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Michael J. Johnson

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math.NA Computational Engineering, Finance, and Science cond-mat.mtrl-sci math.MG physics.app-ph physics.comp-ph physics.med-ph physics.plasm-ph Quantitative Methods

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preprint2026arXiv

Reconstruction of glymphatic transport fields from subject-specific imaging data, with particular emphasis on cerebrospinal fluid flow and tracer conservation

The reconstruction of physically valid transport fields from subject-specific imaging data is a fundamental challenge in image-based computational modeling due to measurement noise, modeling uncertainties and discretization errors. Without a methodology to construct models that faithfully reflect the underlying physics, mechanistic understanding of complex biological systems is inherently limited. In this work, we address this challenge in the glymphatic system, the brain's waste-clearance network, where cerebrospinal fluid (CSF) is transported through perivascular spaces into the brain parenchyma to facilitate metabolic waste removal. We introduce a computational framework for the high-fidelity reconstruction of subject-specific glymphatic transport fields from spatiotemporal imaging data. The formulation utilizes an advection-diffusion model with a velocity decomposition that imposes mass conservation, enabling the recovery of solenoidal (divergence-free) velocity fields through the solution of a constrained inverse problem. The system is discretized using immersed isogeometric analysis with quadratic B-spline basis functions, providing smooth, high-continuity solutions and inherent regularization of imaging noise. We demonstrate the framework's utility by using contrast-enhanced magnetic resonance imaging of tracer transport in a mouse brain, obtaining spatially varying estimates of CSF velocity, diffusivity, and clearance parameters. Forward simulations using the recovered fields show close agreement with experimental observations, validating the framework's ability to characterize complex transport dynamics while preserving physical integrity. This approach provides a generalizable methodology for the robust inference of physically consistent transport fields from imperfect imaging data, with broad applicability to the image-guided modeling of biological and engineering systems.

preprint2021arXiv

Plasma-induced surface cooling

Here we show that, despite a massive incident flux of energetic species, plasmas can induce transient cooling of a material surface. Using time-resolved optical thermometry in-situ with this plasma excitation, we reveal the novel underlying physics that drive this `plasma cooling' that is driven by the diverse chemical and energetic species that comprise this fourth state of matter. We show that the photons and massive particles in the plasma impart energy to different chemical species on a surface, leading to local and temporally changing temperatures that lead to both increases and decreases in temperature on the surface of the sample, even though energy is being imparted to the material. This balance comes from the interplay between chemical reactions, momentum transfer, and energy exchange which occur on different time scales over the course of picoseconds to milliseconds. Thus, we show that through energetically exciting a material with a plasma, we can induce cooling, which can lead to revolutionary advances in refrigeration and thermal mitigation with this new process that is not inhibited by the same limitations in the current state-of-the-art systems.

preprint2017arXiv

Elastic Splines I: Existence

Given interpolation points $P_1,P_2,\ldots,P_n$ in the plane, it is known that there does not exist an interpolating curve with minimal bending energy, unless the given points lie sequentially along a line. We say than an interpolating curve is {\it admissable} if each piece, connecting two consecutive points $P_i$ and $P_{i+1}$, is an s-curve, where an {\it s-curve} is a planar curve which first turns at most $180^\circ$ in one direction and then turns at most $180^\circ$ in the opposite direction. Our main result is that among all admissable interpolating curves there exists a curve with minimal bending energy. We also prove, in a very constructive manner, the existence of an s-curve, with minimal bending energy, which connects two given unit tangent vectors.

preprint2016arXiv

Elastic Splines II: unicity of optimal s-curves and $G^2$ regularity of splines

Given points $P_1,P_2,\ldots,P_m$ in the complex plane, we are concerned with the problem of finding an interpolating curve with minimal bending energy (i.e., an optimal interpolating curve). It was shown previously that existence is assured if one requires that the pieces of the interpolating curve be s-curves. In the present article we also impose the restriction that these s-curves have chord angles not exceeding $π/2$ in magnitude. With this setup, we have identified a sufficient condition for the $G^2$ regularity of optimal interpolating curves. This sufficient condition relates to the stencil angles $\{ψ_j\}$, where $ψ_j$ is defined as the angular change in direction from segment $[P_{j-1},P_j]$ to segment $[P_j,P_{j+1}]$. A distinguished angle $Ψ$ ($\approx 37^\circ$) is identified, and we show that if the stencil angles satisfy $|ψ_j|<Ψ$, then optimal interpolating curves are globally $G^2$. As with the previous article, most of our effort is concerned with the geometric Hermite interpolation problem of finding an optimal s-curve which connects $P_1$ to $P_2$ with prescribed chord angles $(α,β)$. Whereas existence was previously shown, and sometimes uniqueness, the present article begins by establishing uniqueness when $|α|,|β|\leqπ/2$ and $|α-β|<π$.

preprint2014arXiv

On the Conjectures Regarding the 4-Point Atiyah Determinant

For the case of 4 points in Euclidean space, we present a computer aided proof of Conjectures II and III made by Atiyah and Sutcliffe regarding Atiyah's determinant along with an elegant factorization of the square of the imaginary part of Atiyah's determinant.