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Front Propagation of a Sexual Population with Evolution of Dispersion: A Formal Analysis
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 4) |
| Halaman | : | 1441-1460 |
| Abstrak | : | The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the context of invasions, when considering the evolution of a heritable trait that encodes the dispersive ability of individuals, the trait distribution develops a particular spatial structure that leads to the acceleration of the front propagation. That phenomenon is known as spatial sorting. Many biological examples can be cited like the bush cricket in Britain, the cane toad invasion in Australia, or the common myna one in South Africa. Adopting this framework, recent mathematical studies have led to highlighting the influence of the reproductive mode on the front propagation. Asexual populations have been shown to spread with an asymptotic rate of ????3/2 in a minimal reaction-diffusion model, whereas the analogous rate for sexual populations is of ????5/4 (where ???? denotes the time). However, the precise description of the behavior of the front propagation in the sexual case is still an open question. The aim of this paper is to give precise approximations for large times of its position, as well as some features of the local trait distribution at the front. To do so, we solve explicitly the asymptotic problem derived formally. Numerical simulations are shown to confirm these calculations. |
Enhanced Electrodiffusive Transport Across a Mucus Layer
| Pengarang | : | Owen L. Lewis |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 3) |
| Halaman | : | 965-981 |
| Abstrak | : | Diffusive transport of small ionic species through mucus layers is a ubiquitous phenomenon in physiology. However, some debate remains regarding how the various characteristics of mucus (charge of the polymers themselves, binding affinity of ions with mucus) impact the rate at which small ions may diffuse through a hydrated mucus gel. Indeed, it is not even clear if small ionic species diffuse through mucus gel at an appreciably different rate than they do in aqueous solution. Here, we present a mathematical description of the transport of two ionic species (hydrogen and chloride) through a mucus layer based on the Nernst--Planck equations of electrodiffusion. The model explicitly accounts for the binding affinity of hydrogen to the mucus material as well as the Donnan potential that occurs at the interface between regions with and without mucus. Steady-state fluxes of ionic species are quantified, as are their dependencies on the chemical properties of the mucus gel and the composition of the bath solution. We outline a mechanism for generating enhanced diffusive flux of hydrogen across the gel region and hypothesize how this mechanism may be relevant to the apparently contradictory experimental data in the literature. |
Level Set--Based Shape Optimization Approach for Sharp-Interface Reconstructions in Time-Domain Full Waveform Inversion
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 3) |
| Halaman | : | 939-964 |
| Abstrak | : | Velocity models presenting sharp interfaces are highly relevant in seismic imaging, e.g., for imaging the subsurface of the Earth in the presence of salt bodies. In order to mitigate the oversmoothing of classical regularization strategies such as the Tikhonov regularization, we propose a shape optimization approach for the sharp-interface reconstruction in time-domain acoustic full waveform inversion. Our main result includes the shape differentiability of the cost functional measuring the misfit between observed and predicted data. In particular, it reveals the expression of the distributed shape derivative in tensor form, built on a Lagrangian-type approach and regularity results for the wave equation with discontinuous coefficients. Based on the achieved distributed shape derivative and the level set method, we propose a numerical approach and present several numerical tests supporting our approach. |
Analysis of Contagion Maps on a Class of Networks That Are Spatially Embedded in a Torus
| Pengarang | : | Barbara I. Mahler |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 4) |
| Halaman | : | 1416-1440 |
| Abstrak | : | Spreading processes on networks with some underlying spatial structure can be influenced by that structure, and it is insightful to study the extent to which a spreading process follows a network's underlying geometry. We consider a threshold contagion model on networks whose nodes are embedded in a manifold and which have both “geometric edges,” which respect the geometry of the underlying manifold, and “nongeometric edges,” which are not constrained by that geometry. Building on ideas from Taylor et al. [Nat. Commun., 6 (2015), 7723], we examine when a contagion propagates as a wave along a network whose nodes are embedded in a torus and when it jumps via long nongeometric edges to remote areas of the network. We build a “contagion map” for a contagion spreading on such a “noisy geometric network” to produce a point cloud, and we study the dimensionality, geometry, and topology of this point cloud to examine qualitative properties of this spreading process. We identify a region in parameter space in which the contagion propagates predominantly via wavefront propagation. We consider different probability distributions for constructing nongeometric edges---reflecting different decay rates with respect to the distance between nodes in the underlying manifold---and examine the effect of such choices on the qualitative properties of the spreading dynamics. Our work generalizes the analysis in Taylor et al. [Nat. Commun., 6 (2015), 7723] and consolidates contagion maps both as a tool for investigating spreading behavior on spatial networks and as a technique for manifold learning. |
Directional Search-and-Capture Model of Cytoneme-Based Morphogenesis
| Pengarang | : | Paul C. Bressloff |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 3) |
| Halaman | : | 919-938 |
| Abstrak | : | In this paper we develop a directional search-and-capture model of cytoneme-based morphogenesis. We consider a single cytoneme nucleating from a source cell and searching for a set of ???? target cells Ω???? ⊂?????, ???? =1,…,????, with ???? ≥2. We assume that each time the cytoneme nucleates, it grows in a random direction so that the probability of being oriented toward the ????th target is ???????? with ∑????????=1???????? <1. Hence, there is a nonzero probability of failure to find a target unless there is some mechanism for returning to the nucleation site and subsequently nucleating in a new direction. We model the latter as a 1D search process with stochastic resetting, finite return times, and refractory periods. We use a renewal method to calculate the splitting probabilities and conditional mean first passage times for the cytoneme to be captured by a given target cell. We then determine the steady-state accumulation of morphogen over the set of target cells following multiple rounds of search-and-capture events and morphogen degradation. This then yields the corresponding morphogen gradient across the set of target cells whose steepness depends on the resetting rate. We illustrate the theory by considering a single layer of target cells and discuss the extension to multiple cytonemes. |
Morphomechanical Model of the Torsional C-Looping in the Embryonic Heart
| Pengarang | : | Giulia Bevilacqua |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 3) |
| Halaman | : | 897-918 |
| Abstrak | : | Before septation processes shape its four chambers, the embryonic heart is a straight tube that spontaneously bends and twists breaking the left-right symmetry. In particular, the heart tube is subjected to a cell remodeling inducing ventral bending and dextral torsion during the c-looping phase. In this work we propose a morphomechanical model for the torsion of the heart tube that behaves as a nonlinear elastic body. We hypothesize that this spontaneous looping can be modeled as a mechanical instability due to accumulation of residual stresses induced by the geometrical frustration of tissue remodeling, which mimics the cellular rearrangement within the heart tube. Thus, we perform a linear stability analysis of the resulting nonlinear elastic boundary value problem to determine the onset of c-looping as a function of the geometry of the tube and of the internal remodeling rate. We perform numerical simulations to study the fully nonlinear morphological transition, showing that the soft tube develops a realistic self-contacting looped shape in the physiological range of geometrical parameters. |
Simulation of Localized Surface Plasmon Resonances in Two Dimensions via Impedance-Impedance Operators
| Pengarang | : | |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 3) |
| Halaman | : | 871-896 |
| Abstrak | : | It is critically important that engineers be able to numerically simulate the scattering of electromagnetic radiation by bounded obstacles. Additionally, that these simulations be robust and highly accurate is necessitated by many applications of great interest. High-order spectral algorithms applied to interfacial formulations can rapidly deliver high fidelity approximations with a modest number of degrees of freedom. The class of high-order perturbation of surfaces methods has proven to be particularly appropriate for these simulations, and in this contribution we consider questions of both practical implementation and rigorous analysis. For the former we generalize our recent results to utilize the uniformly well-defined impedance-impedance operators rather than the Dirichlet--Neumann operators which occasionally encounter unphysical singularities. For the latter we utilize this new formulation to establish the existence, uniqueness, and analyticity of solutions in non-resonant configurations. We also include results of numerical simulations based on an implementation of our new formulation which demonstrates its noteworthy accuracy and robustness. |
Spontaneous Wave Formation in Stochastic Self-Driven Particle Systems
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 3) |
| Halaman | : | 853-870 |
| Abstrak | : | Waves and oscillations are commonly observed in the dynamics of self-driven agents such as pedestrians or vehicles. Interestingly, many factors may perturb the stability of space homogeneous streaming, leading to the spontaneous formation of collective oscillations of the agents related to stop-and-go waves, jamiton, or phantom jam in the literature. In this article, we demonstrate that even a minimal additive stochastic noise in stable first-order dynamics can initiate stop-and-go phenomena. The noise is not a classic white one but a colored noise described by a Gaussian Ornstein--Uhlenbeck process. It turns out that the joint dynamics of particles and noises forms again a (Gaussian) Ornstein--Uhlenbeck process whose characteristics can be explicitly expressed in terms of parameters of the model. We analyze its stability and characterize the presence of waves through oscillation patterns in the correlation and autocorrelation of the distance spacing between the particles. We determine exact solutions for the correlation functions for the finite system with periodic boundaries and in the continuum limit when the system size is infinite. Finally, we compare experimental trajectories of single-file pedestrian motions to simulation results. |
A Transition-Loss Theory for Waves Reflected and Transmitted by an Overwashed Body
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 3) |
| Halaman | : | 834-852 |
| Abstrak | : | A transition-loss theory for waves reflected by an overwashed step and transmitted by an overwashed plate is presented. The theory is based on a conservation of energy technique to correct the transmission/reflection predicted by linear potential flow theory by taking into account the energy flux into the overwash and the mechanical energy dissipated by the formation of overwash. Wave energy dissipation is calculated by assuming that the transition from deep water to shallow water flow occurs over a sufficiently narrow domain such that it can be modeled as a discontinuity in the flow (akin to a hydraulic jump). Theoretical predictions are compared to CFD model data for the step problem and laboratory experimental measurements for the plate problem. Generally, excellent agreement is found for all cases tested, and the theory gives significant improvements compared to linear models that do not capture overwash effects and a theory that does not account for energy loss in the transition domain. |
Passive Communication with Ambient Noise
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 3) |
| Halaman | : | 814-833 |
| Abstrak | : | Motivated by applications to wireless communications, this paper addresses the propagation of waves transmitted by ambient noise sources and interacting with metamaterials. We discuss a generalized Helmholtz--Kirchhoff identity that is valid in dispersive media and characterize the statistical properties of the empirical cross spectral density of the wave field. We can then introduce and analyze an original communication scheme between two passive arrays that uses only ambient noise illumination. The passive transmitter array does not transmit anything, but it is a tunable metamaterial surface that can modulate its dispersive properties and encode a message in the modulation. The passive receiver array made of two receivers that are half a wavelength apart from each other can decode the message from the empirical cross spectral density of the wave field. |