The Experts below are selected from a list of 11154 Experts worldwide ranked by ideXlab platform

Peder A. Tyvand - One of the best experts on this subject based on the ideXlab platform.

  • An impulsive bathtub vortex
    Physics of Fluids, 2005
    Co-Authors: Peder A. Tyvand, Kjetil B. Haugen
    Abstract:

    The impulsive free-surface flow due to a Point Sink at the bottom of a container with rotating inviscid fluid is investigated analytically by a small-time expansion. Before the Sink is turned on impulsively, there is a steady rigid-body rotation with large Rossby number (small angular velocity). The theory is developed to first order in the inverse Rossby number. The evolution of the free-surface vorticity is investigated. The azimuthal surface velocity is a cubic function of time. It is shown that the influence of the rotation of the earth on an impulsive bathtub vortex is negligible.

  • Free-surface evolution due to an impulsive bottom Sink at uniform depth
    Physics of Fluids, 2003
    Co-Authors: Kjetil B. Haugen, Peder A. Tyvand
    Abstract:

    The free-surface evolution due to an impulsively started Point Sink at the bottom of a uniform horizontal layer of inviscid and incompressible fluid is investigated analytically. A third-order small-time expansion of the full nonlinear problem is performed. The dip formation above the Sink depends on the Froude number of the Sink. An initially critical Froude number 0.1376 is found for the sign change of the third-order elevation above the Point Sink. A physically critical Froude number 0.109 is identified for the threshold for the dip to be swallowed into the Point Sink. The same problem is solved in two dimensions, where a uniform line Sink is turned on impulsively at the bottom.

  • nonlinear transient free surface flow and dip formation due to a Point Sink
    Physics of Fluids, 1993
    Co-Authors: Touvia Miloh, Peder A. Tyvand
    Abstract:

    The early free‐surface flow due to an impulsively started Point Sink in a semi‐infinite fluid is analytically studied by employing a power series expansion in time. The full surface elevation to second order is calculated, as well as the third‐order elevation at the surface center just above the Sink. Gravity enters into the problem only in the third‐order surface elevation. A Froude number is defined here with respect to the Sink strength and the initial submergence depth. A critical value for the Froude number is analytically determined which is related to dip formation at the free surface. Its value is 15−1/2=0.2582. This critical value is shown to be in good agreement with experimental data and earlier works on dip formation in a container that is drained by a hole in the bottom.

  • Nonlinear transient free‐surface flow and dip formation due to a Point Sink
    Physics of Fluids A: Fluid Dynamics, 1993
    Co-Authors: Touvia Miloh, Peder A. Tyvand
    Abstract:

    The early free‐surface flow due to an impulsively started Point Sink in a semi‐infinite fluid is analytically studied by employing a power series expansion in time. The full surface elevation to second order is calculated, as well as the third‐order elevation at the surface center just above the Sink. Gravity enters into the problem only in the third‐order surface elevation. A Froude number is defined here with respect to the Sink strength and the initial submergence depth. A critical value for the Froude number is analytically determined which is related to dip formation at the free surface. Its value is 15−1/2=0.2582. This critical value is shown to be in good agreement with experimental data and earlier works on dip formation in a container that is drained by a hole in the bottom.

Lawrence K. Forbes - One of the best experts on this subject based on the ideXlab platform.

  • unsteady flows induced by a Point source or Sink in a fluid of finite depth
    European Journal of Applied Mathematics, 2017
    Co-Authors: Tim E. Stokes, G C Hocking, Lawrence K. Forbes
    Abstract:

    The time-varying flow in which fluid is withdrawn from or added to a reservoir of infinite or arbitrary finite depth through a Point Sink or source of variable strength beneath a free surface is considered. Backed up by some analytic work, a numerical method is used, and the results are compared with previous work on steady and unsteady flows. In the case of withdrawal for an impulsively started flow, it is found that the critical flow rate increases with reservoir depth, although it changes little as the depth increases beyond double the Sink submergence depth. The largest flow rate at which steady solutions can evolve in source flows follows a similar pattern although at a considerably higher value. Simulations indicate that some of the previously calculated steady state solutions at higher flow rates may be unstable, if they exist at all.

  • The effect of surface tension on free surface flow induced by a Point Sink in a fluid of finite depth
    Computers & Fluids, 2017
    Co-Authors: Graeme C. Hocking, Tim E. Stokes, Ha H. N. Nguyen, Lawrence K. Forbes
    Abstract:

    Solutions are presented to the problem of steady, axisymmetric flow of an inviscid fluid into a Point Sink. The fluid is of finite depth and has a free surface. Two numerical schemes, a spectral method and an integral equation approach, are implemented to confirm results for the maximum-flow-rate steady solution for each configuration. The effects of surface tension and Sink depth are included and constitute the new component of the work. Surface tension has the effect of increasing the maximum flow rate at which steady-state solutions can exist.

  • The effect of surface tension on free-surface flow induced by a Point Sink
    The ANZIAM Journal, 2016
    Co-Authors: Graeme C. Hocking, Lawrence K. Forbes, Ha H. N. Nguyen, Tim E. Stokes
    Abstract:

    The steady, axisymmetric flow induced by a Point Sink (or source) submerged in an inviscid fluid of infinite depth is computed and the resulting deformation of the free surface is obtained. The effect of surface tension on the free surface is determined and is the new component of this work. The maximum Froude numbers at which steady solutions exist are computed. It is found that the determining factor in reaching the critical flow changes as more surface tension is included. If there is zero or a very small amount of surface tension, the limiting factor appears to be the formation of small wavelets on the free surface; but, as the surface tension increases, this is replaced by a tendency for the lowest Point on the free surface to descend sharply as the Froude number is increased.

  • A note on steady flow into a submerged Point Sink
    The ANZIAM Journal, 2014
    Co-Authors: Graeme C. Hocking, Lawrence K. Forbes, Tim E. Stokes
    Abstract:

    The steady, axisymmetric flow induced by a Point Sink (or source) submerged in an unbounded inviscid fluid is computed. The resulting deformation of the free surface is obtained and a limit of steady solutions is found that is quite different to those obtained in past work. More accurate solutions indicate that the old limiting flow rate was too high and that in fact the breakdown of steady solutions at a lower flow rate is characterized by the appearance of spurious wavelets at the free surface. doi:10.1017/S1446181114000303

  • a rational approximation to the evolution of a free surface during fluid withdrawal through a Point Sink
    Anziam Journal, 2010
    Co-Authors: G C Hocking, Tim E. Stokes, Lawrence K. Forbes
    Abstract:

    The time varying flow in which fluid is withdrawn from a reservoir through a Point Sink of variable strength beneath a free surface is considered. Asymptotic techniques are used to derive an approximate solution to the flow that is valid at intermediate times, giving a simple rational approximation to track changes in the free surface for any temporal variations in the Sink strength. Comparisons with numerical simulations are given, showing that the approximation has wide applicability. References M. Abramovitz and I. Stegun, Handbook of Mathematical Functions , Dover, New York, 1972 A. Craya, 1949, Theoretical research on the flow of nonhomogeneous fluids, La Houille Blanche , 4, 44--55. W. R. Debler, 1959, Stratified flow into a line Sink, J. Eng. Mech. Div., ASCE 3, 51--65 D. E. Farrow and G. C. Hocking, 2006, A numerical model for withdrawal from a two layer fluid, J. Fluid Mech. 549, 141--157. doi:10.1017/S0022112005007561 L. K. Forbes and G. C. Hocking, 1990, Flow caused by a Point Sink in a fluid having a free surface, J. Austral. Math. Soc. Ser. B 32, 233--252. doi:10.1017/S0334270000008465 L. K. Forbes, G. C. Hocking and G. A. Chandler, 1996, A note on withdrawal through a Point Sink in fluid of finite depth, J. Austral. Math. Soc. Ser. B 37, 406--416. doi:10.1017/S0334270000008961 L. K. Forbes and G. C. Hocking, 1998, Withdrawal from a two-layer inviscid fluid in a duct, J. Fluid Mech. 361, 275--296. doi:10.1017/S0334270000010742 L. K. Forbes and G. C. Hocking, 2003, On the computation of steady axi-symmetric withdrawal from a two-layer fluid, Computers and Fluids , 32, 385--401. doi:10.1017/S0022112098008805 L. K. Forbes, G. C. Hocking and T. E. Stokes, 2008, On starting conditions for a submerged Sink in a fluid, J. Eng. Math. , 61, 55--68. doi:10.1007/s10665-007-9174-2 I. S. Gradshteyn and I. W. Ryzhik, Table of integrals series and products , Academic Press, New York and London, 1965. G. Hocking, 1985, Cusp-like free-surface flows due to a submerged source or Sink in the presence of a flat or sloping bottom, J. Aust. Math Soc. Ser. B , 26, 470--486. doi:10.1017/S0334270000004665 G. Hocking, 1991, Withdrawal from two-layer fluid through line Sink, J. Hyd. Engng., ASCE , 117(6), 800--805. doi:10.1061/(ASCE)0733-9429(1991)117:6(800) G. Hocking, 1991, Critical withdrawal from a two-layer fluid through a line Sink, J. Eng. Math. , 25, 1--11. doi:10.1007/BF00036598 G. Hocking, 1995, Supercritical withdrawal from a two-layer fluid through a line Sink, J. Fluid Mech. , 297, 37--47. doi:10.1017/S022112095002990 G. C. Hocking and L. K. Forbes, 2001, Supercritical withdrawal from a two-layer fluid through a line Sink if the lower layer is of finite depth, J. Fluid Mech. 428, 333--348. doi:10.1017/S0022112000002780 G. C. Hocking, J-M. Vanden Broeck and L. K. Forbes, 2002, Withdrawal from a fluid of finite depth through a Point Sink, ANZIAM J. , 44, 181--191. doi:10.1017/S1446181100013882 J. Imberger and J. C. Patterson, 1990, Physical Limnology, Adv. in Appl. Mech. , 27, 303--475 H. Lamb, Hydrodynamics , Cambridge Univ. Press, New York, 6th ed. 1993 T. Miloh and P. A. Tyvand, 1993, Nonlinear transient free-surface flow and dip formation due to a Point Sink, Phys. Fluids A 5 (6), 1368--1375. doi:10.1063/1.858572 C. Sautreaux, 1901, Mouvement d'un liquide parfait soumis a lapesanteur. De termination des lignes de courant, J. Math. Pures Appl. 7 (5), 125--159. T. E. Stokes, G. C. Hocking and L. K. Forbes, 2003, Unsteady free-surface flow induced by a line Sink, J. Eng. Maths , 47, 137--160. doi:10.1023/A:1025892915279 T. E. Stokes, G. C. Hocking and L. K. Forbes, 2005, Unsteady flow induced by a withdrawal Point beneath a free surface, ANZIAM J. , 47, 185--202. doi:10.1017/S1446181100009986 T. E. Stokes, G. C. Hocking and L. K. Forbes, 2008, Unsteady free surface flow induced by a line Sink in a fluid of finite depth, Computers and Fluids , 37, 236--249. doi:10.1016/j.compfluid.2007.06.002 E. O. Tuck, and J-M. Vanden Broeck, 1984, A cusp-like free-surface flow due to a submerged source or Sink, J. Aust. Math Soc. Ser. B , 25, 443--450. doi:10.1017/S0334270000004197 P. A. Tyvand, 1992, Unsteady free-surface flow due to a line source, Phys. Fluids A , 4 (4), 671--676. doi:10.1063/1.858285 J-M. Vanden Broeck and J. B. Keller, 1987, Free surface flow due to a Sink, J. Fluid Mech. , 175, 109--117. doi:10.1017/S022112087000314 I. R. Wood, 1968, Selective withdrawal from a stably stratified fluid, J. Fluid Mech. , 32, 209--223. doi:10.1017/S022112068000686 M. Xue and D. K. P. Yue, 1998, Nonlinear free-surface flow due to an impulsively started submerged Point Sink, J. Fluid Mech. , 364, 325--347. doi:10.1017/S022112098001335 C. S. Yih, Dynamics of nonhomogeneous fluids , Macmillan, New York, 1965. Q-N. Zhou and W. P. Graebel, 1990, Axisymmetric draining of a cylindrical tank with a free surface, J. Fluid. Mech. 221, 511--532. doi:10.1017/S022112090003652

Tim E. Stokes - One of the best experts on this subject based on the ideXlab platform.

  • unsteady flows induced by a Point source or Sink in a fluid of finite depth
    European Journal of Applied Mathematics, 2017
    Co-Authors: Tim E. Stokes, G C Hocking, Lawrence K. Forbes
    Abstract:

    The time-varying flow in which fluid is withdrawn from or added to a reservoir of infinite or arbitrary finite depth through a Point Sink or source of variable strength beneath a free surface is considered. Backed up by some analytic work, a numerical method is used, and the results are compared with previous work on steady and unsteady flows. In the case of withdrawal for an impulsively started flow, it is found that the critical flow rate increases with reservoir depth, although it changes little as the depth increases beyond double the Sink submergence depth. The largest flow rate at which steady solutions can evolve in source flows follows a similar pattern although at a considerably higher value. Simulations indicate that some of the previously calculated steady state solutions at higher flow rates may be unstable, if they exist at all.

  • The effect of surface tension on free surface flow induced by a Point Sink in a fluid of finite depth
    Computers & Fluids, 2017
    Co-Authors: Graeme C. Hocking, Tim E. Stokes, Ha H. N. Nguyen, Lawrence K. Forbes
    Abstract:

    Solutions are presented to the problem of steady, axisymmetric flow of an inviscid fluid into a Point Sink. The fluid is of finite depth and has a free surface. Two numerical schemes, a spectral method and an integral equation approach, are implemented to confirm results for the maximum-flow-rate steady solution for each configuration. The effects of surface tension and Sink depth are included and constitute the new component of the work. Surface tension has the effect of increasing the maximum flow rate at which steady-state solutions can exist.

  • The effect of surface tension on free-surface flow induced by a Point Sink
    The ANZIAM Journal, 2016
    Co-Authors: Graeme C. Hocking, Lawrence K. Forbes, Ha H. N. Nguyen, Tim E. Stokes
    Abstract:

    The steady, axisymmetric flow induced by a Point Sink (or source) submerged in an inviscid fluid of infinite depth is computed and the resulting deformation of the free surface is obtained. The effect of surface tension on the free surface is determined and is the new component of this work. The maximum Froude numbers at which steady solutions exist are computed. It is found that the determining factor in reaching the critical flow changes as more surface tension is included. If there is zero or a very small amount of surface tension, the limiting factor appears to be the formation of small wavelets on the free surface; but, as the surface tension increases, this is replaced by a tendency for the lowest Point on the free surface to descend sharply as the Froude number is increased.

  • A note on steady flow into a submerged Point Sink
    The ANZIAM Journal, 2014
    Co-Authors: Graeme C. Hocking, Lawrence K. Forbes, Tim E. Stokes
    Abstract:

    The steady, axisymmetric flow induced by a Point Sink (or source) submerged in an unbounded inviscid fluid is computed. The resulting deformation of the free surface is obtained and a limit of steady solutions is found that is quite different to those obtained in past work. More accurate solutions indicate that the old limiting flow rate was too high and that in fact the breakdown of steady solutions at a lower flow rate is characterized by the appearance of spurious wavelets at the free surface. doi:10.1017/S1446181114000303

  • a rational approximation to the evolution of a free surface during fluid withdrawal through a Point Sink
    Anziam Journal, 2010
    Co-Authors: G C Hocking, Tim E. Stokes, Lawrence K. Forbes
    Abstract:

    The time varying flow in which fluid is withdrawn from a reservoir through a Point Sink of variable strength beneath a free surface is considered. Asymptotic techniques are used to derive an approximate solution to the flow that is valid at intermediate times, giving a simple rational approximation to track changes in the free surface for any temporal variations in the Sink strength. Comparisons with numerical simulations are given, showing that the approximation has wide applicability. References M. Abramovitz and I. Stegun, Handbook of Mathematical Functions , Dover, New York, 1972 A. Craya, 1949, Theoretical research on the flow of nonhomogeneous fluids, La Houille Blanche , 4, 44--55. W. R. Debler, 1959, Stratified flow into a line Sink, J. Eng. Mech. Div., ASCE 3, 51--65 D. E. Farrow and G. C. Hocking, 2006, A numerical model for withdrawal from a two layer fluid, J. Fluid Mech. 549, 141--157. doi:10.1017/S0022112005007561 L. K. Forbes and G. C. Hocking, 1990, Flow caused by a Point Sink in a fluid having a free surface, J. Austral. Math. Soc. Ser. B 32, 233--252. doi:10.1017/S0334270000008465 L. K. Forbes, G. C. Hocking and G. A. Chandler, 1996, A note on withdrawal through a Point Sink in fluid of finite depth, J. Austral. Math. Soc. Ser. B 37, 406--416. doi:10.1017/S0334270000008961 L. K. Forbes and G. C. Hocking, 1998, Withdrawal from a two-layer inviscid fluid in a duct, J. Fluid Mech. 361, 275--296. doi:10.1017/S0334270000010742 L. K. Forbes and G. C. Hocking, 2003, On the computation of steady axi-symmetric withdrawal from a two-layer fluid, Computers and Fluids , 32, 385--401. doi:10.1017/S0022112098008805 L. K. Forbes, G. C. Hocking and T. E. Stokes, 2008, On starting conditions for a submerged Sink in a fluid, J. Eng. Math. , 61, 55--68. doi:10.1007/s10665-007-9174-2 I. S. Gradshteyn and I. W. Ryzhik, Table of integrals series and products , Academic Press, New York and London, 1965. G. Hocking, 1985, Cusp-like free-surface flows due to a submerged source or Sink in the presence of a flat or sloping bottom, J. Aust. Math Soc. Ser. B , 26, 470--486. doi:10.1017/S0334270000004665 G. Hocking, 1991, Withdrawal from two-layer fluid through line Sink, J. Hyd. Engng., ASCE , 117(6), 800--805. doi:10.1061/(ASCE)0733-9429(1991)117:6(800) G. Hocking, 1991, Critical withdrawal from a two-layer fluid through a line Sink, J. Eng. Math. , 25, 1--11. doi:10.1007/BF00036598 G. Hocking, 1995, Supercritical withdrawal from a two-layer fluid through a line Sink, J. Fluid Mech. , 297, 37--47. doi:10.1017/S022112095002990 G. C. Hocking and L. K. Forbes, 2001, Supercritical withdrawal from a two-layer fluid through a line Sink if the lower layer is of finite depth, J. Fluid Mech. 428, 333--348. doi:10.1017/S0022112000002780 G. C. Hocking, J-M. Vanden Broeck and L. K. Forbes, 2002, Withdrawal from a fluid of finite depth through a Point Sink, ANZIAM J. , 44, 181--191. doi:10.1017/S1446181100013882 J. Imberger and J. C. Patterson, 1990, Physical Limnology, Adv. in Appl. Mech. , 27, 303--475 H. Lamb, Hydrodynamics , Cambridge Univ. Press, New York, 6th ed. 1993 T. Miloh and P. A. Tyvand, 1993, Nonlinear transient free-surface flow and dip formation due to a Point Sink, Phys. Fluids A 5 (6), 1368--1375. doi:10.1063/1.858572 C. Sautreaux, 1901, Mouvement d'un liquide parfait soumis a lapesanteur. De termination des lignes de courant, J. Math. Pures Appl. 7 (5), 125--159. T. E. Stokes, G. C. Hocking and L. K. Forbes, 2003, Unsteady free-surface flow induced by a line Sink, J. Eng. Maths , 47, 137--160. doi:10.1023/A:1025892915279 T. E. Stokes, G. C. Hocking and L. K. Forbes, 2005, Unsteady flow induced by a withdrawal Point beneath a free surface, ANZIAM J. , 47, 185--202. doi:10.1017/S1446181100009986 T. E. Stokes, G. C. Hocking and L. K. Forbes, 2008, Unsteady free surface flow induced by a line Sink in a fluid of finite depth, Computers and Fluids , 37, 236--249. doi:10.1016/j.compfluid.2007.06.002 E. O. Tuck, and J-M. Vanden Broeck, 1984, A cusp-like free-surface flow due to a submerged source or Sink, J. Aust. Math Soc. Ser. B , 25, 443--450. doi:10.1017/S0334270000004197 P. A. Tyvand, 1992, Unsteady free-surface flow due to a line source, Phys. Fluids A , 4 (4), 671--676. doi:10.1063/1.858285 J-M. Vanden Broeck and J. B. Keller, 1987, Free surface flow due to a Sink, J. Fluid Mech. , 175, 109--117. doi:10.1017/S022112087000314 I. R. Wood, 1968, Selective withdrawal from a stably stratified fluid, J. Fluid Mech. , 32, 209--223. doi:10.1017/S022112068000686 M. Xue and D. K. P. Yue, 1998, Nonlinear free-surface flow due to an impulsively started submerged Point Sink, J. Fluid Mech. , 364, 325--347. doi:10.1017/S022112098001335 C. S. Yih, Dynamics of nonhomogeneous fluids , Macmillan, New York, 1965. Q-N. Zhou and W. P. Graebel, 1990, Axisymmetric draining of a cylindrical tank with a free surface, J. Fluid. Mech. 221, 511--532. doi:10.1017/S022112090003652

Fengxian Lin - One of the best experts on this subject based on the ideXlab platform.

  • the transient ground surface displacements due to a Point Sink heat source in an elastic half space
    GeoShanghai International Conference 2006, 2006
    Co-Authors: Fengxian Lin
    Abstract:

    Thermoelastic deformation due to a Point heat source is the analog of poroelastic response caused by a Point Sink. In this paper, Biot’s three-dimensional consolidation theory is introduced to derive the analytical solutions of the transient consolidation deformation with a Point Sink in saturated isotropic porous elastic half-space. The transient ground surface displacement produced by a Point heat source is described through analog quantities between poroelasticity and thermoelasticity. Closed-form solutions of the horizontal and vertical displacements are obtained by using Laplace and Hankel integral transforms. Attention is focused on the maximum surface horizontal displacement compared to the maximum surface settlement. Results show that the horizontal displacement is about 30% of the maximum ground surface settlement. The study concludes that horizontal displacement is significant and should be considered in prediction of the transient settlement induced by groundwater withdrawal.

Deepika Janakiraman - One of the best experts on this subject based on the ideXlab platform.

  • Lévy flights in the presence of a Point Sink of finite strength.
    Physical review. E, 2017
    Co-Authors: Deepika Janakiraman
    Abstract:

    In this paper, the absorption of a particle undergoing Lévy flight in the presence of a Point Sink of arbitrary strength and position is studied. The motion of such a particle is given by a modified Fokker-Planck equation whose exact solution in the Laplace domain can be described in terms of the Laplace transform of the unperturbed (absence of the Sink) Green's function. This solution for the Green's function is a well-studied, generic result which applies to both fractional and usual Fokker-Planck equations alike. Using this result, the propagator and the absorption-time distribution are obtained for free Lévy flight and Lévy flight in linear and harmonic potentials in the presence of a delta function Sink, and their dependence on the Sink strength is analyzed. Analytical results are presented for the long-time behavior of the absorption-time distribution in all three above-mentioned potentials. Simulation results are found to corroborate closely with analytical results.

  • l e vy flights in the presence of a Point Sink of finite strength
    arXiv: Statistical Mechanics, 2017
    Co-Authors: Deepika Janakiraman
    Abstract:

    In this paper, the absorption of a particle undergoing L\'{e}vy flight in the presence of a Point Sink of arbitrary strength and position is studied. The motion of such a particle is given by a modified Fokker-Planck equation whose exact solution in the Laplace domain can be described in terms of the Laplace transform of the unperturbed (absence of the Sink) Green's function. This solution for the Green's function is a well-studied, generic result which applies to both fractional and usual Fokker-Planck equations alike. Using this result, the propagator and the absorption time distribution are obtained for free L\'{e}vy flight and L\'{e}vy flight in linear and harmonic potentials in the presence of a delta function Sink, and their dependence on the Sink strength is analyzed. Analytical results are presented for the long-time behaviour of the absorption time distribution in all the three above mentioned potentials. Simulation results are found to corroborate closely with the analytical results.

  • L\'{e}vy flights in the presence of a Point Sink of finite strength
    arXiv: Statistical Mechanics, 2017
    Co-Authors: Deepika Janakiraman
    Abstract:

    In this paper, the absorption of a particle undergoing L\'{e}vy flight in the presence of a Point Sink of arbitrary strength and position is studied. The motion of such a particle is given by a modified Fokker-Planck equation whose exact solution in the Laplace domain can be described in terms of the Laplace transform of the unperturbed (absence of the Sink) Green's function. This solution for the Green's function is a well-studied, generic result which applies to both fractional and usual Fokker-Planck equations alike. Using this result, the propagator and the absorption time distribution are obtained for free L\'{e}vy flight and L\'{e}vy flight in linear and harmonic potentials in the presence of a delta function Sink, and their dependence on the Sink strength is analyzed. Analytical results are presented for the long-time behaviour of the absorption time distribution in all the three above mentioned potentials. Simulation results are found to corroborate closely with the analytical results.

  • levy flights in the presence of a Point Sink of finite strength
    Physical Review E, 2017
    Co-Authors: Deepika Janakiraman
    Abstract:

    In this paper, the absorption of a particle undergoing Levy flight in the presence of a Point Sink of arbitrary strength and position is studied. The motion of such a particle is given by a modified Fokker-Planck equation whose exact solution in the Laplace domain can be described in terms of the Laplace transform of the unperturbed (absence of the Sink) Green's function. This solution for the Green's function is a well-studied, generic result which applies to both fractional and usual Fokker-Planck equations alike. Using this result, the propagator and the absorption-time distribution are obtained for free Levy flight and Levy flight in linear and harmonic potentials in the presence of a delta function Sink, and their dependence on the Sink strength is analyzed. Analytical results are presented for the long-time behavior of the absorption-time distribution in all three above-mentioned potentials. Simulation results are found to corroborate closely with analytical results.