OPAC - Pencarian Artikel Jurnal & Majalah Library USD
Menampilkan semua artikel (Halaman 693 dari 34166, Total: 341652 data)
Halton Sequences Avoid the Origin
klik untuk membaca file PDF
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 48 (No. 3) |
| Halaman | : | 487-503 |
| Abstrak | : | The nth point of the Halton sequence in [0,1]d is shown to have components whose product is larger than Cn-1, where C > 0 depends on d. This property makes the Halton sequence very well suited to quasi-Monte Carlo (QMC) integration of some singular functions that become unbounded as the argument approaches the origin. The Halton sequence avoids a similarly shaped (though differently sized) region around every corner of the unit cube, making it suitable for functions with singularities at all corners. Convergence rates are established for QMC integration based on two assumptions: a growth condition on the integrand, and a measure of how the sample points avoid the boundary. In some settings the error is O(n-1 + epsilon ), while in others the error diverges to infinity. Star discrepancy does not suffice to distinguish the cases. |
Recent Developments in the Modeling, Analysis, and Numerics of Ferromagnetism
| Pengarang | : | Martin Kruzík |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 48 (No. 3) |
| Halaman | : | 439-483 |
| Abstrak | : | Micromagnetics is a continuum variational theory describing magnetization patterns in ferromagnetic media. Its multiscale nature due to different inherent spatiotemporal physical and geometric scales, together with nonlocal phenomena and a nonconvex side-constraint, leads to rich behavior and pattern formation. This variety of effects is also the reason for severe problems in analysis, model validation, reductions, and numerics, which have only recently been accessed and are reviewed in this work. |
Communicating Applied Mathematics: Four Examples
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 48 (No. 2) |
| Halaman | : | 329-356 |
| Abstrak | : | Communicating Applied Mathematics is a writing- and speaking-intensive graduate course at North Carolina State University. The purpose of this article is to provide a brief description of the course objectives and the assignments. Parts A--D of of this article represent the class projects and illustrate the outcome of the course: We introduce a water-supply problem considered by the optimization and hydrology communities for benchmarking purposes. The objective is to drill five wells so that the cost of pumping water out of the ground is minimized. Using the implicit filtering optimization algorithm to locate the wells, we save approximately $2,500 over the cost of a given initial well configuration. The volume of powder poured into a bin with obstructions is found by calculating the height of the surface at every point. This is done using the fast marching algorithm. We look at two different bin geometries and determine the volumes as a function of the powder height under the spout. The surface of the powder satisfies a two-dimensional eikonal equation. This equation is solved using the fast marching method. Resonant tunneling diodes (RTDs) are ultrasmall semiconductor devices that have potential as very high-frequency oscillators. To describe the electron transport within these devices, physicists use the Wigner--Poisson equations which incorporate quantum mechanics to describe the distribution of electrons within the RTD. Continuation methods are employed to determine the steady-state electron distributions as a function of the voltage difference across the device. These simulations predict the operating state of the RTD under different applied voltages and will be a tool to help physicists understand how changing the voltage applied to the device leads to the development of current oscillations. When a thin film flows down an inclined plane, a bulge of fluid, known as a capillary ridge, forms on the leading edge and is subject to a fingering instability in which the fluid is channeled into rivulets. This process is familiar to us in everyday experiments such as painting a wall or pouring syrup over a stack of pancakes. It is also observed that changes in surface tension due to a temperature gradient can draw fluid up an inclined plane. Amazingly, in this situation the capillary ridge broadens and no fingering instability is observed. Numerical and analytical studies of a mathematical model of this process led to the discovery that these observations are associated with a nonclassical shock wave previously unknown to exist in thin liquid films. |
A Nonlinear Filtering Approach to Changepoint Detection Problems: Direct and Differential-Geometric Methods
| Pengarang | : | M. H. Vellekoop |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 48 (No. 2) |
| Halaman | : | 318-325 |
| Abstrak | : | A benchmark change detection problem is considered which involves the detection of a change of unknown size at an unknown time. Both unknown quantities are modeled by stochastic variables, which allows the problem to be formulated within a Bayesian framework. It turns out that the resulting nonlinear filtering problem is much harder than the well-known detection problem for known sizes of the change, and in particular that it can no longer be solved in a recursive manner. An approximating recursive filter is therefore proposed, which is designed using differential-geometric methods in a suitably chosen space of unnormalized probability densities. The new nonlinear filter can be interpreted as an adaptive version of the celebrated Shiryayev--Wonham equation for the detection of a priori known changes, combined with a modified Kalman filter structure to generate estimates of the unknown size of the change. This intuitively appealing interpretation of the nonlinear filter and its excellent performance in simulation studies indicates that it may be of practical use in realistic change detection problems. |
Difference of Sums Containing Products of Binomial Coefficients and Their Logarithms
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 48 (No. 2) |
| Halaman | : | 318-325 |
| Abstrak | : | Properties of the difference of two sums containing products of binomial coefficients and their logarithms which arise in the application of Shannon's information theory to a certain class of covert channels are deduced. Some allied consequences of the latter are also recorded. |
Solving Ordinary Differential Equations with Range Conditions. Applications
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 48 (No. 2) |
| Halaman | : | 307-317 |
| Abstrak | : | This paper introduces the problem of solving ordinary differential equationswith extra linear conditions written in terms of ranges, and deals with the corresponding existence and uniqueness problems. Some methods for analyzing the existence of solutions and obtaining the set of all solutions, based on the theory of cones and polyhedra, are given. These solutions are found by first converting the problem to a system of linear algebraic equations and then applying the corresponding well-known theory for solving and discussing the existence and uniqueness of solutions of these systems. Finally, the methods are illustrated by their application to some practical examples of the beam problem. |
The Dynamics of Legged Locomotion: Models, Analyses, and Challenges
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 48 (No. 2) |
| Halaman | : | 207-304 |
| Abstrak | : | Cheetahs and beetles run, dolphins and salmon swim, and bees and birds fly with grace and economy surpassing our technology. Evolution has shaped the breathtaking abilities of animals, leaving us the challenge of reconstructing their targets of control and mechanisms of dexterity. In this review we explore a corner of this fascinating world. We describe mathematical models for legged animal locomotion, focusing on rapidly running insects and highlighting past achievements and challenges that remain. Newtonian body--limb dynamics are most naturally formulated as piecewise-holonomic rigid body mechanical systems, whose constraints change as legs touch down or lift off. Central pattern generators and proprioceptive sensing require models of spiking neurons and simplified phase oscillator descriptions of ensembles of them. A full neuromechanical model of a running animal requires integration of these elements, along with proprioceptive feedback and models of goal-oriented sensing, planning, and learning. We outline relevant background material from biomechanics and neurobiology, explain key properties of the hybrid dynamical systems that underlie legged locomotion models, and provide numerous examples of such models, from the simplest, completely soluble "peg-leg walker" to complex neuromuscular subsystems that are yet to be assembled into models of behaving animals. This final integration in a tractable and illuminating model is an outstanding challenge. |
An Application of Computer Algebra to Pharmacokinetics: The Bateman Equation
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 48 (No. 1) |
| Halaman | : | 133-146 |
| Abstrak | : | Exponentially decaying functions can be successfully introduced as early as high school. However, obtaining the equations for the resulting effect of absorption and elimination of drug processes acting simultaneously, even in simplified models like the single dose case in a one-compartment model with an order 1 kinetic (Bateman equation), requires one to solve a nontrivial differential equation. Therefore, this equation is normally taught to second- or third-year students in the schools of medicine and pharmacy. An alternative approach is presented that uses a computer algebra system to calculate a limit and allows one to bypass the use of differential equations. |
A Polylogarithmic Approximation of the Minimum Bisection
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 48 (No. 1) |
| Halaman | : | 99-130 |
| Abstrak | : | A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size . The bisection cost is the number of edges connecting the two sets. The problem of finding a bisection of minimum cost is prototypical to graph partitioning problems, which arise in numerous contexts. This problem is NP-hard. We present an algorithm that finds a bisection whose cost is within a factor of from the minimum. For graphs excluding any fixed graph as a minor (e.g., planar graphs) we obtain an improved approximation ratio of . The previously known approximation ratio for bisection was roughly . |
Computing the Coefficients in Laplace's Method
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 48 (No. 1) |
| Halaman | : | 76-96 |
| Abstrak | : | Laplace's method is a preeminent technique in the asymptotic approximation of integrals. Its utility was enhanced enormously in 1956 when Erdélyi found a way to apply Watson's lemma and thereby obtain an infinite asymptotic expansion valid, in principle, for any integral of Laplace type. Erdélyi's formulation requires tedious computation of coefficients for each specific application of the method, and traditionally this has involved reverting a series. Recently, it was shown that the coefficients can be computed via a simple, explicit expression that is probably computationally optimal, which avoids the reversion approach altogether. The formula is made possible by recognizing the central role of Faà di Bruno's formula, alongside Watson's lemma, in Erdélyi's formulation of Laplace's classical method. Laplace's method can now be implemented cleanly and relatively quickly, provided one has the luck and the patience to get to the point where implementation becomes automatic. The present paper outlines the recent discovery of the role of Faà di Bruno's formula in Laplace's method, gives examples of the application of the explicit expression for the coefficients and provides grounds for a possible generalization of the result. |