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A MODEL OF SEASONAL SAVANNA DYNAMICS
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 122-143 |
| Abstrak | : | We introduce a mathematical model of savanna vegetation dynamics. The usual approach of nonequilibrium ecology is extended by including the impact of wet and dry seasons. We present and rigorously analyze a model describing a mixed woodland-grassland ecosystem with stochastic environmental noise in the form of vegetation biomass losses manifesting fires. Both the probability of ignition and the strength of these losses depend on the current season (as well as vegetation growth rates, etc.). Formally it requires an introduction and analysis of a system that is a piecewise deterministic Markov process with parameters switching between given constant periods of time. We study the long time behavior of time averages for such processes. |
FOURIER REPRESENTATION OF THE DIFFUSION MRI SIGNAL USING LAYER POTENTIALS
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 99-121 |
| Abstrak | : | The diffusion magnetic resonance imaging (MRI) signal arising from biological tissues can be numerically simulated by solving the Bloch-Torrey partial differential equation. Numerical simulations can facilitate the investigation of the relationship between the diffusion MRI signals and cellular structures. With the rapid advance of available computing power, the diffusion MRI community has begun to employ numerical simulations for model formulation and validation, as well as for imaging sequence optimization. Existing simulation frameworks use the finite difference method, the finite element method, or the Matrix Formalism method to solve the Bloch-Torrey partial differential equation. We propose a new method based on the efficient evaluation of layer potentials. In this paper, the mathematical framework and the numerical implementation of the new method are described. We demonstrate the convergence of our method via numerical experiments and analyze the errors linked to various model and simulation parameters. Since our method provides a Fourier-type representation of the diffusion MRI signal, it can potentially facilitate new physical and biological signal interpretations in the future. |
KP-IIAPPROXIMATIONFORASCALARFERMI-PASTA-ULAM SYSTEM ON A 2D SQUARE LATTICE
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 79-98 |
| Abstrak | : | WeconsiderascalarFermi-Pasta-Ulam(FPU)systemonasquaretwo-dimensional lattice. TheKadomtsev-Petviashvili (KP-II) equationcanbederivedbymeansofmultiple scale expansionstodescribeunidirectional longwavesof smallamplitudewithslowlyvaryingtransverse modulations.WeshowthattheKP-IIapproximationmakescorrectpredictionsaboutthedynamics of theoriginalFPUsystem.Anexistingapproximationresult isextendedtoanarbitrarydirection ofwavepropagation.ThemainnoveltyofthisworkistheuseofaFouriertransformintheanalysis oftheFPUsysteminstrainvariables. |
EQUIVALENT FORMULATIONS OF THE OXYGEN DEPLETION PROBLEM, OTHER IMPLICIT MOVING BOUNDARY VALUE PROBLEMS, AND IMPLICATIONS FOR NUMERICAL APPROXIMATION
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 52-78 |
| Abstrak | : | The oxygen depletion problem is an implicit moving boundary value problem. The dynamics allow topological changes in the moving boundary. We show several mathematical formu lations of this model from the literature and give a new formulation based on a gradient flow with constraint. All formulations are shown to be equivalent. We explore the possibilities for the numeri cal approximation of the problem that arise from the different formulations. We show a convergence result for an approximation based on the gradient flow with constraint formulation that applies to the general dynamics including topological changes. More general (vector, higher order) implicit moving boundary value problems are discussed. Several open problems are described. |
PARAXIAL WAVE PROPAGATION IN RANDOM MEDIA WITH LONG-RANGE CORRELATIONS
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 25-51 |
| Abstrak | : | We study the paraxial wave equation with a randomly perturbed index of refraction, which can model the propagation of a wave beam in a turbulent medium. The random perturbation is a stationary and isotropic process with a general form of the covariance that may or may not be integrable. We focus attention mostly on the nonintegrable case, which corresponds to a random perturbation with long-range correlations, that is, relevant for propagation through a cloudy turbu lent atmosphere. The analysis is carried out in a high-frequency regime where the forward scattering approximation holds. It reveals that the randomization of the wave field is multiscale: The travel time of the wave front is randomized at short distances of propagation, and it can be described by a fractional Brownian motion. The wave field observed in the random travel time frame is affected by the random perturbations at long distances, and it is described by a Schr\"odinger-type equation driven by a standard Brownian field. We use these results to quantify how scattering leads to decor relation of the spatial and spectral components of the wave field and to a deformation of the pulse emitted by the source. These are important questions for applications, such as imaging and free space communications with pulsed laser beams through a turbulent atmosphere. We also compare the results with those used in the optics literature, which are based on the Kolmogorov model of turbulence. We show explicitly that the commonly used approximations for the decorrelation of spatial and spectral components are appropriate for the Kolmogorov model but fail for models with long-range correlations. |
WAVE PROPAGATION ON A STRING RESTING ON A GENERAL NONLINEAR SUBSTRATE
| Pengarang | : | Demeio, Lucio,Lenci, Stefano |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 1-24 |
| Abstrak | : | Traveling waves propagating on a taut cable resting on an elastic substrate are in vestigated by an equivalent mechanical model based on the classical Klein-Gordon equation. The formulation is devised for an elastic response of generally arbitrary shape, and permits one to compute the propagation wave velocity without solving the equation of motion, thus providing a unified the oretical framework for a large class of response functions, linear or nonlinear, smooth or nonsmooth. The general solution is then applied to the cases of a general polynomial substrate, a bilinear sub strate, a bilinear substrate with a cubic correction, and a negative linear stiffness substrate, all of them falling within the realm of nonsmooth systems when a piecewise continuous stiffness is chosen; in the second one, we recover results present in the literature and obtained by employing a method based on matching conditions, which are spared in the approach used in this paper. Finally, the application to the sine-Gordon equation is considered. |
The Vitruvian Man: An Introduction to Measurement and Data Analysis
| Pengarang | : | Freek Pols |
| Nama Majalah/Jurnal | : | The Physics Teacher |
| Volume / Edisi | : | 62 (No. 5) |
| Halaman | : | 356-359 |
| Abstrak | : | Valuable learning objectives of (experimental) physics education include developing in students the ability to design adequate methods and procedures, analyze data, and draw appropriate conclusions, including the specification of limitations to the validity.1 We have specified these learning goals as the understandings of evidence (UoE)2—insights and views that an experimental researcher relies on in constructing and evaluating scientific evidence. To build a foundation on which we can further develop these insights in my first-year physics lab course, I have redesigned an activity that is part of a teaching–learning sequence on scientific inquiry in secondary education.3 With this activity, deep questions about science, methodology, and validity are raised using simple means. I present the details pertaining to the intervention, the learning goals, and questions that can be addressed during this activity. Possibilities to adopt, adapt, and expand the activity are provided. |
Analyzing Vertical Circular Motion and Damped Oscillations Using a Smartphone Accelerometer
| Pengarang | : | Sándor Egri |
| Nama Majalah/Jurnal | : | The Physics Teacher |
| Volume / Edisi | : | 62 (No. 5) |
| Halaman | : | 350-355 |
| Abstrak | : | The simpler forms of circular motion are uniform and uniformly accelerating circular motion, which are part of the primary and secondary school physics curriculum in most countries. The more complicated case, with constantly changing tangential acceleration, also appears in many course books at advanced levels.1 Indeed, this kind of movement is often present in everyday life. Take, for example, the typical school experiment of placing a glass of water on a tray suspended on strings, and then rotating the tray in a vertical circle. If one is skillful enough and rotates the tray at a high enough speed, not a single drop of water will flow out of the glass, even when it is upside down (see Fig. 1). A similar kind of motion investigated using a smartphone in Ref. 2. |
Experimental Evidence for the Direction of Friction on a Pulled Spool
| Pengarang | : | Bjarne Schmidt |
| Nama Majalah/Jurnal | : | The Physics Teacher |
| Volume / Edisi | : | 62 (No. 5) |
| Halaman | : | 346-349 |
| Abstrak | : | Even though the concepts of force and moments of force are key ideas taught in any preuniversity physics course, it is well known that many students face severe difficulties because of faulty or incomplete understanding of these notions even in higher education.1 Not only do the students struggle with understanding these concepts at a qualitative level, but the difficulties may go undetected in traditional problem solving because a student with some superficial knowledge and formula manipulation techniques can mask their inadequate comprehension of the underlying concepts. The basic misconceptions are highly resistant to change, and they are remarkably similar to misconceptions treated as early as the 17th century by Galileo!2 |
HEAT GENERATION USING LORENTZIAN NANOPARTICLES. THE FULL MAXWELL SYSTEM
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 1) |
| Halaman | : | 285-315 |
| Abstrak | : | We analyze and quantify the amount of heat generated by a nanoparticle, injected in a background medium, while excited by incident electromagnetic waves. These nanoparticles are dispersive with electric permittivity following the Lorentz model. The purpose is to determine the quantity of heat generated extremely close to the nanoparticle (at a distance proportional to the radius of the nanoparticle). This study extends our previous results, derived in the 2D TM and TE regimes, to the full Maxwell system. We show that by exciting the medium with incident frequencies close to the plasmonic or Dielectric resonant frequencies, we can generate any desired amount of heat close to the injected nanoparticle while the amount of heat decreases away from it. These results offer a wide range of potential applications in the areas of photo-thermal therapy, drug delivery, and material science, to cite a few. To do so, we employ time-domain integral equations and asymptotic analysis techniques to study the corresponding mathematical model for heat generation. This model is given by the heat equation where the body source term comes from the modulus of the electric field generated by the used incident electromagnetic field. Therefore, we first analyze the dominant term of this electric field by studying the full Maxwell scattering problem in the presence of plasmonic or all-dielectric nanoparticles. As a second step, we analyze the propagation of this dominant electric f ield in the estimation of the heat potential. For both the electromagnetic and parabolic models, the presence of the nanoparticles is translated into the appearance of large scales in the contrasts for the heat-conductivity (for the parabolic model) and the permittivity (for the full Maxwell system) between the nanoparticle and its surroundings. |