balls
Luke K. Davis, Alexander R. Klotz
We develop an analytical theory for the dense packing of hard spheres in cylinders. Physically, our theory consists of a finite cylindrical masking of a close-packed three-dimensio…
Tight Bounds for Tight Links: Ropelength of T(Q,Q) torus links
Alexander R. Klotz
Ropelength, L, is a parameter characterizing the minimum contour length of a knot or link. There exist upper and lower bounds on ropelength with respect to crossing number, C, incl…
Dynamics of polymers in coarse-grained nematic solvents
Zahra Valei, Karolina Wamsler, Alex J. Parker +3
Polymers are a primary building block in many biomaterials, often interacting with anisotropic backgrounds. While previous studies have considered polymer dynamics within nematic s…
Chirality Effects in Molecular Chainmail
Alexander R. Klotz, Caleb J. Anderson, Michael S. Dimitriyev
Motivated by the observation of positive Gaussian curvature in kinetoplast DNA networks, we consider the effect of linking chirality in square lattice molecular chainmail networks…
Borromean Hypergraph Formation in Dense Random Rectangles
Alexander R. Klotz
We develop a minimal system to study the stochastic formation of Borromean links within topologically entangled networks without requiring the use of knot invariants. Borromean lin…
Revisiting the Second Vassiliev (In)variant for Polymer Knots
Alexander R. Klotz, Benjamin Estabrooks
Knots in open strands such as ropes, fibers, and polymers, cannot typically be described in the language of knot theory, which characterizes only closed curves in space. Simulation…
Linear Polycatenanes from Kinetoplast Edge Loops
Josh Ragotskie, Nathaniel Morrison, Christopher Stackhouse +2
We use graph theory simulations and single molecule experiments to investigate percolation properties of kinetoplasts, the topologically linked mitochondrial DNA from trypanosome p…
Ropelength and writhe quantization of 12-crossing knots
Alexander R. Klotz, Caleb J. Anderson
The ropelength of a knot is the minimum length required to tie it. Computational upper bounds have previously been computed for every prime knot with up to 11 crossings. Here, we p…
Exactly-Solvable Self-Trapping Lattice Walks. Part I: Trapping in Ladder Graphs
Alexander R. Klotz, Everett Sullivan
A growing self-avoiding walk (GSAW) is a stochastic process that starts from the origin on a lattice and grows by occupying an unoccupied adjacent lattice site at random. A suffici…
Percolation and Dissolution of Borromean Networks
Donald G. Ferschweiler, Ryan Blair, Alexander R. Klotz
Inspired by experiments on topologically linked DNA networks, we consider the connectivity of Borromean networks, in which no two rings share a pairwise-link, but groups of three r…
The tightest knot is not necessarily the smallest
Alexander R. Klotz
In this note, we attempt to find counterexamples to the conjecture that the ideal form of a knot, that which minimizes its contour length while respecting a no-overlap constraint,…
Flatness and Intrinsic Curvature of Linked-Ring Membranes
James M. Polson, Edgar J. Garcia, Alexander R. Klotz
Recent experiments have elucidated the physical properties of kinetoplasts, which are chain-mail-like structures found in the mitochondria of trypanosome parasites formed from cate…
The Ropelength of Complex Knots
Alexander R. Klotz, Matthew Maldonado
The ropelength of a knot is the minimum contour length of a tube of unit radius that traces out the knot in three dimensional space without self-overlap, colloquially the minimum a…
Trapping in Self-Avoiding Walks with Nearest-Neighbor Attraction
Wyatt Hooper, Alexander R. Klotz
The statistics of self-avoiding random walks have been used to model polymer physics for decades. A self-avoiding walk that grows one step at a time on a lattice will eventually tr…
Relativistic minimization with constraints: A smooth trip to Alpha Centauri
Riccardo Antonelli, Alexander R. Klotz
We consider the relativistic generalization of the problem of the "least uncomfortable" linear trajectory from point A to point B. The traditional problem minimizes the time-integr…
Waves of DNA: Propagating Excitations in Extended Nanoconfined Polymers
Alexander R. Klotz, Hendrick W. de Haan, Walter W. Reisner
We use a nanofluidic system to investigate the emergence of thermally driven collective phenomena along a single polymer chain. In our approach, a single DNA molecule is confined i…
A Guided Tour of Planetary Interiors
Alexander R. Klotz
We explore the gravitational dynamics of falling through planetary interiors. Two trajectory classes are considered: a straight cord between two surface points, and the brachistoch…
The Gravity Tunnel in a Non-Uniform Earth
Alexander R. Klotz
How long does it take to fall down a tunnel through the center of the Earth to the other side? Assuming a uniformly dense Earth, it would take 42 minutes, but this assumption has n…
Bubble Dynamics in N Dimensions
Alexander R. Klotz
Cavitation and bubble dynamics are central concepts in engineering, the natural sciences, and the mathematics of fluid mechanics. Due to the nonlinear nature of their dynamics, the…