arXiv subjects

Yoichiro Mori

Publications and source records attributed to Yoichiro Mori.

At least 19 recordsLinked to original sources

arXiv2026

A Cartesian Grid Method for Advection-Diffusion Equations with Robin Boundary Conditions on Moving Domains

We develop a Cartesian grid method for advection--diffusion equations with Robin boundary conditions on moving domains. The moving-domain problem is reformulated as an interface problem on a box, with an unknown density introduced on the moving interface to enforce the Robin condition. The bulk equation is discretized by a cell-centered finite-difference scheme on the Cartesian grid, while interface corrections are obtained from local problems in a narrow band around the interface. The resulting method requires only modest computational geometry, avoids remeshing and cut cells, and is compatible with geometric multigrid and matrix-free GMRES. The GMRES iteration count is essentially independent of the mesh size, and the computational cost scales linearly with the number of bulk degrees of freedom. For the one-dimensional scheme, first-order convergence in time and second-order convergence in space are proved. Numerical examples in one and two dimensions, including manufactured solutions and an active transport problem without an exact solution, demonstrate the accuracy and efficiency of the method.

math.NA↗

arXiv2026

On the global asymptotic stability for the 3D Peskin Problem at critical regularity

We prove global well-posedness and asymptotic stability for the three-dimensional Peskin problem, which models a closed, elastic membrane immersed in an incompressible Stokes fluid. We work with initial data in the optimal regularity space $W^{1,\infty}(\mathbb{S}^2)$, which may contain infinitely many corners. These initial configurations are instantly desingularized by the flow's parabolic smoothing effect, becoming smooth for all $t > 0$. Then we establish that the solutions converge exponentially in the $C^1$ topology to a translated and dilated conformal sphere. The stability is achieved by combining our nonlinear estimates with an exact structural decoupling of the 10-dimensional manifold of conformal steady states, demonstrating that the infinite-dimensional dissipative perturbation is strictly controlled. The core of our analysis is a functional framework on the sphere $\mathbb{S}^2$ that uses spectral Littlewood-Paley projections to control the highly singular multilinear operators arising from the fluid nonlinearity

math.AP↗

arXiv2026

Stability and equilibria of a compressible elastic membrane in Stokes flow

We formulate a continuum model for a compressible lipid-bilayer membrane immersed in Stokes flow, replacing exact local area inextensibility by conservation of an areal phospholipid density. The membrane free energy combines Helfrich bending, spontaneous curvature, and a finite area-compression penalty, so that membrane tension becomes a constitutive response to lipid-density variation rather than a Lagrange multiplier enforcing local area conservation. The resulting interfacial stress includes normal elastic forces and tangential Marangoni stresses generated by lipid redistribution; these stresses arise from membrane compressibility and can produce an effective negative tension when the local lipid density exceeds its preferred value. We further derive the linear stability of circular membranes in two dimensions and spherical membranes in three dimensions under full Stokes hydrodynamic coupling. In both cases, bending stabilizes the base shape, while excess lipid density destabilizes it by favoring increased membrane area. The first instability occurs in the lowest nontrivial shape mode, m = 2 in two dimensions and j = 2 in three dimensions. Energy expansions near onset show that the two-dimensional instability is a pitchfork bifurcation, whereas the three-dimensional instability is generically transcritical because prolate and oblate perturbations are geometrically distinct. These results provide a controlled compressible extension of classical vesicle mechanics and directly connect lipid-density variation, membrane tension, hydrodynamic coupling, and shape instability.

cond-mat.soft↗

arXiv2026

Coercivity and Local Convergence of Physical Learning in Linear Circuits

Physical learning methods train physical networks to perform computational tasks using only local update rules, exploiting the physics of the system to handle the global transfer of information. We provide the first local convergence analysis of three such methods -- Equilibrium Propagation (EP), Coupled Learning (CL), and a new method we call Adjoint Coupled Learning (AL) -- for linear circuits, in the limit of small-nudging for both discrete and continuous time. EP and AL perform gradient descent on a natural loss function, while CL follows modified dynamics with an additional cubic correction. Assuming the existence of a solution, we identify a coercivity condition, expressed as a rank condition on a matrix built from the network's incidence structure, under which the training loss decays exponentially and the parameters converge to the solution manifold. We show that coercivity can fail by exhibiting a kite circuit in which a symmetry causes the coercivity constant to degenerate on the solution manifold, but prove using Sard's theorem that such degeneracies are non-generic: coercivity holds at every point of the solution manifold for almost every choice of desired output.

math.OC↗

arXiv2026

A Conservation Law for Equilibrium Propagation and Coupled Learning

In this paper we show that the physical learning methods known as coupled learning (CL) and equilibrium propagation (EP) conserve a mass-like quantity in the trainable parameters in the continuous-time, small-nudging limit. We prove that this conservation holds in a broad range of physically relevant settings. We then show that the conservation law constrains the training dynamics in a way that makes convergence reliable in important settings for linear circuits. We conclude by discussing some practical implications of this conservation law.

math.OC↗

arXiv2026

Bulk-surface coupled PDE with an open boundary

We study a bulk-surface coupled Laplace system involving an embedded open boundary. The problem is reformulated as an integro-differential equation using boundary integral representations, for which we establish existence and uniqueness of the solution. A Wiener-Hopf technique is employed to study the solution regularity and derive asymptotic expressions for the edge singularity. Building on these results, we develop a finite element method that incorporates the singularity structure and provide a rigorous error analysis. Numerical experiments confirm the theoretical convergence rates.

math.NA↗

arXiv2026

Surfing on metachronal waves: ciliary transport by inertial coasting

Motile cilia drive biological fluid transport through whip-like beating motions that synchronize into metachronal waves. The lengths of these cilia span three orders of magnitude, from microns in human airways to millimeters in ctenophores. While recent studies have considered ciliary flows at intermediate Reynolds numbers, the effect of inertia on coordinated particle transport remains unexplored. Here, we address this gap using "Pufflets," the inertial counterparts of Stokeslets. These Pufflets describe rapidly accelerating flows generated by short-lived impulses, encoded by spatiotemporally singular momentum injections. To produce such rapid impulses experimentally, we designed an Atwood machine that generates long-lived Pufflet flows, which we capture with high-speed PIV measurements that agree well with analytical theory and simulations. Moreover, we find that pairs of equal and opposite Pufflets can drive net particle displacements and mixing due to time reversal symmetry breaking, which would be impossible in Stokes flow. Finally, we consider metachronal waves of Pufflets. Remarkably, we discover that particles can surf on these waves by coasting inertially from one cilium to the next, leading to highly efficient particle transport. This work paves the way toward understanding rapidly accelerating flows and collective transport driven by biological and artificial cilia.

physics.bio-ph↗

arXiv2026

Error analysis of an acceleration corrected diffusion approximation of Langevin dynamics with background flow

We consider the problem of approximating the Langevin dynamics of inertial particles being transported by a background flow. In particular, we study an acceleration corrected advection-diffusion approximation to the Langevin dynamics, a popular approximation in the study of turbulent transport. We prove error estimates in the averaging regime in which the dimensionless relaxation timescale $\varepsilon$ is the small parameter. We show that for any finite time interval, the approximation error is of order $\mathcal{O}(\varepsilon)$ in the strong sense and $\mathcal{O}(\varepsilon^2)$ in the weak sense, whose optimality is checked against computational experiment. Furthermore, we present numerical evidence suggesting that this approximation also captures the long-time behavior of the Langevin dynamics.

math.PR↗

arXiv2026

Well-posedness of the Langmuir film problem

We analyze the inviscid Langmuir layer--Stokesian subfluid (ILLSS) model for two-phase Langmuir monolayers coupled to a Stokes flow in the underlying subfluid. Eliminating the bulk variables, we reformulate the coupled three-dimensional system as an evolution on the film involving the Dirichlet-to-Neumann (DtN) operator. We identify the Fourier symbol of the DtN operator and show it coincides with that of the fractional Laplacian, which yields an explicit Fourier-multiplier representation and allows construction of the corresponding fundamental solution. Using this representation we express the surface velocity as a convolution of the fundamental solution with the interfacial curvature forcing and analyze its normal limit to derive a boundary integral equation for the moving curve. Independently, exploiting the DtN representation we establish a curve-shortening identity: the interfacial perimeter decreases monotonically and its time derivative is controlled by $\dot{H}^{1/2}(\mathbb{R}^2)$-norm of the surface velocity. Building on the boundary integral equation, we prove local well-posedness via maximal $L^2$-regularity for quasilinear parabolic systems, employing a DeTurck-type reparametrization, and show equivalence with the original ILLSS system. Finally, we introduce a linearly implicit parametric finite-element scheme which captures experimentally observed relaxation dynamics.

math.AP↗

arXiv2025

Sharp Interface Dynamics in a Minimal Non-Reciprocal Cahn-Hilliard System

Interest in non-reciprocally coupled systems recently led to the introduction of a minimal non-reciprocally coupled Cahn-Hilliard (CH) model by Brauns and Marchetti in 2024 arXiv:2306.08868, which we refer to as the Brauns-Marchetti (BM) model. This model can be seen as a conservative counterpart to the spatially extended FitzHugh-Nagumo model. Lacking a gradient structure, the BM model was observed to exhibit interesting dynamics including traveling periodic wave-trains and other coherent structures, as well as spatiotemporal chaos in certain parameter regimes. In this paper, we derive an effective equation for the interface dynamics of solutions to the BM model in $\mathbb{R}^2$ in the sharp-interface limit. The resulting system of equations is a generalization of the classical Mullins-Sekerka (MS) equations, which we refer to as the modified MS equations. We show that the modified MS equation shares some properties with its classical counterpart, but importantly, it is not in general a length minimizing flow. To illustrate the utility of this asymptotic reduction in the sharp interface limit, we perform a detailed analysis of stationary and periodic wave-trains, systematically deriving expressions for wave-train speeds and stability thresholds. The methods used here should be applicable to other non-reciprocally coupled CH models and therefore provide another avenue for their more detailed analysis.

math-ph↗

arXiv2025

Isochronal Phase Reduction and Speed Correction of a Pulse in a Stochastic Kinematic Model

We develop a method for computing the stochastic wave speed of pulse solutions in kinematic equations subject to small stochastic forcing based on the isochronal phase reduction. These kinematic equations arise as the singular limit of sharp pulse solutions in the FitzHugh-Nagumo system, and our approach contributes a new perspective and method to the growing body of work on stochastic wave propagation in excitable media. The method yields an effective Itô process for the wave's position. The coefficients of the Itô process can be computed deterministically allowing for efficient computation. We demonstrate the efficiency and accuracy of our method through numerical demonstrations.

math.DS↗

arXiv2025

Modeling and Simulation of Open Membranes in Stokes Flow with Mixed-Dimensional Coupling

In this work, we present a mathematical and computational framework to model the dynamics of open lipid bilayer membranes interacting with ambient Stokes flow. The model explicitly couples the three-dimensional viscous fluid, the two-dimensional membrane surface, and its one-dimensional free edge. We develop an axisymmetric hybrid BEM-FEM method that solves the problem with an effective one-dimensional formulation. A key component is a local mesh refinement strategy designed to accurately resolve singularities and boundary layers originating at the membrane edge. Several numerical examples are provided to showcase its ability to capture intricate edge dynamics and multiscale fluid-membrane coupling.

math.NA↗

arXiv2025

Self-construction and destruction of living transport networks

Biological transport networks adapt through dynamic interactions between material transport and structural modification during growth and development. In this work, we present a model of transport network growth driven by local material concentration. Using an advection-diffusion framework on a metric graph with a tip growth rule, we investigate how successive construction and destruction influence network development. Our results reveal that while repeated cycles of elongation and retraction can facilitate growth enhancement, a network need to have a structure that mitigates material dissipation. This finding suggests that additional regulatory mechanisms are necessary for networks to efficiently redistribute resources following structural retraction.

physics.bio-ph↗

arXiv2025

Strong convergence with error estimates for a stochastic compartmental model of electrophysiology

This paper presents a rigorous mathematical analysis, alongside simulation studies, of a spatially extended stochastic electrophysiology model, the Hodgkin-Huxley model of the squid giant axon being a classical example. Although most studies in electrophysiology do not account for stochasticity, it is well known that ion channels regulating membrane voltage open and close randomly due to thermal fluctuations. We introduce a spatially extended compartmental model in which this stochastic behavior is captured through a piecewise-deterministic Markov process (PDMP). Space is discretized into n compartments each of which has at most one ion channel. We also devise a numerical method to simulate this stochastic model and illustrate the numerical method by simulation studies. We show that a classical system of partial differential equations (PDEs) approximates the stochastic system as $n \to \infty$. Unlike existing results, which focus on weak convergence or convergence in probability, we establish an almost sure convergence result with a precise error bound of order $n^{1/3}$. Our findings broaden the current understanding of stochastic effects in spatially structured neuronal models and have potential applications in studying random ion channel configurations in neurobiology. Additionally, our proof leverages ideas from homogenization theory in PDEs and can potentially be applied to other PDMPs or accommodate other ion channel distributions with random spacing or defects.

math.PR↗

arXiv2024

The Immersed Inextensible Interface Problem in 2D Stokes Flow

We study the dynamics of an inextensible, closed interface subject to bending forces and immersed in a two-dimensional and incompressible Stokes fluid. We formulate the problem as a boundary integral equation in terms of the tangent angle and demonstrate the well-posedness in suitable time-weighted spaces of the resulting nonlinear and nonlocal system. The solution is furthermore shown to be smooth for positive times. Numerical computations are performed to initiate the study of the long-time behavior of the interface.

math.AP↗

arXiv2023

Finite population effects on optimal communication for social foragers

Foraging is crucial for animals to survive. Many species forage in groups, as individuals communicate to share information about the location of available resources. For example, eusocial foragers, such as honey bees and many ants, recruit members from their central hive or nest to a known foraging site. However, the optimal level of communication and recruitment depends on the overall group size, the distribution of available resources, and the extent of interference between multiple individuals attempting to forage from a site. In this paper, we develop a discrete-time Markov chain model of eusocial foragers, who communicate information with a certain probability. We compare the stochastic model and its corresponding infinite-population limit. We find that foraging efficiency tapers off when recruitment probability is too high -- a phenomenon that does not occur in the infinite-population model, even though it occurs for any finite population size. The marginal inefficiency at high recruitment probability increases as the population increases, similar to a boundary layer. In particular, we prove there is a significant gap between the foraging efficiency of finite and infinite population models in the extreme case of complete communication. We also analyze this phenomenon by approximating the stationary distribution of foragers over sites in terms of mean escape times from multiple quasi-steady states. We conclude that for any finite group of foragers, an individual who has found a resource should only sometimes recruit others to the same resource. We discuss the relationship between our analysis and multi-agent multi-arm bandit problems.

q-bio.PE↗

arXiv2023

The Tension Determination Problem for an Inextensible Interface in 2D Stokes Flow

Consider an inextensible closed filament immersed in a 2D Stokes fluid. Given a force density $\mathbf{F}$ defined on this filament, we consider the problem of determining the tension $σ$ on this filament that ensures the filament is inextensible. This is a subproblem of dynamic inextensible vesicle and membrane problems, which appear in engineering and biological applications. We study the well-posedness and regularity properties of this problem in Hölder spaces. We find that the tension determination problem admits a unique solution if and only if the closed filament is {\em not} a circle. Furthermore, we show that the tension $σ$ gains one derivative with respect to the imposed line force density $\mathbf{F}$, and show that the tangential and normal components of $\mathbf{F}$ affect the regularity of $σ$ in different ways. We also study the near singularity of the tension determination problem as the interface approaches a circle, and verify our analytical results against numerical experiment.

math.AP↗

arXiv2023

Well-Posedness of the 3D Peskin Problem

This paper introduces the 3D Peskin problem: a two-dimensional elastic membrane immersed in a three-dimensional steady Stokes flow. We obtain the equations that model this free boundary problem and show that they admit a boundary integral reduction, providing an evolution equation for the elastic interface. We consider general nonlinear elastic laws, i.e., the fully nonlinear Peskin problem, and prove that the problem is well-posed in low-regularity Hölder spaces. Moreover, we prove that the elastic membrane becomes smooth instantly in time.

math.AP↗