Filters

Results

**1**-**10**of**51** Results

**1**-**10**of**51**. Search took:**0.016**secondsSort by: date | relevance |

AbstractAbstract

[en] In the present paper, two classes of invariant tori are derived which lie on energy surfaces large enough to accommodate the charged particles in the Van Allen radiation belt. In spite of an idealized treatment, where particle interactions are ignored and idealized assumptions concerning the nature of the earth's magnetic field are made, the results have significant physical relevance in that the special (quasi-periodic) orbits persist in the presence of small perturbations, and most of the omitted effects may be considered as a small perturbation of the idealized problem

Primary Subject

Record Type

Journal Article

Journal

SIAM Journal of Applied Mathematics; ISSN 0036-1399; ; v. 37 p. 664-668

Country of publication

Publication YearPublication Year

Reference NumberReference Number

INIS VolumeINIS Volume

INIS IssueINIS Issue

AbstractAbstract

[en] The spatially varying transients that occur during a self-induced high-activation-energy thermal explosion in a vessel with constant wall temperature are examined. The induction period equations are solved numerically for a system confined to a slot-like region. A stiff-equation integrator is used to delineate the nature of the thermal runaway process. A well defined hot spot is observed to form in the vicinity of the symmetry line. The development of the hot spot is described within the framework of an asymptotic theory which is valid close to the explosion time. The solution is constructed in terms of a slowly varying conduction-controlled outer region surrounding a much smaller zone in which the relatively rapid chemical kinetics determine how the hot spots therein develops

Primary Subject

Record Type

Journal Article

Journal

SIAM Journal of Applied Mathematics; ISSN 0036-1399; ; v. 39 p. 412-430

Country of publication

Publication YearPublication Year

Reference NumberReference Number

INIS VolumeINIS Volume

INIS IssueINIS Issue

AbstractAbstract

[en] Physical phenomena involving rapid and sudden transitions, such as snap buckling of elastic shells, explosions, and earthquakes, are characterized mathematically as a small disturbance causing a large-amplitude response. Because of this, standard asymptotic and perturbation methods are ill-suited to these problems. In the present paper, a new method of analyzing jump phenomena is proposed. The principal feature of the method is the representation of the response in terms of rational functions. For illustration, the method is applied to the snap buckling of an elastic arch and to a simple combustion problem

Primary Subject

Record Type

Journal Article

Journal

SIAM Journal of Applied Mathematics; ISSN 0036-1399; ; v. 39 p. 440-455

Country of publication

Publication YearPublication Year

Reference NumberReference Number

INIS VolumeINIS Volume

INIS IssueINIS Issue

AbstractAbstract

[en] The modulations of N-phase Korteweg-de Vries (KdV) wavetrains in the presence of external perturbations is investigated. An invariant representation of these modulation equations in terms of differentials on a Riemann surface is derived from averaged perturbed conservation laws. In particular, the explicit dependence of the representation on the external perturbation is obtained. This invariant representation is used to place the equation in a Riemann diagonal form, whose dependence on the external perturbation is explicitly computed. 15 references

Primary Subject

Record Type

Journal Article

Journal

SIAM Journal of Applied Mathematics; ISSN 0036-1399; ; v. 44 p. 287-300

Country of publication

Publication YearPublication Year

Reference NumberReference Number

INIS VolumeINIS Volume

INIS IssueINIS Issue

AbstractAbstract

[en] Elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the well-posedness of the problem. Examples of practical applications include the Helmholtz equation and Laplace's equation. Computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition at infinity by a boundary condition on a finite artificial surface. Direct imposition of the condition at infinity along the finite boundary results in large errors. A sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain. Estimates of the error due to the finite boundary are obtained for several cases. Computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions. The examples are based on a finite element formulation but finite difference methods can also be used

Primary Subject

Record Type

Journal Article

Journal

SIAM Journal of Applied Mathematics; ISSN 0036-1399; ; v. 42(2); p. 430-451

Country of publication

Publication YearPublication Year

Reference NumberReference Number

INIS VolumeINIS Volume

INIS IssueINIS Issue

AbstractAbstract

[en] The scattering matrix of mathematical scattering theory is derived from the classical version with a simple reinterpretation of the classical scattering matrix, and it is shown that the complex poles of the scattering matrix are present also in the solution of an integral equation for the density function involved in a representation for the scattered field. The scattering matrix is first derived and applied to the sphere and circular cylinder in order to exhibit complex poles. It is then shown that the density function involved in a representation of the scattered field also has a set of complex poles which is precisely the set of complex poles of the scattering matrix

Primary Subject

Secondary Subject

Record Type

Journal Article

Journal

SIAM Journal of Applied Mathematics; ISSN 0036-1399; ; v. 43 p. 584-593

Country of publication

Publication YearPublication Year

Reference NumberReference Number

INIS VolumeINIS Volume

INIS IssueINIS Issue

AbstractAbstract

[en] Ackerberg-O'Malley resonance in the singularly perturbed turning point problem is considered. A variational approach suggested by Grasman and Matkowsky is exploited to explain previously overlooked resonance phenomena. Several examples are presented

Primary Subject

Record Type

Journal Article

Journal

SIAM Journal of Applied Mathematics; ISSN 0036-1399; ; v. 41(2); p. 288-293

Country of publication

Publication YearPublication Year

Reference NumberReference Number

INIS VolumeINIS Volume

INIS IssueINIS Issue

AbstractAbstract

[en] Changes of density which occur naturally in phase change problems introduce movement of bulk material. It is customary in analyzing such problems to ignore this unpleasant complication and consider the densities to be equal. But for one-dimensional problems the complexities introduced by this bulk movement can easily be circumvented. The key idea is posing the problem in local coordinates which are fixed in each phase. We show how to define suitable moving coordinates and, using them, pose and give an explicit solution for a one-dimensional, multi-phase Stefan problem with phases of distinct densities. This explicit solution is essentially a similarity solution in the local coordinates. However, the local coordinates could be used with finite element or finite difference schemes to analyze problems for which similarity solutions do not exist

Primary Subject

Record Type

Journal Article

Journal

SIAM Journal of Applied Mathematics; ISSN 0036-1399; ; v. 42(6); p. 1195-1201

Country of publication

Publication YearPublication Year

Reference NumberReference Number

INIS VolumeINIS Volume

INIS IssueINIS Issue

AbstractAbstract

[en] We investigate a system of partial differential equations which model the reaction-diffusion dynamics of the Belousov-Zhabotinskii chemical reaction. Our system is developed from the Oregonator model of Field and Noyes. Over a physically reasonable range of parameters for which the system exhibits no temporal oscillations, we show that the equations have a solitary traveling wave solution. These waves appear to correspond to the trigger waves observed experimentally in the reaction. In addition we show that if the autocatalytic reaction is sufficiently slow, then as expected from the chemistry, the model has no solitary traveling wave solutions. We numerically compute the wave speed and it is shown to be close to the observed speed of the trigger waves. Also, the dependence of the wave speed on the various measurable physical parameters in the model is computed and shown to be in excellent agreement with that observed

Primary Subject

Record Type

Journal Article

Journal

SIAM Journal of Applied Mathematics; ISSN 0036-1399; ; v. 37(3); p. 561-587

Country of publication

Publication YearPublication Year

Reference NumberReference Number

INIS VolumeINIS Volume

INIS IssueINIS Issue

AbstractAbstract

[en] A random walk on a one-dimensional lattice is considered. The walk is asymmetric but with different asymmetry on the right and left halves of the line. As the parameter space describing the two asymmetries is covered, several qualitatively different distributions result: limiting distribution, unimodal diffusion and biomodal diffusion. The corresponding parameter space phase boundaries are obtained, as well as the precise form of the distributions

Primary Subject

Record Type

Journal Article

Journal

SIAM Journal of Applied Mathematics; ISSN 0036-1399; ; v. 40(3); p. 485-497

Country of publication

Publication YearPublication Year

Reference NumberReference Number

INIS VolumeINIS Volume

INIS IssueINIS Issue

1 | 2 | 3 | Next |