arXiv subjects

Jeffrey Tithof

Publications and source records attributed to Jeffrey Tithof.

7 recordsLinked to original sources

arXiv2025

One-dimensional modeling of blood flow: A comprehensive yet concise review

One-dimensional (1D) blood flow simulations are extensively used in cardiovascular research due to their computational efficiency and effectiveness in analyzing pulse wave dynamics. Despite their versatility and simplicity, there is a lack of a unified, step-by-step guide integrating theoretical derivations with practical implementation details. In this work, we summarize key components for comprehensive 1D blood flow simulations, including the derivation of reduced-order governing equations, the method of characteristics (Riemann invariants), a finite volume-based numerical scheme, boundary conditions (application of Riemann invariants for reflective/non-reflective and 3-element Windkessel outlet boundaries), junction treatments, verification of presented methodologies, and relevant practical applications. Additionally, we provide detailed step-by-step instructions for implementing the numerical scheme, applying boundary conditions, and treatment of junctions. By integrating rigorous theory with practical guidance for implementation, we seek to improve accessibility of 1D blood flow simulations. We anticipate that this guide will serve as a valuable resource and foundational reference for both novice and experienced researchers in cardiovascular modeling.

q-bio.QM↗

arXiv2018

Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like Flow

Recent studies suggest that unstable, non-chaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role of unstable equilibrium solutions and their invariant manifolds in a weakly turbulent, electromagnetically driven, shallow fluid layer. Identifying instants when turbulent evolution slows down, we compute 31 unstable equilibria of a realistic two-dimensional model of the flow. We establish the dynamical relevance of these unstable equilibria by showing that they are closely visited by the turbulent flow. We also establish the dynamical relevance of unstable manifolds by verifying that they are shadowed by turbulent trajectories departing from the neighborhoods of unstable equilibria over large distances in state space.

physics.flu-dyn↗

arXiv2017

Bifurcations in a Quasi-Two-Dimensional Kolmogorov-Like Flow

We present a combined experimental and theoretical study of the primary and secondary instabilities in a Kolmogorov-like flow. The experiment uses electromagnetic forcing with an approximately sinusoidal spatial profile to drive a quasi-two-dimensional (Q2D) shear flow in a thin layer of electrolyte suspended on a thin lubricating layer of a dielectric fluid. Theoretical analysis is based on a 2D model (Suri ${\it et al.}$ 2014), derived from first principles by depth-averaging the full three-dimensional Navier-Stokes equations. As the strength of the forcing is increased, the Q2D flow in the experiment undergoes a series of bifurcations, which is compared with results from direct numerical simulations of the 2D model. The effects of confinement and the forcing profile are studied by performing simulations that assume spatial periodicity and strictly sinusoidal forcing, as well as simulations with realistic no-slip boundary conditions and an experimentally validated forcing profile. We find that only the simulation subject to physical no-slip boundary conditions and a realistic forcing profile provides close, quantitative agreement with the experiment. Our analysis offers additional validation of the 2D model as well as a demonstration of the importance of properly modelling the forcing and boundary conditions.

physics.flu-dyn↗

arXiv2016

Forecasting Fluid Flows Using the Geometry of Turbulence

The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics exhibit clear signatures of numerous unstable equilibrium solutions, which are computed using a combination of flow measurements from the experiment and fully-resolved numerical simulations. We demonstrate the dynamical importance of these solutions by showing that turbulent flows visit their state space neighborhoods repeatedly. Furthermore, we find that the unstable manifold associated with one such unstable equilibrium predicts the evolution of turbulent flow in both experiment and simulation for a considerable period of time.

nlin.CD↗

arXiv2015

Analysis of Kolmogorov Flow and Rayleigh-Bénard Convection using Persistent Homology

We use persistent homology to build a quantitative understanding of large complex systems that are driven far-from-equilibrium; in particular, we analyze image time series of flow field patterns from numerical simulations of two important problems in fluid dynamics: Kolmogorov flow and Rayleigh-Bénard convection. For each image we compute a persistence diagram to yield a reduced description of the flow field; by applying different metrics to the space of persistence diagrams, we relate characteristic features in persistence diagrams to the geometry of the corresponding flow patterns. We also examine the dynamics of the flow patterns by a second application of persistent homology to the time series of persistence diagrams. We demonstrate that persistent homology provides an effective method both for quotienting out symmetries in families of solutions and for identifying multiscale recurrent dynamics. Our approach is quite general and it is anticipated to be applicable to a broad range of open problems exhibiting complex spatio-temporal behavior.

math.AT↗

arXiv2013

Velocity Profile in a Two-Layer Kolmogorov-Like Flow

In this article we discuss flows in shallow, stratified horizontal layers of two immiscible fluids. The top layer is an electrolyte which is electromagnetically driven and the bottom layer is a dielectric fluid. Using a quasi-two-dimensional approximation, we derive the depth-averaged two-dimensional (2D) vorticity equation which includes a prefactor to the advection term, previously unaccounted for. In addition, we study how the horizontal components of velocity vary in the vertical direction. For a Kolmogorov-like flow, we evaluate analytical expressions for the coefficients in the generalized 2D vorticity equation, uncovering their dependence on experimental parameters. To test the accuracy of these estimates, we experimentally measure the horizontal velocity fields at the free-surface and at the electrolyte-dielectric interface using particle image velocimetry (PIV). We show that there is excellent agreement between the analytical predictions and the experimental measurements. Our analysis shows that by increasing the viscosity of the electrolyte relative to that of the dielectric, one may significantly improve the uniformity of the flow along the vertical direction.

physics.flu-dyn↗

arXiv2008

Bounds on new light particles from high-energy and very small momentum transfer np elastic scattering data

We found that spin-one new light particle exchanges are strongly bounded by high-energy and small momentum transfer np elastic scattering data; the analogous bound for a scalar particle is considerably weaker, while for a pseudoscalar particle no bounds can be set. These bounds are compared with the bounds extracted from low-energy n-Pb scattering experiments and from the bounds of pi0 and K+ meson decays.

hep-ph↗