John Gemmer

John Gemmer
Wake Forest University | WFU · Department of Mathematics

Ph.D.

About

23
Publications
2,725
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
244
Citations
Introduction
Additional affiliations
July 2013 - July 2016
Brown University
Position
  • PostDoc Position
July 2012 - July 2013
The University of Arizona
Position
  • PostDoc Position

Publications

Publications (23)
Article
We develop a path integral framework for determining most probable paths for a class of systems of stochastic differential equations with piecewise-smooth drift and additive noise. This approach extends the Freidlin–Wentzell theory of large deviations to cases where the system is piecewise-smooth and may be non-autonomous. In particular, we conside...
Article
Full-text available
The spread of an infectious disease depends on intrinsic properties of the disease as well as the connectivity and actions of the population. This study investigates the dynamics of an SIR type model which accounts for human tendency to avoid infection while also maintaining preexisting, interpersonal relationships. Specifically, we use a network m...
Preprint
Full-text available
We develop a path integral framework for determining most probable paths in a class of systems of stochastic differential equations with piecewise-smooth drift and additive noise. This approach extends the Freidlin-Wentzell theory of large deviations to cases where the system is piecewise-smooth and may be non-autonomous. In particular, we consider...
Preprint
Full-text available
The spread of an infectious disease depends on intrinsic properties of the disease as well as the connectivity and actions of the population. This study investigates the dynamics of an SIR type model which accounts for human tendency to avoid infection while also maintaining preexisting, interpersonal relationships. Specifically, we use a network m...
Article
A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals, and marine invertebrates. We investigate this morphology from the perspective of non-Euclidean plate theory. We identify a novel type of defect, a branch-point of the normal map, that allows for t...
Preprint
Full-text available
A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals and marine invertebrates. We investigate this morphology from the perspective of non-Euclidean plate theory. We identify a novel type of defect, a branch-point of the normal map, that allows for th...
Article
We consider a periodically forced 1D Langevin equation that possesses two stable periodic solutions in the absence of noise. We ask the question: is there a most likely noise-induced transition path between these periodic solutions that allows us to identify a preferred phase of the forcing when tipping occurs? The quasistatic regime, where the for...
Article
Full-text available
We consider a simple periodically-forced 1-D Langevin equation which possesses two stable periodic orbits in the absence of noise. We ask the question: is there a most likely transition path between the stable orbits that would allow us to identify a preferred phase of the periodic forcing for which tipping occurs? The regime where the forcing peri...
Article
Full-text available
We explore regularity properties of solutions to a two-phase elliptic free boundary problem near a Neumann fixed boundary in two dimensions. Consider a function u, which is harmonic where it is not zero and satisfies a gradient jump condition weakly along the free boundary. Our main result is that u is Lipschitz continuous up to the Neumann fixed b...
Article
Self-motion triggers complementary visual and vestibular reflexes supporting image-stabilization and balance. Translation through space produces one global pattern of retinal image motion (optic flow), rotation another. We examined the direction preferences of direction-sensitive ganglion cells (DSGCs) in flattened mouse retinas in vitro. Here we s...
Article
Full-text available
In this paper we study the brachistochrone problem in an inverse-square gravitational field on the unit disk. We show that the time optimal solutions consist of either smooth strong solutions to the Euler-Lagrange equation or weak solutions formed by appropriately patched together strong solutions. This combination of weak and strong solutions comp...
Article
The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology (i) emerges even in zero strain configurations, and (ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key role of branch-point (or "mon...
Article
Full-text available
The edge of torn elastic sheets and growing leaves often form a hierarchical buckling pattern. Within non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian metrics. With this motivation we study the isometric immersion problem in strip and disk geometries. By finding...
Article
We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to the one arising in phase retrieval. Using the uncertainty principle we prove rigorous lower bounds on the func...
Article
Full-text available
Gaussian-apodized Bessel beams can be used to create a Bessel-like axial line focus at a distance from the focusing lens. For many applications it is desirable to create an axial intensity profile that is uniform along the Bessel zone. In this article, we show that this can be accomplished through phase-only shaping of the wavefront in the far fiel...
Article
We present and summarize the results of recent studies on non-Euclidean plates with imposed constant negative Gaussian curvature in both the F\"oppl - von K\'arm\'an and Kirchhoff approximations. Motivated by experimental results we focus on annuli with a periodic profile. We show that in the F\"oppl - von K\'arm\'an approximation there are only tw...
Article
Full-text available
We investigate the behavior of non-Euclidean plates with constant negative Gaussian curvature using the F\"oppl-von K\'arm\'an reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In...
Article
Full-text available
In this dissertation we investigate the behavior of radially symmetric non-Euclidean plates of thickness t with constant negative Gaussian curvature. We present a complete study of these plates using the Foppl-von Karman and Kirchhoff reduced theories of elasticity. Motivated by experimental results, we focus on deformations with a periodic profile...
Article
We investigate isometric immersions of disks with constant negative curvature into $\mathbb{R}^3$, and the minimizers for the bending energy, i.e. the $L^2$ norm of the principal curvatures over the class of $W^{2,2}$ isometric immersions. We show the existence of smooth immersions of arbitrarily large geodesic balls in $\mathbb{H}^2$ into $\mathbb...
Article
Full-text available
Consider a frictionless surface S in a gravitational field that need not be uniform. Given two points A and B on S, what curve is traced out by a particle that starts at A and reaches B in the shortest time? This paper considers this problem on simple surfaces such as surfaces of revolution and solves the problem two ways: First, we use conservatio...

Network

Cited By