Results 1  10
of
65
On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
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Cited by 219 (4 self)
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Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
Geometrical aspects of stability theory for Hill’s equations
 Arch. Rat. Mech. Anal
, 1995
"... There is by now a vast analytic theory of Mathieu's equation 5i + (a + bp(t))x = O, p(t) p(t + 2~), (1) where a and b are real parameters. Apparently, the first stability diagram was drawn in the classical paper by B. vaN DER POL & M. J. O. STI~UTT [15]. Since then ..."
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Cited by 23 (11 self)
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There is by now a vast analytic theory of Mathieu's equation 5i + (a + bp(t))x = O, p(t) p(t + 2~), (1) where a and b are real parameters. Apparently, the first stability diagram was drawn in the classical paper by B. vaN DER POL & M. J. O. STI~UTT [15]. Since then
Path Integral Approach for Superintegrable Potentials on Spaces of Nonconstant Curvature: I. Darboux . . .
, 2006
"... In this paper the Feynman path integral technique is applied for superintegrable potentials on twodimensional spaces of nonconstant curvature: these spaces are Darboux spaces DI and DII, respectively. On DI there are three and on DII four such potentials, respectively. We are able to evaluate the ..."
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Cited by 17 (8 self)
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In this paper the Feynman path integral technique is applied for superintegrable potentials on twodimensional spaces of nonconstant curvature: these spaces are Darboux spaces DI and DII, respectively. On DI there are three and on DII four such potentials, respectively. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wavefunctions, and the discrete energyspectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is either determined by a transcendental equation involving parabolic cylinder functions (Darboux space I), or by a higher order polynomial equation. The solutions on DI in particular show that superintegrable systems are not necessarily degenerate. We can also show how the limiting cases of flat space (constant curvature zero) and the twodimensional hyperboloid (constant negative curvature) emerge.
Penrose limit and string theories on various brane backgrounds,” JHEP 0211
, 2002
"... We investigate the Penrose limit of various brane solutions including Dpbranes, NS5branes, fundamental strings, (p,q) fivebranes and (p,q) strings. We obtain special null geodesics with the fixed radial coordinate (critical radius), along which the Penrose limit gives string theories with constant ..."
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Cited by 17 (0 self)
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We investigate the Penrose limit of various brane solutions including Dpbranes, NS5branes, fundamental strings, (p,q) fivebranes and (p,q) strings. We obtain special null geodesics with the fixed radial coordinate (critical radius), along which the Penrose limit gives string theories with constant mass. We also study string theories with timedependent mass, which arise from the Penrose limit of the brane backgrounds. We examine equations of motion of the strings in the asymptotic flat region and around the critical radius. In particular, for (p,q) fivebranes, we find that the string equations of motion in the directions with the B field are explicitly The Penrose limits [1, 2] of backgrounds of the M theory and type II superstring theories are useful for studying the holography between string theories and conformal field theories [3, 4]. This is based on the fact that the type IIB GreenSchwarz superstring on the ppwave background is solved exactly in the lightcone gauge [5, 6].
A.N.: Path Integral Discussion for SmorodinskyWinternitz Potentials: I. Two and ThreeDimensional Euclidean Space. Fortschr.Phys
, 1995
"... Path integral formulations for the SmorodinskyWinternitz potentials in two and threedimensional Euclidean space are presented. We mention all coordinate systems which separate the SmorodinskyWinternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate s ..."
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Cited by 14 (7 self)
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Path integral formulations for the SmorodinskyWinternitz potentials in two and threedimensional Euclidean space are presented. We mention all coordinate systems which separate the SmorodinskyWinternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integral formulation is not possible, we list in all soluble cases the path integral evaluations explicitly in terms of the propagators and the spectral expansions into the wavefunctions. Supported by Deutsche Forschungsgemeinschaft under contract number GR 1031/2–1.
Spectral estimates and nonselfadjoint perturbations of spheroidal wave operators,” mathph/0405010
, 2006
"... We derive a spectral representation for the oblate spheroidal wave operator which is holomorphic in the aspherical parameter Ω in a neighborhood of the real line. For real Ω, estimates are derived for all eigenvalue gaps uniformly in Ω. The proof of the gap estimates is based on detailed estimates f ..."
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Cited by 12 (10 self)
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We derive a spectral representation for the oblate spheroidal wave operator which is holomorphic in the aspherical parameter Ω in a neighborhood of the real line. For real Ω, estimates are derived for all eigenvalue gaps uniformly in Ω. The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex Ω is obtained using the theory of slightly nonselfadjoint perturbations. 1
Spectral gaps of Schrödinger operators with periodic singular potentials
"... Abstract. By using quasi–derivatives we develop a Fourier method for studying the spectral gaps of one dimensional Schrödinger operators with periodic singular potentials v. Our results reveal a close relationship between smoothness of potentials and spectral gap asymptotics under a priori assumptio ..."
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Cited by 11 (5 self)
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Abstract. By using quasi–derivatives we develop a Fourier method for studying the spectral gaps of one dimensional Schrödinger operators with periodic singular potentials v. Our results reveal a close relationship between smoothness of potentials and spectral gap asymptotics under a priori assumption v ∈ H −1 loc (R). They extend and strengthen similar results proved in the classical
Irreducibility of some spectral determinants
, 2010
"... This is a complement to our paper arXiv:0802.1461. We study irreducibility of spectral determinants of some oneparametric eigenvalue problems in dimension one with polynomial potentials. ..."
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Cited by 10 (7 self)
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This is a complement to our paper arXiv:0802.1461. We study irreducibility of spectral determinants of some oneparametric eigenvalue problems in dimension one with polynomial potentials.
Exact results for a semiflexible polymer chain in an aligning field
 Macromolecules
, 2004
"... ABSTRACT: We provide exact results for the Laplacetransformed partition function of a wormlike chain subject to a tensile force and in a nematic field, in both two and three dimensions. The results are in the form of infinite continued fractions, which are obtained by exploiting the hierarchical st ..."
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Cited by 8 (0 self)
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ABSTRACT: We provide exact results for the Laplacetransformed partition function of a wormlike chain subject to a tensile force and in a nematic field, in both two and three dimensions. The results are in the form of infinite continued fractions, which are obtained by exploiting the hierarchical structure of a momentbased expansion of the partition function. The case of an imaginary force corresponds to the endtoend distance distribution in LaplaceFourier space. We illustrate the utility of these exact results by examining the structure factor of a wormlike chain, the deformation free energy of a chain in a nematic field, and the selfconsistentfield solution for the isotropicnematic transition of wormlike chains. 1.
Curvilinear coordinate systems in which the Helmholtz equation separates
 IMA Journal of Applied Mathematics
, 1981
"... Part I of this paper describes a numbeT of the more complicated coordinate systems in which the Helmholtz equation is separable, and discusses the geometrical relationships between them and the ellipsoidal system, which is the most general of such systems. Part II describes the ellipsoidal system i ..."
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Cited by 7 (0 self)
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Part I of this paper describes a numbeT of the more complicated coordinate systems in which the Helmholtz equation is separable, and discusses the geometrical relationships between them and the ellipsoidal system, which is the most general of such systems. Part II describes the ellipsoidal system in detail, using the Jacobian form in which nearly all recent work has been done, with particular emphasis on the difficulties which occur in applications. Part III examines the analytic processes of degeneracy from the ellipsoidal system to others, including the degeneracy of the separated ordinary differential equations. The Appendix gives a summary of the properties of Jacobian elliptic functions used in Parts II and III. 1.