Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2004.03835

Finite transition times for multispecies diffusion in heterogeneous media coupled via first-order reaction networks

Elliot J. Carr·Jonah J. Klowss
View original source ↗Read source document ↗Export metadata ↓

Abstract

Calculating how long a coupled multi-species reactive-diffusive transport process in a heterogeneous medium takes to effectively reach steady state is important in many applications. In this paper, we show how the time required for such processes to transition to within a small specified tolerance of steady state can be calculated accurately without having to solve the governing time-dependent model equations. Our approach is valid for general first-order reaction networks and an arbitrary number of species. Three numerical examples are presented to confirm the analysis and investigate the efficacy of the approach. A key finding is that for sequential reactions our approach works better provided the two smallest reaction rates are well separated. MATLAB code implementing the methodology and reproducing the results in the paper is made available.

Explore related subjects

physics.bio-phphysics.comp-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Elliot J. Carr, Jonah J. Klowss. 2020-07-14. Finite transition times for multispecies diffusion in heterogeneous media coupled via first-order reaction networks. https://doi.org/10.1103/physreve.102.012107

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Tracking and distinguishing slime mold solutions to traveling salesperson problems through synchronized amplification in the non-equilibrium steady state

The plasmodium of the true slime mold Physarum polycephalum-an ancient, unicellular, aneural organism-serves as a platform for studying the information-processing capacities of active matter. Previous experiments used Physarum's intricate morphological dynamics and photoavoidance in stellate chips to solve $N$-city traveling salesperson problems (TSPs) of up to eight cities, scaling linearly in time with TSP size. Optical feedback controlled by a modified Hopfield network illuminated specific lanes at regular intervals, prompting Physarum to elongate or retract selected branches. When the illumination pattern stabilized in a non-equilibrium steady state, branches bifurcated reproducibly into solution and non-solution groups, with the former exhibiting lower-frequency, higher-amplitude, and more synchronized oscillations than the latter across 41 trials with valid TSP solutions. Physarum's synchronization dynamics efficiently predict 100% of selected solutions by the midpoint of the optical-feedback interval, achieving statistically significant (paired t-test, $p<0.005$) discrimination from alternate tours well before the non-equilibrium steady state. Observed frequency downconversions and synchronized power amplifications scale linearly and quadratically, respectively, for small-to-moderate TSP size, as captured by a toy model of energy redistribution with saturating optical absorption. Tuning these features in native biomolecular chromophore networks may thus improve both the quality and efficiency of TSP solutions from Physarum-based biocomputers, which exploit the effects of organismal-scale coherence.

physics.bio-ph↗
arXiv2026

How do incorrect ligands help detect a correct ligand?

Intrigued by the response of T cell receptors to the presence of a few agonist ligands, we propose a minimal model that can achieve similar performance. The model consists of a small cluster of immobile receptors that bind reversibly to two types (correct/incorrect) of ligands in the environment, with slightly weaker binding strength for the incorrect one. It features binding-state coupling between nearest-neighbor receptors, and receptors in the bound/free states are activated/deactivated by specific enzymes, with rates that allow kinetic proofreading. It is found that, for a range of binding-state coupling strength, incorrect ligands alone cannot activate the receptors, but the binding of merely one correct ligand to a receptor is sufficient to promote the activation of other receptors via induced binding to incorrect ligands. Both response time and signal amplification increase as the receptor binding-state coupling strength increases until it reaches an optimal range to achieve the most rapid and sensitive response. These results suggest a possible mechanism for a speedy and specific response of receptors to very few correct ligands in biological and artificial systems at the subcellular scale.

physics.bio-ph↗
arXiv2026

Coherence in Biological Systems

When does a collection of autonomous cells become a multicellular individual? We propose that coherence provides a physical description of this transition. Coherence is treated as a global property arising when distinguishable constituents admit a physically meaningful collective state-space description. Using the center of mass and an interaction-based construction, we show that such collective states can be defined for classical bodies before dynamics is introduced, with normal modes emerging as a particular dynamical realization. We apply this framework to multicellular organization, where cells retain their identities while their independent individuality is replaced by participation in the organized whole. In \emph{Dictyostelium discoideum}, cAMP-mediated coupling produces population-level collective modes, while starvation provides an experimentally controlled energetic constraint on the transition to multicellularity. The framework yields direct tests through interaction-derived collective eigenstates and the energetic cost of maintaining autonomous versus collective organization. Coherence may thus provide a general physical description of multicellular individuality without requiring microscopic quantum coherence or intrinsic wave character.

physics.bio-ph↗