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BOUND-PRESERVING FINITE-VOLUME SCHEMES FOR SYSTEMS OF CONTINUITY EQUATIONS WITH SATURATION
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1315-1339 |
| Abstrak | : | We propose finite-volume schemes for general continuity equations which preserve positivity and global bounds that arise from saturation effects in the mobility function. In the case of gradient flows, the schemes dissipate the free energy at the fully discrete level. Moreover, these schemes are generalized to coupled systems of nonlinear continuity equations, such as multispecies models in mathematical physics or biology, preserving the bounds and the dissipation of the energy whenever applicable. These results are illustrated through extensive numerical simulations which explore known behaviors in biology and showcase new phenomena not yet described by the literature. |
TIME- VERSUS FREQUENCY-DOMAIN INVERSE ELASTIC SCATTERING: THEORY AND EXPERIMENT
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1296-1324 |
| Abstrak | : | This study formally adapts the time-domain linear sampling method (TLSM) for ultrasonic imaging of stationary and evolving fractures in safety-critical components. The TLSM indicator is then applied to the laboratory test data of [F. Pourahmadian and H. Yue, Inverse Problems, 37 (2021), 055012; F. Pourahmadian, Mech. Syst. Signal Process., 161 (2021), 108029] and the obtained reconstructions are compared to their frequency-domain counterparts. The results highlight the unique capability of the time-domain imaging functional for high-fidelity tracking of evolving damage, and its relative robustness to sparse and reduced-aperture data at moderate noise levels. A comparative analysis of the TLSM images against the multifrequency LSM maps of [F. Pourahmadian and H. Yue, Inverse Problems, 37 (2021), 055012] further reveals that thanks to the full-waveform inversion in time and space, the TLSM generates images of remarkably higher quality with the same dataset. |
OPTIMAL STOCHASTIC CONTROL PROBLEM FOR A CARBON EMISSION REDUCTION PROCESS
| Pengarang | : | Huang, Wenlin,Liang, Jin,Dong, Yuchao |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1272-1295 |
| Abstrak | : | In this paper, we study a stochastic optimization control problem for carbon emis sion reduction with two control variables, one of which is the stochastic emission reduction control strategy, and the other is the auction amount of carbon allowances. We optimize the total emission reduction cost by a two- step process. Fixing the auction amount, we optimize the emission reduction control strategy, and then relate the value function to a Hamilton-Jacobi-Bellman (HJB) equation. The existence and uniqueness of the classical solution of the equation are provedso as to describe the optimal control strategy. After that, we find the optimal auction amount by determiningthe zero point of the derivative. We then show that the auction amount minimizingthe total cost is unique in a special case. Finally, the relationships between the optimal auction amount and the total cost and various parameters are discussed through numerical results. |
ACCUMULATION OF PARTICLES TOWARDS THE ENVELOPE OF A FLUID-INFUSED PATCH UNDER EVAPORATION
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1245-1271 |
| Abstrak | : | We study the dynamics of unsaturated flows within a fluid-infused wet patch in a thin porous layer, coupled with the transport of passive particles, partly inspired by some art practice and environmental and industrial activities. The role of wetting and capillary forces and the influence of evaporation are both emphasized. Two coupled partial differential equations (PDEs) are first derived to describe the time evolution of the fluid saturation and concentration of passive particles. Three dimensionless parameters are identified after appropriate nondimensionalization of the coupled PDEs, the influence of which is demonstrated through asymptotic and numerical solutions at both the early and late times. With evaporation, in particular, the fluid front first arrives at a maximum location after an initial period of spreading. Thereafter, the front starts to recede until the fluid drains out at a finite time. Correspondingly, the concentration of particles blows up at a finite time, when the size of the wet region shrinks to zero. Meanwhile, the spatial distribution of particles evolves towards a universal curve near the front at late times, as the particles gradually accumulate at the front of the wet patch. It is recognized that, while the spreading of fluid within a porous layer behaves similar to that of a viscous gravity current subject to volume loss, the frontal structure for the concentration of particles, to some extent, is similar to that of an intruding inviscid gravity current |
PHASE REDUCTION OF WAVES, PATTERNS, AND OSCILLATIONS SUBJECT TO SPATIALLY EXTENDED NOISE
| Pengarang | : | Maclaurin, J. |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1215-1244 |
| Abstrak | : | In this paper we present a framework in which one can rigorously study the effect of spatio-temporal noise on traveling waves, stationary patterns, and oscillations that are invariant under the action of a finite-dimensional set of continuous isometries (such as translation or rotation). This formalism can accommodate patterns, waves, and oscillations in reaction-diffusion systems and neural field equations. To do this, we define the phase by precisely projecting the infinite-dimensional system onto the manifold of isometries. We outline a precise stochastic differential equation for the phase. The phase is then used to show that the probability of the system leaving the attracting basin of the manifold after an exponentially long period of time (in \epsilon - 2, the magnitude of the noise) is exponentially unlikely. |
ON ANINVERSE PROBLEM FOR THE PLATE EQUATION WITH PASSIVE MEASUREMENT
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1196-1214 |
| Abstrak | : | This paper focuses on an inverse problem associated with the plate equation which is derived from models in fluid mechanics and elasticity. We establish the unique identifying results in simultaneously determining both the unknown density and the internal sources from the passive boundary measurement. The proof mainly relies on the asymptotic analysis and harmonic analysis on integral transforms. |
AGRO-ECOLOGICAL CONTROL OF A PEST-HOST SYSTEM: PREVENTING SPREADING
| Pengarang | : | Giardin, Leo,Maucourt, Baptiste |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1172-1195 |
| Abstrak | : | We consider an agro-ecologically motivated coupling between a prey-predator system and a vector-borne epidemic system. The coupled system contains one ODE, two reaction-diffusion PDEs, and one reaction-diffusion-advection PDE; it has no complete variational or monotonic struc ture and coefficients are spatially heterogeneous. We study the long-time behavior of solutions of the Cauchy-Neumann problem, which turns out to be largely decided by a linear stability criterion but still involves nonlinear subtleties. Then we consider an optimal control problem. Although it remains elusive analytically, we show numerically the variety of outcomes and the strong impact of the initial conditions. |
THE DYNAMICS OF A COLLAPSING POLYELECTROLYTE GEL
| Pengarang | : | PK Purwadi |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1146-1171 |
| Abstrak | : | We analyse the dynamics of different routes to collapse of a constrained polyelec trolyte gel in contact with an ionic bath. The evolution of the gel is described by a model that incorporates non-linear elasticity, Stefan-Maxwell diffusion and interfacial gradient free energy to account for phase separation of the gel. A bifurcation analysis of the homogeneous equilibrium states reveals three solution branches at low ion concentrations in the bath, giving way to only one above a critical ion concentration. We present numerical solutions that capture both the spatial heterogeneity and the multiple timescales involved in the process of collapse. These solutions are complemented by two analytical studies. Firstly, a phase-plane analysis that reveals the existence of a depletion front for the transition from the highly swollen to the new collapsed equilibrium state. This depletion front is initiated after the fast ionic diffusion has set the initial condition for this time regime. Secondly, we perform a linear stability analysis about the homogeneous states that show that for a range of ion concentrations in the bath, spinodal decomposition of the swollen state gives rise to localized solvent-rich(poor) and, due to the electroneutrality condition, ion-poor(rich) phases that coarsen on the route to collapse. This dynamics of a collapsing polyelectrolyte gel has not been described before. |
APODIZER DESIGN TO EFFICIENTLY COUPLE LIGHT INTO A FIBER BRAGG GRATING
| Pengarang | : | Adriazola, Jimmie,Goodman, Roy H. |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1126-1145 |
| Abstrak | : | We provide an optimal control framework for efficiently coupling light in a bare fiber into Bragg gratings with cubic nonlinearity. The light-grating interaction excites gap solitons, a type of localized nonlinear coherent state which propagates with a central frequency in the forbidden band gap, resulting in a dramatically slower group velocity. Due to the nature of the band gap, a substantial amount of light is back-reflected by the grating's strong reflective properties. We optimize, via a projected gradient descent method, the transmission efficiency of previously designed nonuniform grating structures in order to couple more slow light into the grating. We further explore the space of possible grating designs, using genetic algorithms, along with a previously unexplored design parameter: the grating chirp. Through these methods, we find structures that couple a greater fraction of light into the grating with the added bonus of creating slower pulses. |
MODELING IMMUNITY TO MALARIA WITH AN AGE-STRUCTURED PDE FRAMEWORK
| Pengarang | : | Qu, Zhiolin [et al...] |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1098-1125 |
| Abstrak | : | Malaria is one of the deadliest infectious diseases globally, causing hundreds of thou sands of deaths each year. It disproportionately affects young children, with two-thirds of fatalities occurring in under-fives. Individuals acquire protection from disease through repeated exposure, and this immunity plays a crucial role in the dynamics of malaria spread. We develop a novel age structured PDE malaria model, which couples vector-host epidemiological dynamics with immunity dynamics. Our model tracks the acquisition and loss of antidisease immunity during transmission and its corresponding nonlinear feedback onto the transmission parameters. We derive the basic reproduction number (\scrR 0) as the threshold condition for the stability of disease-free equilibrium; we also interpret \scrR 0 probabilistically as a weighted sum of cases generated by infected individu als at different infectious stages and different ages. We parametrize our model using demographic and immunological data from sub-Saharan regions. Numerical bifurcation analysis demonstrates the existence of an endemic equilibrium, and we observe a forward bifurcation in \scrR 0. Our numerical simulations reproduce the heterogeneity in the age distributions of immunity profiles and infection status created by frequent exposure. Motivated by the recently approved RTS,S vaccine, we also study the impact of vaccination; our results show a reduction in severe disease among young children but a small increase in severe malaria among older children due to lower acquired immunity from delayed exposure. |