107 citations · 419 across the 18 of their papers we have counts for
19 papers
Spectral stability for strong ideal-gas shock layers
Jeffrey Humpherys
We give a purely analytical proof of one-dimensional spectral stability of sufficiently strong shock layers for the full ideal-gas Navier--Stokes equations with constant viscosity…
Riccati Stability Without Auxiliary Matrices
Jeffrey Humpherys
In the 2004 collection \emph{Unsolved Problems in Mathematical Systems and Control Theory}, Erik Verriest posed the problem of characterizing Riccati stability ``without invoking a…
The De Cock--De Moor Conjecture: Proof, Normal Form, and Indefinite Angles
Jeffrey Humpherys
De Cock and De Moor conjectured that two matrices built from the solutions of three coupled Lyapunov equations always share their eigenvalues, an identity linking principal angles…
Tandem Blocks in Deep Convolutional Neural Networks
Chris Hettinger, Tanner Christensen, Jeffrey Humpherys +1
Due to the success of residual networks (resnets) and related architectures, shortcut connections have quickly become standard tools for building convolutional neural networks. The…
Forward Thinking: Building and Training Neural Networks One Layer at a Time
Chris Hettinger, Tanner Christensen, Ben Ehlert +3
We present a general framework for training deep neural networks without backpropagation. This substantially decreases training time and also allows for construction of deep networ…
Forward Thinking: Building Deep Random Forests
Kevin Miller, Chris Hettinger, Jeffrey Humpherys +2
The success of deep neural networks has inspired many to wonder whether other learners could benefit from deep, layered architectures. We present a general framework called forward…
Balanced flux formulations for multidimensional Evans function computations for viscous shocks
Blake Barker, Jeffrey Humpherys, Gregory Lyng +1
The Evans function is a powerful tool for the stability analysis of viscous shock profiles; zeros of this function carry stability information. In the one-dimensional case, it is t…
Multidimensional stability of large-amplitude Navier-Stokes shocks
Jeffrey Humpherys, Gregory Lyng, Kevin Zumbrun
Extending results of Humpherys-Lyng-Zumbrun in the one-dimensional case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the m…
Viscous hyperstabilization of detonation waves in one space dimension
Blake Barker, Jeffrey Humpherys, Gregory Lyng +1
It has long been a standard practice to neglect diffusive effects in stability analyses of detonation waves. Here, with the principal aim of quantifying the impact of these oft-neg…
Stability of viscous weak detonation waves for Majda's model
Jeffrey Hendricks, Jeffrey Humpherys, Gregory Lyng +1
Continuing the program initiated by Humpherys, Lyng, & Zumbrun [17] for strong detonation waves, we use a combination of analytical and numerical Evans-function techniques to analy…
Stability of viscous detonations for Majda's model
Jeffrey Humpherys, Gregory Lyng, Kevin Zumbrun
Using analytical and numerical Evans-function techniques, we examine the spectral stability of strong-detonation-wave solutions of Majda's scalar model for a reacting gas mixture w…
Efficient numerical stability analysis of detonation waves in ZND
Jeffrey Humpherys, Kevin Zumbrun
As described in the classic works of Lee--Stewart and Short--Stewart, the numerical evaluation of linear stability of planar detonation waves is a computationally intensive problem…
One-dimensional stability of parallel shock layers in isentropic magnetohydrodynamic
Blake Barker, Jeffrey Humpherys, Kevin Zumbrun
Extending investigations of Barker, Humpherys, Lafitte, Rudd, and Zumbrun for compressible gas dynamics and Freistühler and Trakhinin for compressible magnetohydrodynamics, we stud…
On the shock wave spectrum for isentropic gas dynamics with capillarity
Jeffrey Humpherys
We consider the stability problem for shock layers in Slemrod's model of an isentropic gas with capillarity. We show that these traveling waves are monotone in the weak capillarity…
Computing expected transition events in reducible Markov chains
Brian D. Ewald, Jeffrey Humpherys, Jeremy West
We present a closed-form, computable expression for the expected number of times any transition event occurs during the transient phase of a reducible Markov chain. Examples of eve…
Stability of strong ideal-gas shock layers
Jeffrey Humpherys, Gregory Lyng, Kevin Zumbrun
Extending recent results in the isentropic case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the spectral stability of sho…
Spectral stability of noncharacteristic isentropic Navier-Stokes boundary layers
Nicola Costanzino, Jeffrey Humpherys, Toan Nguyen +1
Building on work of Barker, Humpherys, Lafitte, Rudd, and Zumbrun in the shock wave case, we study stability of compressive, or "shock-like", boundary layers of the isentropic comp…
Stability of viscous shocks in isentropic gas dynamics
Blake Barker, Jeffrey Humpherys, Keith Rudd +1
In this paper, we examine the stability problem for viscous shock solutions of the isentropic compressible Navier--Stokes equations, or -system with real viscosity. We first rev…
An efficient shooting algorithm for Evans function calculations in large systems
Jeffrey Humpherys, Kevin Zumbrun
In Evans function computations of the spectra of asymptotically constant-coefficient linear operators, a basic issue is the efficient and numerically stable computation of subspace…