38 citations · 102 across the 16 of their papers we have counts for
18 papers
Active matter within flexible boundaries: a novel experimental approach with T. aceti nematodes
Christina M. Ceballos, Matthew S. Mizuhara, Mykhailo Potomkin +1
We experimentally explore the collective behavior of the nematode T. Aceti inside flexible boundaries showing the emergence of previously unreported states. These nematodes have be…
Mixed higher-order coupling stabilizes new states
Per Sebastian Skardal, Federico Battiston, Maxime Lucas +3
Understanding how higher-order interactions affect collective behavior is a central problem in nonlinear dynamics and complex systems. Most works have focused on a single higher-or…
The Kuramoto model on the Sierpinski Gasket II: Twisted states
Georgi S. Medvedev, Matthew S. Mizuhara
We study the Kuramoto model (KM) of coupled phase oscillators on graphs approximating the Sierpinski gasket (SG). As the size of the graph tends to infinity, the limit points of th…
A bounded confidence model to predict how group work affects student math anxiety
Matthew S. Mizuhara, Katherine Toms, Maya Williams
Math anxiety is negatively correlated with student performance and can result in avoidance of further math/STEM classes and careers. Cooperative learning (i.e., group work) is a pr…
Bifurcations and patterns in the Kuramoto model with inertia
Hayato Chiba, Georgi S. Medvedev, Matthew S. Mizuhara
In this work, we analyze the Kuramoto model (KM) with inertia on a convergent family of graphs. It is assumed that the intrinsic frequencies of the individual oscillators are sampl…
A global bifurcation organizing rhythmic activity in a coupled network
Georgi S. Medvedev, Matthew S. Mizuhara, Andrew Phillips
We study a system of coupled phase oscillators near a saddle-node on an invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control para…
Stability of twisted states on lattices of Kuramoto oscillators
Monica Goebel, Matthew S Mizuhara, Sofia Stepanoff
Real world systems comprised of coupled oscillators have the ability to exhibit spontaneous synchronization and other complex behaviors. The interplay between the underlying networ…
Chimeras unfolded
Georgi S. Medvedev, Matthew S. Mizuhara
The instability of mixing in the Kuramoto model of coupled phase oscillators is the key to understanding a range of spatiotemporal patterns, which feature prominently in collective…
Instability of mixing in the Kuramoto model: From bifurcations to patterns
Hayato Chiba, Georgi S. Medvedev, Matthew S. Mizuhara
We study patterns observed right after the loss of stability of mixing in the Kuramoto model of coupled phase oscillators with random intrinsic frequencies on large graphs, which c…
Dynamics of a cell motility model near the sharp interface limit
Nicolas Bolle, Matthew S. Mizuhara
Phase-field models have recently had great success in describing the dynamic morphologies and motility of eukaryotic cells. In this work we investigate the minimal phase-field mode…
Fluid-Structure Interaction for the Classroom: Speed, Accuracy, Convergence, and Jellyfish!
Nicholas A. Battista, Matthew S. Mizuhara
When is good, good enough? This question lingers in approximation theory and numerical methods as a competition between accuracy and practicality. Numerical Analysis is traditional…
Bifurcations in the Kuramoto model on graphs
Hayato Chiba, Georgi S. Medvedev, Matthew S. Mizuhara
In his classical work, Kuramoto analytically described the onset of synchronization in all-to-all coupled networks of phase oscillators with random intrinsic frequencies. Specifica…
Minimal Model of Directed Cell Motility on Patterned Substrates
Matthew S. Mizuhara, Leonid Berlyand, Igor S. Aronson
Crawling cell motility is vital to many biological processes such as wound healing and the immune response. Using a minimal model we investigate the effects of patterned substrate…
Uniqueness and traveling waves in a cell motility model
Matthew S. Mizuhara, Peng Zhang
We study a non-linear and non-local evolution equation for curves obtained as the sharp interface limit of a phase-field model for crawling motion of eukaryotic cells on a substrat…
Extension of a proof of the Ramanujan congruences for multipartitions
Oleg Lazarev, Matthew S. Mizuhara, Benjamin Reid +1
Recently Lachterman, Schayer, and Younger published an elegant proof of the Ramanujan congruences for the partition function . Their proof uses only the classical theory of m…
A periodic approach to plane partition congruences
Matthew S. Mizuhara, James A. Sellers, Holly Swisher
Ramanujan's celebrated congruences of the partition function have inspired a vast amount of results on various partition functions. Kwong's work on periodicity of rational p…
On an evolution equation in a cell motility model
Matthew S. Mizuhara, Leonid Berlyand, Volodymyr Rybalko +1
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a…
On groups with a class-preserving outer automorphism
Peter A. Brooksbank, Matthew S. Mizuhara
In 1911, Burnside asked whether or not there exist groups that have an outer automorphism which preserves conjugacy classes. Two years later he answered his own question by constru…