OPAC - Pencarian Artikel Jurnal & Majalah Library USD
Menampilkan semua artikel (Halaman 230 dari 34169, Total: 341690 data)
Near-Exact Radiating Fins via Boundary Tracing
klik untuk membaca file PDF
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1356-1368 |
| Abstrak | : | In contexts such as space travel, thermal radiation is the primary mode of heat transfer. The Stefan--Boltzmann law gives rise to a boundary flux which is quartic in temperature, and this nonlinearity renders even the simplest of conduction--radiation problems analytically insurmountable in more than one dimension. An unconventional approach known as boundary tracing allows for analytical inroads into flux boundary value problems that would otherwise require numerical study. In this paper, the method of boundary tracing is used to generate near-exact results for an infinite family of conduction--radiation domains representing radiating fins; realistic lengths and temperatures can be realized. |
Time and Energy Costs for Synchronization of Kuramoto-Oscillator Networks With or Without Noise Perturbation
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1336-1355 |
| Abstrak | : | In this paper, time and energy costs for achieving synchronization of the Kuramoto-oscillator network with or without noise perturbation are investigated. In order to achieve synchronization and optimize time and energy consumption, a novel switching controller is designed, which combines the advantages of both the proportional feedback control method and the finite-time control technology. Sufficient conditions for achieving synchronization are established, and the estimates of time and energy costs are obtained mathematically as well. Particularly, the theoretical analysis and simulating calculation show that there exists a trade-off between time and energy costs. That is to say, the energy consumption can be reduced by adjusting the control parameters, but the time cost will increase inevitably, and vice versa. Further, we find that for fixed weights of time and energy costs of the performance index, the optimal values of parameters can be chosen to minimize the total cost. |
High Spots for the Ice-Fishing Problem with Surface Tension
| Pengarang | : | Nathan Willis |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1312-1335 |
| Abstrak | : | In the ice-fishing problem, a half-space of fluid lies below an infinite rigid plate (``the ice'') with a hole. We investigate the ice-fishing problem including the effects of surface tension on the free surface. The dimensionless number that describes the effect of surface tension is called the Bond number. For holes that are infinite parallel strips or circular holes, we transform the problem to an equivalent eigenvalue integro-differential equation on an interval and expand in the appropriate basis (Legendre and radial polynomials, respectively). We use computational methods to demonstrate that the high spot, i.e., the maximal elevation of the fundamental sloshing profile, for the ice-fishing problem is in the interior of the free surface for large Bond numbers, but for a sufficiently small Bond number the high spot is on the boundary of the free surface. While several papers have proven high spot results in the absence of surface tension as it depends on the shape of the container, to the best of our knowledge, this is the first study investigating the effects of surface tension on the location of the high spot. |
On the Half-Space Matching Method for Real Wavenumber
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1287-1311 |
| Abstrak | : | The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of two-dimensional scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary conditions. Based on half-plane representations for the solution, the scattering problem is rewritten as a system coupling (1) a standard finite element discretization localized around the scatterer and (2) integral equations whose unknowns are traces of the solution on the boundaries of a finite number of overlapping half-planes contained in the domain. While satisfactory numerical results have been obtained for real wavenumbers, well-posedness and equivalence of this HSM formulation to the original scattering problem have been established for complex wavenumbers only. In the present paper we show, in the case of a homogeneous background, that the HSM formulation is equivalent to the original scattering problem also for real wavenumbers, and so is well-posed, provided the traces satisfy radiation conditions at infinity analogous to the standard Sommerfeld radiation condition. As a key component of our argument we show that if the trace on the boundary of a half-plane satisfies our new radiation condition, then the corresponding solution to the half-plane Dirichlet problem satisfies the Sommerfeld radiation condition in a slightly smaller half-plane. We expect that this last result will be of independent interest, in particular in studies of rough surface scattering. |
Tilt Grain Boundaries of Hexagonal Structures: A Spectral Viewpoint
| Pengarang | : | Kai Jiang |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1267-1286 |
| Abstrak | : | We propose a spectral viewpoint for grain boundaries that are generally quasiperiodic. To accurately capture the spectra computationally, it is crucial to adopt the projection method for quasiperiodic functions. Armed with the Lifshitz--Petrich free energy, we take the spectral viewpoint to examine tilt grain boundaries of the hexagonal phase. Several ingredients of grain boundaries are extracted, which are not easy to obtain from real-space profiles. We find that only a few spectra substantially contribute to the formation of grain boundaries. Their linear relation to the intrinsic spectra of the bulk hexagonal phase is independent of the tilt angle. By examining the feature of the spectral intensities, we propose a definition of the interface width. The widths calculated from this definition are consistent with visual estimation. |
Doubly Stochastic Pairwise Interactions for Agreement and Alignment
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1246-1266 |
| Abstrak | : | Random pairwise encounters often occur in large populations or groups of mobile agents, and various types of local interactions that happen at encounters account for emergent global phenomena. In particular, in the fields of swarm robotics, sociobiology, and social dynamics, several types of local pairwise interactions were proposed and analyzed leading to spatial gathering, clustering, agreement, or coordinated motion in teams of robotic agents, in animal herds, or in human societies. We here propose a very simple stochastic interaction at encounters that leads to agreement or geometric alignment in swarms of simple agents and analyze the process of converging to consensus. Consider a group of agents whose “states" evolve in time by pairwise interactions: the state of an agent is either a real value (a randomly initialized position within an interval) or a vector that is either unconstrained (e.g., the location of the agent in the plane) or constrained to have unit length (e.g., the direction of the agent's motion). The interactions are doubly stochastic in the sense that, at discrete time steps, pairs of agents are randomly selected and their new states are independently and uniformly set at random in (local) domains or intervals defined by the states of the interacting pair. We show that such processes lead, in finite expected time (measured by the number of interactions that occurred) to agreement in case of unconstrained states and alignment when the states are unit vectors. |
Existence, Uniqueness, and Numerical Modeling of Wine Fermentation Based on Integro-Differential Equations
| Pengarang | : | Christina Schenk |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1220-1245 |
| Abstrak | : | Predictive modeling is key for saving time and resources in manufacturing processes such as fermentation arising in food and chemical manufacturing. To make reliable predictions, realistic models representing the most important process features are required. Several models describing the white wine fermentation process already exist. However, all of these models lack a combination of features, such as the importance of oxygen at the beginning of the process, the consumption of sugar due to yeast activity, and the toxicity of alcohol on the yeast cells combined with the single-cell yeast dynamics. This work introduces a new population balance model representing all these features in one model. It is based on a system of highly nonlinear weakly hyperbolic partial/ordinary integro-differential equations which poses a number of theoretical and numerical challenges. This paper increases the understanding of the latter and of the process itself by combining theoretical with numerical investigations. Existence and uniqueness of solutions to a simplified problem are studied based on semigroup theory. For the numerical solution of the problem, a numerical methodology based on a finite volume scheme combined with a time implicit scheme is derived. The impact of the initial cell distribution on the dynamics is studied. The detailed model is compared to a simpler model based on ordinary differential equations. The observed differences for different initial cell distributions and distinct models turn out to be smaller than expected. The outcomes of this paper are specifically relevant for applied mathematicians, winemakers, and process engineers. |
Oscillations in a Becker--Do?ring Model with Injection and Depletion
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1194-1219 |
| Abstrak | : | We study the Becker--Do?ring bubblelator, a variant of the Becker--Do?ring coagulation-fragmentation system that models the growth of clusters by gain or loss of monomers. Motivated by models of gas evolution oscillators from physical chemistry, we incorporate the injection of monomers and depletion of large clusters. For a wide range of physical rates, the Becker--Do?ring system itself exhibits a dynamic phase transition as mass density increases past a critical value. We connect the Becker--Do?ring bubblelator to a transport equation coupled with an integrodifferential equation for the excess monomer density by formal asymptotics in the near-critical regime. For suitable injection/depletion rates, we argue that time-periodic solutions appear via a Hopf bifurcation. Numerics confirm that the generation and removal of large clusters can become desynchronized, leading to temporal oscillations associated with bursts of large-cluster nucleation. |
A Multiscale Poromechanics Model Integrating Myocardial Perfusion and the Epicardial Coronary Vessels
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1167-1193 |
| Abstrak | : | The importance of myocardial perfusion at the outset of cardiac disease remains largely understudied. To address this topic we present a mathematical model that considers the systemic circulation, the coronary vessels, the myocardium, and the interactions among these components. The core of the whole model is the description of the myocardium as a multicompartment poromechanics system. A novel decomposition of the poroelastic Helmholtz potential involved in the poromechanics model allows for a quasi-incompressible model that adequately describes the physical interaction among all components in the porous medium. We further provide a rigorous mathematical analysis that gives guidelines for the choice of the Helmholtz potential. To reduce the computational cost of our integrated model we propose decoupling the deformation of the tissue and systemic circulation from the porous flow in the myocardium and coronary vessels, which allows us to apply the model also in combination with precomputed cardiac displacements, obtained form other models or medical imaging data. We test the methodology through the simulation of a heartbeat in healthy conditions that replicates the systolic impediment phenomenon, which is particularly challenging to capture as it arises from the interaction of several parts of the model. |
Reconstructing Stieltjes Functions from Their Approximate Values: A Search for a Needle in a Haystack
| Pengarang | : | Yury Grabovsky |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1135-1166 |
| Abstrak | : | Material response of real, passive, linear, time-invariant media to external influences is described by complex analytic functions of frequency that can always be written in terms of Stieltjes functions---a special class of analytic functions mapping a complex upper half-plane into itself. Reconstructing such functions from their experimentally measured values at specific frequencies is one of the central problems that we address in this paper. A definitive reconstruction algorithm that produces a certificate of optimality as well as a graphical representation of the uncertainty of reconstruction is proposed. Its effectiveness is demonstrated in the context of the electrochemical impedance spectroscopy. |