The Experts below are selected from a list of 9732 Experts worldwide ranked by ideXlab platform
Gautam Iyer - One of the best experts on this subject based on the ideXlab platform.
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a stochastic Lagrangian Representation of the three dimensional incompressible navier stokes equations
Communications on Pure and Applied Mathematics, 2008Co-Authors: Peter Constantin, Gautam IyerAbstract:In this paper we derive a probabilistic Representation of the deterministic three-dimensional Navier-Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey SDEs driven by a uniform Wiener process; the inviscid Weber formula for the Euler equations of ideal fluids is used to recover the velocity field. This method admits a self-contained proof of local existence for the nonlinear stochastic system and can be extended to formulate stochastic Representations of related hydrodynamic-type equations, including viscous Burgers equations and Lagrangian-averaged Navier-Stokes alpha models. © 2007 Wiley Periodicals, Inc.
Yukio Kaneda - One of the best experts on this subject based on the ideXlab platform.
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Singularity formation in the shape of a vortex sheet in three dimensions-numerical simulation
ESAIM: Proceedings, 1996Co-Authors: Takashi Ishihara, Yukio KanedaAbstract:The evolution of a small but finite three-dimensional disturbance on a flat uniform vortex sheet is studied numerically on the basis of a Lagrangian Representation of the motion. The numerical simulations confirm the asymptotic analysis by Ishihara and Kaneda (1995; J. Fluid Mech., 300, 339-366) for the spontaneous singularity formation in the shape of the vortex sheet. They also suggest that the singularities appear along curves, which have a rather simple dependence on the spanwise-coordinate. Reflecting the three-dimensionality of the vortex dynamics, the singularity-curve is not along any of the vortex lines.
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A Representation of the motion of a vortex sheet in a three‐dimensional flow
Physics of Fluids A: Fluid Dynamics, 1990Co-Authors: Yukio KanedaAbstract:A Lagrangian Representation of the three‐dimensional motion of an infinitely thin vortex sheet in an ideal fluid is derived by using an invariance property of the jump of the velocity potential across the vortex sheet.
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On the three‐dimensional motion of an infinitely thin vortex sheet in an ideal fluid
Physics of Fluids A: Fluid Dynamics, 1990Co-Authors: Yukio KanedaAbstract:The three‐dimensional motion of an infinitely thin vortex sheet in an ideal fluid is studied on the basis of a Lagrangian Representation of the motion. Some conservation properties associated with the motion are derived from the Representation. The motion of an axisymmetric vortex sheet of a small area located far from the symmetry axis is analyzed in some detail.
Justin Dressel - One of the best experts on this subject based on the ideXlab platform.
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acoustic versus electromagnetic field theory scalar vector spinor Representations and the emergence of acoustic spin
arXiv: Classical Physics, 2020Co-Authors: Lucas Burns, Konstantin Y Bliokh, Franco Nori, Justin DresselAbstract:We construct a novel Lagrangian Representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian Representation with a ${\it scalar}$ potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement ${\it vector}$ potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether currents. The results are consistent with recent theoretical analyses and experiments. Furthermore, by an analogy with dual-symmetric electromagnetic field theory that combines electric- and magnetic-potential Representations, we put forward an acoustic ${\it spinor}$ Representation combining the scalar and vector Representations. This approach also includes naturally coupling to sources. The strong analogies between electromagnetism and acoustics suggest further productive inquiry, particularly regarding the nature of the apparent spacetime symmetries inherent to acoustic fields.
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Acoustic field theory: scalar, vector, spinor Representations and the emergence of acoustic spin
arXiv: Classical Physics, 2019Co-Authors: Lucas Burns, Konstantin Y Bliokh, Franco Nori, Justin DresselAbstract:We construct a novel Lagrangian Representation of acoustic field theory that accounts for the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach describes the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian Representation with a scalar potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement vector potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether currents. The results are consistent with recent theoretical analyses and experiments. Furthermore, by an analogy with dual-symmetric electromagnetic field theory that combines electric- and magnetic-potential Representations, we put forward an acoustic spinor Representation combining the scalar and vector Representations. This approach also includes naturally coupling to sources. The strong analogies between electromagnetism and acoustics suggest further productive inquiry, particularly regarding the nature of the apparent spacetime symmetries inherent to acoustic fields.
Werner Varnhorn - One of the best experts on this subject based on the ideXlab platform.
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Steady and Unsteady Navier–Stokes Flow with Lagrangian Differences
Differential and Difference Equations with Applications, 2018Co-Authors: Werner VarnhornAbstract:The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier–Stokes system (N). This description corresponds to the so-called Eulerian approach. We develop a new approximation method for (N) in both the steady and the nonsteady case by a suitable coupling of the Eulerian and the Lagrangian Representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity, which contains a convergent subsequence with limit function v such that v is a weak solution on (N).
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The Navier- Stokes Equations with Lagrangian Differences
2015Co-Authors: Werner VarnhornAbstract:Abstract: The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations (N). This description corresponds to the so-called Eulerian approach. We develop a new approximation method for (N) in both the stationary and the nonstationary case by a suitable coupling of the Eulerian and the Lagrangian Representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity, which contains a convergent subsequence with limit function v such that v is a weak solution on (N). Key–Words: Navier-Stokes equations, Lagrangian Representation, weak solutions
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Lagrangian approximations and weak solutions of the Navier-Stokes equations
Parabolic and Navier–Stokes equations, 2008Co-Authors: Werner VarnhornAbstract:The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian Representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity containing a convergent subsequence with limit function v such that v is a weak solution of the Navier-Stokes equations. AMS–MSC (2000): 35B65, 35D05, 76D05 Key–Words: Navier-Stokes equations, Lagrangian Representation, weak solutions
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The Navier-Stokes Equations with Lagrangian Differences
2006Co-Authors: Werner VarnhornAbstract:The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations (N). This description corresponds to the so-called Eulerian approach. We develop a new approximation method for (N) in both the stationary and the nonstationary case by a suitable coupling of the Eulerian and the Lagrangian Representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity, which contains a convergent subsequence with limit function v such that v is a weak solution on (N).
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On Eulerian and Lagrangian Representation of steady incompressible fluid flow
Nonlinear Analysis: Theory Methods & Applications, 1993Co-Authors: Werner VarnhornAbstract:FOR THE description of fluid flow there are, in principle, two approaches, the Eulerian approach and the Lagrangian approach. The first one describes the flow of its velocity u = (u,(x), v,(x), uJx)) = u(x) in every point x = (xi, x2, x3) of the domain G containing the fluid. The second one uses the trajectory x = (xi(t), x2(t), x3(t)) = x(t) = X(t, x0) of a single particle of fluid, which at initial time t = 0 is located at some point x0 E G. This second approach is of great importance for the numerical analysis and computation of fluid flow [l-4], while the first one has often also been used in connection with theoretical questions [5-81. In the present paper we consider the stationary motion of a viscous incompressible fluid in a bounded domain G c R3 with a sufficiently smooth boundary S. Because for steady flow the streamlines and the trajectories of the fluid particles coincide, both approaches mentioned above are correlated by the autonomous system of characteristic ordinary differential equations
Lucas Burns - One of the best experts on this subject based on the ideXlab platform.
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acoustic versus electromagnetic field theory scalar vector spinor Representations and the emergence of acoustic spin
arXiv: Classical Physics, 2020Co-Authors: Lucas Burns, Konstantin Y Bliokh, Franco Nori, Justin DresselAbstract:We construct a novel Lagrangian Representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian Representation with a ${\it scalar}$ potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement ${\it vector}$ potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether currents. The results are consistent with recent theoretical analyses and experiments. Furthermore, by an analogy with dual-symmetric electromagnetic field theory that combines electric- and magnetic-potential Representations, we put forward an acoustic ${\it spinor}$ Representation combining the scalar and vector Representations. This approach also includes naturally coupling to sources. The strong analogies between electromagnetism and acoustics suggest further productive inquiry, particularly regarding the nature of the apparent spacetime symmetries inherent to acoustic fields.
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Acoustic field theory: scalar, vector, spinor Representations and the emergence of acoustic spin
arXiv: Classical Physics, 2019Co-Authors: Lucas Burns, Konstantin Y Bliokh, Franco Nori, Justin DresselAbstract:We construct a novel Lagrangian Representation of acoustic field theory that accounts for the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach describes the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian Representation with a scalar potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement vector potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether currents. The results are consistent with recent theoretical analyses and experiments. Furthermore, by an analogy with dual-symmetric electromagnetic field theory that combines electric- and magnetic-potential Representations, we put forward an acoustic spinor Representation combining the scalar and vector Representations. This approach also includes naturally coupling to sources. The strong analogies between electromagnetism and acoustics suggest further productive inquiry, particularly regarding the nature of the apparent spacetime symmetries inherent to acoustic fields.
