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  • 1
    Electronic Resource
    Electronic Resource
    THE BLACK-SCHOLES EQUATION REVISITED: ASYMPTOTIC EXPANSIONS AND SINGULAR PERTURBATIONS (2005)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishing, Inc.
    Mathematical finance 15 (2005), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper, novel singular perturbation techniques are applied to price European, American, and barrier options. Employment of these methods leads to a significant simplification of the problem in all cases, by reducing the number of parameters. For American options, the valuation problem is reduced to a procedure that may be performed on a rudimentary handheld calculator. The method also sheds light on the evolution of option prices for all of the cases considered, the results being particularly illuminating for American and barrier options.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2005.00224.x
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  • 2
    Electronic Resource
    Electronic Resource
    On the unsteady low-Rossby number flow of a rotating fluid past a circular cylinder (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 600-614 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The unsteady flow of a homogeneous viscous fluid past a straight circular cylinder (radius l*) confined between two infinite parallel plates (a distance d* apart) relative to a rapidly rotating frame is considered. The cylinder is impulsively started from rest to a uniform velocity. The unsteady form of the boundary-layer equations for a rotating fluid is used to examine the flow Rossby number Ro∼O(E1/2), where E(very-much-less-than)1 is the Ekman number. A range of values of the non-dimensional parameter N=lE1/2/Ro (where l=l*/d*) is considered. For 0≤N〈1, the flow pattern resembles that of the non-rotating case (N=0). Initially, the wall shear around the cylinder is positive everywhere. After a time, flow reversal begins at the rear stagnation point and then the position of zero wall shear moves upstream, towards the front stagnation point. The boundary-layer thickness in the region of reversed flow grows with time until a singularity/eruption at a point in the flow occurs. The boundary-layer equations are written in terms of Lagrangian coordinates in order to numerically investigate the finite-time singularity for 0≤N〈1. The flow close to the rear stagnation point is also examined in detail for a range of values of N and results are compared with the large-time asymptotic forms for the growth of the displacement thickness. The analysis suggests the displacement thickness in this region grows exponentially with time, for certain ranges of N. For 0〈N〈1, the displacement thickness grows exponentially with time in a manner similar to the non-rotating case. For N〉1, the wall shear remains positive for all time. However, for 1≤N〈2, the displacement thickness of the boundary layer close to the rear stagnation point again grows exponentially with time. For 2〈N〈3 the flow close to the rear stagnation point also grows exponentially with time, although the form of solution differs from that for 0≤N〈2. For N〉3, the solution tends to a truly steady limit, consistent with previous studies on the steady problem. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869220
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  • 3
    Electronic Resource
    Electronic Resource
    The effect of three-dimensional freestream disturbances on the supersonic flow past a wedge (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 456-467 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The interaction between a shock wave (attached to a wedge) and small amplitude, three-dimensional disturbances of a uniform, supersonic, freestream flow are investigated. The paper extends the two-dimensional study of Duck et al. [P W. Duck, D. G. Lasseigne, and M. Y. Hussaini, "On the interaction between the shock wave attached to a wedge and freestream disturbances," Theor. Comput. Fluid Dyn. 7, 119 (1995) (also ICASE Report No. 93-61)] through the use of vector potentials, which render the problem tractable by the same techniques as in the two-dimensional case, in particular by expansion of the solution by means of a Fourier-Bessel series, in appropriately chosen coordinates. Results are presented for specific classes of freestream disturbances, and the study shows conclusively that the shock is stable to all classes of disturbances (i.e., time periodic perturbations to the shock do not grow downstream), provided the flow downstream of the shock is supersonic (loosely corresponding to the weak shock solution). This is shown from our numerical results and also by asymptotic analysis of the Fourier-Bessel series, valid far downstream of the shock. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869140
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  • 4
    Electronic Resource
    Electronic Resource
    The effects of viscosity on centre modes in the incompressible stability of a trailing line vortex (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 1455-1463 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The effects of viscosity on centre-modes of instability/stability are considered, with particular emphasis on the trailing line vortex. These effects are shown to be particularly significant when the axial wavenumber is within O(Re−1/(2+λ)) of the critical (inviscid) value, where Re is the Reynolds number, and λ is a (positive) parameter defined explicitly in the paper. Also examined are the critical (singular) layers that arise within the flow, which are shown to have thickness O(Re−2λ/3(4+2λ)). A number of numerical results are presented, and these show that viscosity seems to generally play a stabilising role on the stability of the flow. In the Appendix, wavenumbers somewhat closer to the critical inviscid value are examined, and the effects of viscosity are shown to substantially permeate outside of the critical layers, and lead to a system similar to that discussed by Stewartson, Ng and Brown [Philos. Trans. R. Soc. London Ser. A 324, 473 (1988)] in the context of swirling Poiseuille flow. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868922
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  • 5
    Electronic Resource
    Electronic Resource
    The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 1541-1557 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for Mach numbers 2.8 and 3.8, revealing that curvature and choice of wall conditions both have a significant effect on the stability of the flow. The asymptotic, large azimuthal wave-number solution is obtained for the inviscid stability of the flow and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858427
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  • 6
    Electronic Resource
    Electronic Resource
    The effects of viscosity on the stability of a trailing-line vortex in compressible flow (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 7 (1995), S. 2265-2270 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We consider the effects of viscosity on the inviscid stability of the Batchelor [J. Fluid Mech. 20, 645 (1964)] vortex in a compressible flow. The problem is tackled asymptotically, in the limit of large (streamwise and azimuthal) wavenumbers, together with large Mach numbers. This problem, with viscous effects neglected, was discussed in Stott and Duck [J. Fluid Mech. 268, 323 (1994)]. The authors found that the nature of the solution passes through different regimes as the Mach number increases, relative to the wave number. This structure persists when viscous effects are included in the analysis. In the present study, as in that mentioned above, the mode present in the incompressible case ceases to be unstable at high Mach numbers and a center mode forms, whose stability characteristics are determined primarily by conditions close to the vortex axis. We find generally that viscosity has a stabilizing influence on the flow, whilst in the case of center modes, viscous effects become important at much larger Reynolds numbers than for the first class of disturbance. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868474
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  • 7
    Electronic Resource
    Electronic Resource
    The inviscid stability of supersonic flow past a sharp cone (1990)
    Springer
    Theoretical and computational fluid dynamics 2 (1990), S. 139-163 
    Details
    ISSN: 1432-2250
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract In this paper we consider the laminar boundary layer which forms on a sharp cone in a supersonic freestream, where lateral curvature plays a key role in the physics of the problem. This flow is then analysed from the point of view of linear, temporal, inviscid stability. Indeed, the basic, nonaxisymmetric disturbance equations are derived for general flows of this class, and a so-called “triply generalized” inflexion condition is found for the existence of “subsonic” neutral modes of instability. This condition is analogous to the well-known generalized inflexion condition found in planar flows, although in the present case the condition depends on both axial and azimuthal wave numbers. Extensive numerical results are presented for the stability problem at a freestream Mach number of 3.8, for a range of streamwise locations. These results reveal that a new mode of instability may occur, peculiar to flows of this type involving lateral curvature. This mode occurs at small wave numbers, but under certain circumstances may in fact be the most unstable (and hence important) mode. Additionally, asymptotic analyses valid close to the tip of the cone and far downstream from the cone are presented, and these give a partial (asymptotic) description of this additional mode of instability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00271601
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  • 8
    Electronic Resource
    Electronic Resource
    On the interaction between the shock wave attached to a wedge and freestream disturbances (1995)
    Springer
    Theoretical and computational fluid dynamics 7 (1995), S. 119-139 
    Details
    ISSN: 1432-2250
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract We present a study of the interaction of small amplitude, unsteady, freestream disturbances with a shock wave induced by a wedge in supersonic flow. These disturbances may be acoustic waves, vorticity waves, or entropy waves (or indeed a combination of all three). Their interactions then generate behind the shock disturbances of all three classes, an aspect that is investigated in some detail. Also, the possibility of enhanced mixing owing to additional vorticity produced by the shock-body coupling is investigated. It is shown that disturbances behind the shock may either decay downstream, or alternatively experience sustained oscillations. The precise regimes under which either behaviour is found are stated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00311809
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