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Mohit P. Dalwadi

Publications and source records attributed to Mohit P. Dalwadi.

At least 19 recordsLinked to original sources
arXiv2026

Spatiotemporal Oscillations Driven by Spatial Heterogeneity and Growth

Temporal oscillations arise naturally in biological systems with feedback loops or explicit delays. When incorporating spatial effects, the travel times of propagating signals can also generate intrinsic delays, and this behaviour is complicated further in the presence of spatial heterogeneity. In this work, we investigate the mechanistic origin and dynamics of spatiotemporal oscillations driven by intrinsic diffusive delays in a representative activator-inhibitor system with spatial heterogeneity using a combination of mathematical modelling, simulations and numerical methods. In contrast to delay-differential equation models where delays are explicitly prescribed, in the partial differential equation system we consider here delays are an intrinsic consequence of signal travel time through space. We demonstrate that undamped oscillations can arise as a result of spatially heterogeneous feedback when the system size increases through a critical length. At this critical length the time for systems to reach steady-state diverges, and the systems first exhibit an eigenvalue with a positive real part and non-zero imaginary part, corresponding to a Hopf bifurcation. We infer that this critical length could define a theoretical upper limit for the size of systems where oscillations hinder function. The analysis pipeline derived in this work offers a novel route for understanding the onset of spatiotemporal oscillations and Hopf bifurcations in a diverse array of biological systems where interactions are mediated by diffusive species.

physics.bio-ph↗
arXiv2026

A nonlinear theory for chemotactic fronts of mixed populations

Collective migration of heterogeneous cell populations is central to many biological and physiological processes, including development and immune response. Recent experimental and theoretical advances have shown how asymmetric interactions with self-generated chemical gradients shape the spatial distribution of distinct cell types within migrating collectives. However, the principles governing robust spatial organisation of heterogeneous cell populations remain poorly understood. Here, we use asymptotic analysis to systematically derive a nonlinear analytical theory for heterogeneous cell collectives guided by self-generated chemotaxis. Our theory disentangles how heterogeneity in cell diffusivity, chemoattractant consumption, and chemotactic sensitivity shape the density profiles of migrating heterogeneous collectives, revealing four distinct dynamical behaviours that together capture all possible regimes. We calibrate our framework to experimental data on the co-migration of dendritic and T cells. We predict that this system operates in a parameter regime that balances intercellular mixing with T-cell localisation at the leading front of the migrating collective. Our theory reveals that this behaviour is enabled by intermediate long-range chemoattractant signalling generated through strong chemoattractant consumption by dendritic cells. Overall, our framework provides general principles for understanding how non-reciprocal chemical interactions shape robust collective migration in heterogeneous cell populations.

q-bio.CB↗
arXiv2026

Bacterial adhesion to curved surfaces in fluid flow

Minimising bacterial surface adhesion and subsequent biofilm formation in industrial and medical settings requires understanding how bacteria are transported and adhere to complex surface geometries in the presence of non-uniform flow. In this paper, we consider the transport of a dilute suspension of motile bacteria through a corrugated two-dimensional channel with perfectly adhesive walls. We asymptotically analyse the diffusive boundary layer that forms in high velocity flows using a curvilinear coordinate system based on the fluid streamfunction, presenting a similarity solution to the diffusivity-varying diffusion-type equation that arises. From this solution, we derive an analytical expression for the bacterial adhesion rate as a function of surface arclength and the spatially varying wall shear rate. Our model predicts that bacterial adhesion becomes localised on curved surfaces, with bacteria showing preferential adhesion to wall `peaks' at lower shear rates and preferential adhesion to wall `valleys' at higher shear rates. More broadly, our results highlight how spatially varying flows generated by complex geometries can lead to localised bacterial adhesion, with potential implications for both enhancing and minimising biofilm formation.

cond-mat.soft↗
arXiv2026

Far-field approximations for multi-timescale microswimmers near a boundary

Hydrodynamic interactions with boundaries can significantly affect the trajectories of microscale swimmers. In simple swimmer models, a common assumption is that swimmer shape remains constant, essentially averaging over the rapid oscillations in geometry and associated fluid flows that often are the source of propulsion. Previous work in minimal force-dipole models has shown how the inclusion of time-dependent swimmer changes can lead to a fundamentally wider class of behaviours than for their classic (implicitly averaged) counterparts. However, since force dipole models correspond to the leading-order term in the far-field description of the swimmer-induced flow, they break down as the swimmer approaches a boundary and predictions can become qualitatively inaccurate. Here, we extend the minimal force-dipole model by incorporating higher order flow singularities, systematically accounting for rapid oscillations in shape and singularity strength through a multiscale analysis. We demonstrate that the inclusion of time-dependence into these higher order models significantly expands the reachable parameter space, in particular by increasing its dimensionality. In these extended dynamics, we observe three distinct behaviours: crashing, escaping and hovering. Notably, hovering states are absent from the dynamics predicted by the simplest models, but are observed in more complex models.

physics.flu-dyn↗
arXiv2026

Modelling Intermediate-Current Transitions in Asymmetric-Valence Binary Electrolytes

Asymmetric valences in a binary electrolyte can significantly affect the performance of systems such as reverse electrodialysis cells, batteries, and supercapacitors. To generate a theoretical understanding of this effect, we consider a steady one-dimensional Poisson-Nernst-Planck model of an electrolytic cell with imposed constant ionic fluxes, focusing on varying ion valences in a general asymmetric binary electrolyte. Numerical simulations reveal a smooth transition between the qualitatively distinct near-equilibrium and strongly non-equilibrium steady-state regimes. These regimes are distinguished by a valence-dependent transition point at an intermediate current where the classical Debye-scale boundary layer vanishes. We characterise this transition using asymptotic analysis, recovering the Gouy-Chapman and limiting-current results in the appropriate limits, and determining the correct transition results when neither is appropriate. We provide implicit solutions for the potential and ion concentrations of general asymmetric binary electrolytes and, notably, we provide explicit analytic expressions for the asymptotic composite solutions for 2z:z, z:2z, and z:z electrolytes. We show how the results can be presented in a collapsed phase diagram that can be used to predict qualitative intermediate-current steady-state behaviour in terms of ion valences and fluxes.

physics.chem-ph↗
arXiv2026

Theory of adhesion-driven self-organisation in growing tissues

Cell invasion and spatial pattern formation are two distinct manifestations of cellular self-organisation in development, regeneration, and disease. Here, we develop and analyse a unified theoretical framework that links these two seemingly different behaviours within a single mechanistic model for adhesion-mediated self-organisation in growing cell populations. Using a multiscale analysis, we show that the balance between cell-cell adhesion, self-diffusion, and proliferation controls the emergence of distinct collective dynamics. We find that for weak adhesion, tissues invade through stable monotone fronts. As adhesion increases, invasion slows, fronts become unstable, leading to aggregates and spatial patterns emerging behind the advancing edge. In two spatial dimensions, these instabilities generate fingering morphologies reminiscent of dysregulated invasion in cancer. Crucially, we show that density-dependent regulation of adhesion suppresses these instabilities and restores cohesive tissue expansion. Together, our results identify adhesion strength and its regulation as key determinants of whether tissues invade cohesively or fragment into patterns, and provide a unified framework for understanding collective migration, morphogenesis, and dysregulated growth.

q-bio.TO↗
arXiv2026

A multiscale discrete-to-continuum framework for structured population models

Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions can improve analytical tractability and scalability of numerical solutions. Common upscaling approaches based solely on Taylor expansions may, however, introduce ambiguities in truncation order, uniform validity and boundary conditions. To address this, here we introduce a discrete multiscale framework to systematically derive continuum approximations of structured population models. Using the method of multiple scales and matched asymptotic expansions applied to discrete systems, we identify regions of structure space for which a continuum representation is appropriate and derive the corresponding partial differential equations. The leading-order dynamics are given by a nonlinear advection equation in the bulk domain and advection-diffusion processes in small inner layers about the leading wavefronts and stagnation point. We further derive discrete boundary layer descriptions for regions where a continuum representation is fundamentally inappropriate. Finally, we demonstrate the method on a simple lipid-structured model for early atherosclerosis and verify consistency between the discrete and continuum descriptions. The multiscale framework we present can be applied to other heterogeneous systems with discrete structure in order to obtain appropriate upscaled dynamics with asymptotically consistent boundary conditions.

q-bio.PE↗
arXiv2026

Chemotaxis of cell aggregates: morphology and dynamics of migrating active droplets

Biological tissues have been observed to display emergent fluid-like properties, owing to physical interactions between cells. However, it remains unclear in general how these fluid-like properties affect tissue structure and function. Here, we are motivated by recent experiments in which cell aggregates were observed to behave as active droplets during collective migration along chemical gradients, or chemotaxis. To understand this process, we develop a minimal model of a growing thin active droplet driven by a self-generated chemical gradient. In broad agreement with the experiments, dynamic simulations reveal that chemotacting droplets exhibit proliferation-driven morphological transitions. To fully characterise these transitions, we perform a multiple scales analysis to show that the droplet dynamics follow a sequence of travelling wave solutions defined by a nonlinear eigenvalue problem parametrised by the slowly increasing droplet volume. Our analysis reveals that morphological transitions can occur continuously or through a discontinuous bifurcation. Further asymptotic analysis of the travelling wave problem reveals that these morphological transitions arise from exponentially small ("beyond-all-orders") asymptotic terms that originate from the rear and front contact lines. Moreover, we show that the nature of the transitions is fully determined by two key dimensionless parameters, which quantify the internal stress balance within the droplet and the strength of the coupling between the droplet migration dynamics and the external chemical field. Overall, our results provide a complete characterisation of the morphodynamics of a class of migrating active thin droplets, with implications in a range of biological systems where cell aggregates exhibit fluid-like behaviour.

cond-mat.soft↗
arXiv2026

Effective permeability conditions for diffusive transport through impermeable membranes with gaps

Membranes regulate transport in a wide variety of industrial and biological applications. The microscale geometry of the membrane can significantly affect overall transport through the membrane, but the precise nature of this multiscale coupling is not well characterised in general. Motivated by the application of transport across a bacterial membrane, in this paper we use formal multiscale analysis to derive explicit effective coupling conditions for macroscale transport across a two-dimensional impermeable membrane with periodically spaced gaps, and validate these with numerical simulations. We derive analytic expressions for effective macroscale quantities associated with the membrane, such as the permeability, in terms of the microscale geometry. Our results generalise the classic constitutive membrane coupling conditions to a wider range of membrane geometries and time-varying scenarios. Specifically, we demonstrate that if the exterior concentration varies in time, for membranes with long channels, the transport gains a memory property where the coupling conditions depend on the system history. By applying our effective conditions in the context of small molecule transport through gaps in bacterial membranes called porins, we predict that bacterial membrane permeability is primarily dominated by the thickness of the membrane. Furthermore, we predict how alterations to membrane microstructure, for example via changes to porin expression, might affect overall transport, including when external concentrations vary in time. These results will apply to a broad range of physical applications with similar membrane structures, from medical and industrial filtration to carbon capture.

cond-mat.soft↗
arXiv2025

A Weakly Nonlinear Theory for Pattern Formation in Structured Models with Localized Solutions

Structured models, such as PDEs structured by age or phenotype, provide a setting to study pattern formation in heterogeneous populations. Classical tools to quantify the emergence of patterns, such as linear and weakly nonlinear analyses, pose significant mathematical challenges for these models due to sharply peaked or singular steady states. Here, we present a weakly nonlinear framework that extends classical tools to structured PDE models in settings where the base state is spatially uniform, but exponentially localized in the structured variable. Our approach utilizes WKBJ asymptotics and an analysis of the Stokes phenomenon to systematically resolve the solution structure in the limit where the steady state tends to a Dirac-delta function. To demonstrate our method, we consider a chemically structured (nonlocal) model of motile bacteria that interact through quorum sensing. For this example, our analysis yields an amplitude equation that governs the solution dynamics near a linear instability, and predicts a pitchfork bifurcation. From the amplitude equation, we deduce an effective parameter grouping whose sign determines whether the pitchfork bifurcation is subcritical or supercritical. Although we demonstrate our framework for a specific example, our techniques are broadly applicable.

math.AP↗
arXiv2025

A shear-induced limit on bacterial surface adhesion in fluid flow

Controlling bacterial surface adhesion and subsequent biofilm formation in fluid systems is crucial for the safety and efficacy of medical and industrial processes. Here, we theoretically examine the transport of bacteria close to surfaces, isolating how the key processes of bacterial motility and fluid flow interact and alter surface adhesion. We exploit the disparity between the fluid velocity and the swimming velocity of common motile bacteria and, using a hybrid asymptotic-computational approach, we systematically derive the coarse-grained bacterial diffusivity close to surfaces as a function of swimming speed, rotational diffusivity, and shape. We calculate an analytical upper bound for the bacterial adhesion rate by considering the scenario in which bacteria adhere irreversibly to the surface on first contact. Our theory predicts that maximal adhesion occurs at intermediate flow rates: at low flow rates, increasing flow increases surface adhesion, while at higher flow rates, adhesion is decreased by shear-induced cell reorientation.

cond-mat.soft↗
arXiv2025

Integral Asymptotics, Coalescing Saddles, and Multiple-scales Analysis of a Generalised Swift-Hohenberg Equation

Integral asymptotics play an important role in the analysis of differential equations and in a variety of other settings. In this work, we apply an integral asymptotics approach to study spatially localized solutions of a heterogeneous generalised Swift-Hohenberg equation. The outer solution is obtained via WKBJ asymptotics, while the inner solution requires the method of coalescing saddles. We modify the classic method of Chester et al. to account for additional technicalities, such as complex branch selection and local transformation to a cubic polynomial. By integrating our results, we construct an approximate global solution to the generalised Swift-Hohenberg problem and validate it against numerical contour integral solutions. We also demonstrate an alternative approach that circumvents the complexity of integral asymptotics by analyzing the original differential equation directly through a multiple-scales analysis and show that this generates the same leading-order inner solution obtained using the coalescing saddles method at least for one of the cases considered via integral asymptotics. Our findings reinforce the significance of integral asymptotics in approximating the fourth order differential equations found in the linear stability analysis for generalisations of the Swift Hohenberg equations. This study has also highlighted a conjecture that, in certain cases, the method of coalescing saddles can be systematically replaced by multiple-scales analysis using an intermediary differential equation, a hypothesis for future investigation.

nlin.PS↗
arXiv2024

Rapidly yawing spheroids in viscous shear flow: Emergent loss of symmetry

We investigate the emergent three-dimensional (3D) dynamics of a rapidly yawing spheroidal swimmer interacting with a viscous shear flow. We show that the rapid yawing generates non-axisymmetric emergent effects, with the active swimmer behaving as an effective passive particle with two orthogonal planes of symmetry. We also demonstrate that this effective asymmetry generated by the rapid yawing can cause chaotic behaviour in the emergent dynamics, in stark contrast to the emergent dynamics generated by rapidly rotating spheroids, which are equivalent to those of effective passive spheroids. In general, we find that the shape of the equivalent effective particle under rapid yawing is different to the average shape of the active particle. Moreover, despite having two planes of symmetry, the equivalent passive particle is not an ellipsoid in general, except for specific scenarios in which the effective shape is a spheroid. In these scenarios, we calculate analytically the equivalent aspect ratio of the effective spheroid. We use a multiple scales analysis for systems to derive the emergent swimmer behaviour, which requires solving a nonautonomous nonlinear 3D dynamical system, and we validate our analysis via comparison to numerical simulations.

physics.flu-dyn↗
arXiv2024

A homogenised model for dispersive transport and sorption in a heterogeneous porous medium

When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous medium; however, this dependence remains poorly understood. For idealised microstructures, one can use the mathematical framework of homogenisation to examine this dependence, but strongly heterogeneous materials are more challenging. Here, we consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium. We use homogenisation via the method of multiple scales to systematically upscale a microscale problem involving non-periodic cells of varying area to obtain effective continuum equations for macroscale transport and sorption. The equations are characterised by the local porosity, an effective local adsorption rate and an effective local anisotropic solute diffusivity. All of these macroscale properties depend nontrivially on the two degrees of microstructural geometric freedom in our problem; obstacle size and obstacle spacing. Further, the coefficient of effective diffusivity comprises the molecular diffusivity, the suppressive effect of the presence of obstacles and the enhancing effect of dispersion. To illustrate the mathematical model, we focus on a simple example geometry comprising circular obstacles on a hexagonal lattice, for which we numerically determine the macroscale permeability and effective diffusivity. We find a power law for the dispersive component of solute transport, consistent with classical Taylor dispersion.

physics.flu-dyn↗
arXiv2024

An agent-based modelling framework to study growth mechanisms in EGFR-L858R mutant alveolar type II cells

Mutations in the epidermal growth factor receptor (EGFR) are common in non-small cell lung cancer (NSCLC), particularly in never-smoker patients. However, these mutations are not always carcinogenic, and have recently been reported in histologically normal lung tissue from patients with and without lung cancer. To investigate the outcome of EGFR mutation in healthy lung stem cells, we grew murine alveolar type-II organoids monoclonally in a 3D Matrigel. Our experiments showed that the \textit{EGFR-L858R} mutation induced a change in organoid structure: mutated organoids displayed more `budding', in comparison to non-mutant controls, which were nearly spherical. We perform on-lattice computational simulations, which suggest that this can be explained by the concentration of division amongst a small number of cells on the surface of the organoid, which may arise from several possible biological mechanisms. These results suggest that the L858R mutation produces structures which expand quickly from surface protrusions. We are currently unable to distinguish the cell-based mechanisms that lead to this spatial heterogeneity in growth, but suggest a number of future experiments which could be used to do so. We suggest that the likelihood of L858R-fuelled tumorigenesis is affected not just by random fluctuations in cell fitness, but by whether the mutation arises in a spatial environment that allows mutant cells to reproduce without being forced to encounter each other. These data may have implications for cancer prevention strategies and for understanding NSCLC progression.

q-bio.CB↗
arXiv2023

Generalised Jeffery's equations for rapidly spinning particles. Part 2: Helicoidal objects with chirality

In this two-part study, we investigate the motion of rigid, active objects in shear Stokes flow, focusing on bodies that induce rapid rotation as part of their activity. In Part 2, we derive and analyse governing equations for rapidly spinning complex-shaped particles - general helicoidal objects with chirality. Using the multiscale framework we develop in Part 1 (arXiv:2301.11311), we systematically derive emergent equations of motion for the angular and translational dynamics of these chiral spinning objects. We show that the emergent dynamics due to rapid rotation can be described by effective generalised Jeffery's equations, which differ from the classic versions via the inclusion of additional terms that account for chirality and other asymmetries. Furthermore, we use our analytic results to characterise and quantify the explicit effect of rotation on the effective hydrodynamic shape of the chiral objects, significantly expanding the scope of Jeffery's seminal study.

physics.flu-dyn↗
arXiv2023

Generalised Jeffery's equations for rapidly spinning particles. Part 1: Spheroids

The observed behaviour of passive objects in simple flows can be surprisingly intricate, and is complicated further by object activity. Inspired by the motility of bacterial swimmers, in this two-part study we examine the three-dimensional motion of rigid active particles in shear Stokes flow, focusing on bodies that induce rapid rotation as part of their activity. Here, in Part 1, we develop a multiscale framework to investigate these emergent dynamics and apply it to simple spheroidal objects. In Part 2 (arXiv:2301.11032), we apply our framework to understand the emergent dynamics of more complex shapes; helicoidal objects with chirality. Via a multiple-scales asymptotic analysis for nonlinear systems, we systematically derive emergent equations of motion for long-term trajectories that explicitly account for the strong (leading-order) effects of fast spinning. Supported by numerical examples, we constructively link these effective dynamics to the well-known Jeffery's orbits for passive spheroids, deriving an explicit closed-form expression for the effective shape of the active particle, broadening the scope of Jeffery's seminal study to spinning spheroids.

physics.flu-dyn↗
arXiv2022

Emergent rheotaxis of shape-changing swimmers in Poiseuille flow

A simple model for the motion of shape-changing swimmers in Poiseuille flow was recently proposed and numerically explored by Omori et al. (2022). These explorations hinted that a small number of interacting mechanics can drive long-time behaviours in this model, cast in the context of the well-studied alga Chlamydomonas and its rheotactic behaviours in such flows. Here, we explore this model analytically via a multiple-scale asymptotic analysis, seeking to formally identify the causal factors that shape the behaviour of these swimmers in Poiseuille flow. By capturing the evolution of a Hamiltonian-like quantity, we reveal the origins of the long-term drift in a single swimmer-dependent constant, whose sign determines the eventual behaviour of the swimmer. This constant captures the nonlinear interaction between the oscillatory speed and effective hydrodynamic shape of deforming swimmers, driving drift either towards or away from rheotaxis.

physics.flu-dyn↗