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Glauber T Silva - One of the best experts on this subject based on the ideXlab platform.
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acoustic radiation force and torque exerted on a small viscoelastic particle in an Ideal Fluid
Ultrasonics, 2016Co-Authors: J P Leaoneto, Glauber T SilvaAbstract:We provide a detailed analysis on the acoustic radiation force and torque exerted on a homogeneous viscoelastic particle in the long-wave limit (i.e. the particle radius is much smaller than the incident wavelength) by an arbitrary wave. We assume that the particle behaves as a linear viscoelastic solid, which obeys the fractional Kelvin-Voigt model. Simple analytical expressions for the radiation force and torque are obtained. The developed theory is used to describe the interaction of acoustic waves (traveling and standing plane waves, and zero- and first-order Bessel beams) in the MHz-range with polymeric particles, namely lexan, low-density (LDPE) and high-density (HDPE) polyethylene. We found that particle absorption is chiefly the cause of the radiation force due to a traveling plane wave and zero-order Bessel beam when the frequency is smaller than 5MHz (HDPE), 3.9MHz (LDPE), and 0.9MHz (lexan). Whereas in a standing wave field, the radiation force is mildly changed due to dispersion inside the particle. We also show that the radiation torque caused by a first-order Bessel beam varies nearly quadratic with frequency. These findings may enable new possibilities of particle handling in acoustophoretic techniques.
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Acoustic Interaction Forces and Torques Acting on Suspended Spheres in an Ideal Fluid
IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 2016Co-Authors: Henrique J. Lopes, Mahdi Azarpeyvand, Glauber T SilvaAbstract:In this paper, the acoustic interaction forces and torques exerted by an arbitrary time-harmonic wave on a set of N objects suspended in an inviscid Fluid are theoretically analyzed. We utilize the partial-wave expansion method with translational addition theorem and re-expansion of multipole series to solve the related multiple scattering problem. We show that the acoustic interaction force and torque can be obtained using the farfield radiation force and torque formulas. To exemplify the method, we calculate the interaction forces exerted by an external traveling and standing plane wave on an arrangement of two and three olive-oil droplets in water. The droplets' radii are comparable to the wavelength (i.e., Mie scattering regime). The results show that the acoustic interaction forces present an oscillatory spatial distribution which follows the pattern formed by interference between the external and rescattered waves. In addition, acoustic interaction torques arise on the absorbing droplets whenever a nonsymmetric wavefront is formed by the external and rescattered waves' interference.
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acoustic radiation force and torque exerted on a small viscoelastic particle in an Ideal Fluid
arXiv: Classical Physics, 2015Co-Authors: J P Leaoneto, Glauber T SilvaAbstract:We provide a detailed analysis on the acoustic radiation force and torque exerted on a homogeneous viscoelastic particle in the long-wave limit (the particle radius is much smaller than the incident wavelength) by an arbitrary wave. We assume that the particle behaves as a linear viscoelastic solid, which obeys the fractional Kelvin-Voigt model. Simple analytical expressions for the radiation force and torque are obtained considering the low- and high-frequency approximation in the viscoelastic model. The developed theory is used to describe the interaction of acoustic waves (traveling and standing plane waves, and zero- and first-order Bessel beams) with a low- and high-density polyethylene particle chosen as examples. Negative axial radiation force and torque are predicted when the ratio of the longitudinal to shear relaxation times is smaller than a constant that depends on the speed of sound in the particle. In addition, a full 3D tractor Bessel vortex beam acting on the high-density polyethylene is depicted. These predictions may enable new possibilities of particle handling in acoustophoretic techniques.
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acoustic interaction forces between small particles in an Ideal Fluid
Physical Review E, 2014Co-Authors: Glauber T Silva, Henrik BruusAbstract:We present a theoretical expression for the acoustic interaction force between small spherical particles suspended in an Ideal Fluid exposed to an external acoustic wave. The acoustic interaction force is the part of the acoustic radiation force on one given particle involving the scattered waves from the other particles. The particles, either compressible liquid droplets or elastic microspheres, are considered to be much smaller than the acoustic wavelength. In this so-called Rayleigh limit, the acoustic interaction forces between the particles are well approximated by gradients of pair-interaction potentials with no restriction on the interparticle distance. The theory is applied to studies of the acoustic interaction force on a particle suspension in either standing or traveling plane waves. The results show aggregation regions along the wave propagation direction, while particles may attract or repel each other in the transverse direction. In addition, a mean-field approximation is developed to describe the acoustic interaction force in an emulsion of oil droplets in water.
Uriel Frisch - One of the best experts on this subject based on the ideXlab platform.
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time analyticity of lagrangian particle trajectories in Ideal Fluid flow
Journal of Fluid Mechanics, 2014Co-Authors: Vladislav Zheligovsky, Uriel FrischAbstract:It is known that the Eulerian and Lagrangian structures of Fluid flow can be drastically different; for example, Ideal Fluid flow can have a trivial (static) Eulerian structure, while displaying chaotic streamlines. Here, we show that Ideal flow with limited spatial smoothness (an initial vorticity that is just a little better than continuous) nevertheless has time-analytic Lagrangian trajectories before the initial limited smoothness is lost. To prove these results we use a little-known Lagrangian formulation of Ideal Fluid flow derived by Cauchy in 1815 in a manuscript submitted for a prize of the French Academy. This formulation leads to simple recurrence relations among the time-Taylor coefficients of the Lagrangian map from initial to current Fluid particle positions; the coefficients can then be bounded using elementary methods. We first consider various classes of incompressible Fluid flow, governed by the Euler equations, and then turn to highly compressible flow, governed by the Euler–Poisson equations, a case of cosmological relevance. The recurrence relations associated with the Lagrangian formulation of these incompressible and compressible problems are so closely related that the proofs of time-analyticity are basically identical.
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Time-analyticity of Lagrangian particle trajectories in Ideal Fluid flow
Journal of Fluid Mechanics, 2014Co-Authors: Vladislav Zheligovsky, Uriel FrischAbstract:It is known that the Eulerian and Lagrangian structures of Fluid flow can be drastically different; for example, Ideal Fluid flow can have a trivial (static) Eulerian structure, while displaying chaotic streamlines. Here we show that Ideal flow with limited spatial smoothness (an initial vorticity that is just a little better than continuous), nevertheless has time-analytic Lagrangian trajectories before the initial limited smoothness is lost. For proving such results we use a little-known Lagrangian formulation of Ideal Fluid flow derived by Cauchy in 1815 in a manuscript submitted for a prize of the French Academy. This formulation leads to simple recurrence relations among the time-Taylor coefficients of the Lagrangian map from initial to current Fluid particle positions; the coefficients can then be bounded using elementary methods. We first consider various classes of incompressible Fluid flow, governed by the Euler equations, and then turn to a case of compressible flow of cosmological relevance, governed by the Euler-Poisson equations.
Nikolai Nadirashvili - One of the best experts on this subject based on the ideXlab platform.
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Shear Flows of an Ideal Fluid and Elliptic Equations in Unbounded Domains
Communications on Pure and Applied Mathematics, 2017Co-Authors: François Hamel, Nikolai NadirashviliAbstract:We prove that, in a two-dimensional strip, a steady flow of an Ideal incompressible Fluid with no stationary point and tangential boundary conditions is a shear flow. The same conclusion holds for a bounded steady flow in a half-plane. The proofs are based on the study of the geometric properties of the streamlines of the flow and on one-dimensional symmetry results for solutions of some semilinear elliptic equations. Some related rigidity results of independent interest are also shown in n-dimensional slabs in any dimension n.
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shear flows of an Ideal Fluid and elliptic equations in unbounded domains
Communications on Pure and Applied Mathematics, 2017Co-Authors: François Hamel, Nikolai NadirashviliAbstract:We prove that, in a two-dimensional strip, a steady flow of an Ideal incompressible Fluid with no stationary point and tangential boundary conditions is a shear flow. The same conclusion holds for a bounded steady flow in a half-plane. The proofs are based on the study of the geometric properties of the streamlines of the flow and on one-dimensional symmetry results for solutions of some semilinear elliptic equations. Some related rigidity results of independent interest are also shown in n-dimensional slabs in any dimension n. © 2016 Wiley Periodicals, Inc.
Stephan Rosswog - One of the best experts on this subject based on the ideXlab platform.
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astrophysical smooth particle hydrodynamics
New Astronomy Reviews, 2009Co-Authors: Stephan RosswogAbstract:Abstract The paper presents a detailed review of the smooth particle hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that are necessary for a practical implementation of the method in a working SPH code. Much of SPH’s success relies on its excellent conservation properties and therefore the numerical conservation of physical invariants receives much attention throughout this review. The self-consistent derivation of the SPH equations from the Lagrangian of an Ideal Fluid is the common theme of the remainder of the text. We derive a modern, Newtonian SPH formulation from the Lagrangian of an Ideal Fluid. It accounts for changes of the local resolution lengths which result in corrective, so-called “grad-h-terms”. We extend this strategy to special relativity for which we derive the corresponding grad-h equation set. The variational approach is further applied to a general-relativistic Fluid evolving in a fixed, curved background space-time. Particular care is taken to explicitly derive all relevant equations in a coherent way.
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astrophysical smooth particle hydrodynamics
arXiv: Instrumentation and Methods for Astrophysics, 2009Co-Authors: Stephan RosswogAbstract:The paper presents a detailed review of the smooth particle hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that are necessary for a practical implementation of the method in a working SPH code. Much of SPH's success relies on its excellent conservation properties and therefore the numerical conservation of physical invariants receives much attention throughout this review. The self-consistent derivation of the SPH equations from the Lagrangian of an Ideal Fluid is the common theme of the remainder of the text. We derive a modern, Newtonian SPH formulation from the Lagrangian of an Ideal Fluid. It accounts for changes of the local resolution lengths which result in corrective, so-called "grad-h-terms". We extend this strategy to special relativity for which we derive the corresponding grad-h equation set. The variational approach is further applied to a general-relativistic Fluid evolving in a fixed, curved background space-time. Particular care is taken to explicitely derive all relevant equations in a coherent way.
A Troisi - One of the best experts on this subject based on the ideXlab platform.
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cosmological viability of f r gravity as an Ideal Fluid and its compatibility with a matter dominated phase
Physics Letters B, 2006Co-Authors: Salvatore Capozziello, Shinichi Nojiri, Sergei D Odintsov, A TroisiAbstract:Abstract We show that f ( R ) -gravity can, in general, give rise to cosmological viable models compatible with a matter-dominated epoch evolving into a late accelerated phase. We discuss the various representations of f ( R ) -gravity as an Ideal Fluid or a scalar–tensor gravity theory, taking into account conformal transformations. We point out that mathematical equivalence does not correspond, in several cases, to the physical equivalence of Jordan frame and Einstein frame. Finally, we show that wide classes of f ( R ) gravity models, including matter and accelerated phases, can be phenomenologically reconstructed by means of observational data. In principle, any popular quintessence models could be “reframed” as an f ( R ) -gravity model.
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cosmological viability of f r gravity as an Ideal Fluid and its compatibility with a matter dominated phase
Physics Letters B, 2006Co-Authors: Salvatore Capozziello, Shinichi Nojiri, Sergei D Odintsov, A TroisiAbstract:Abstract We show that f ( R ) -gravity can, in general, give rise to cosmological viable models compatible with a matter-dominated epoch evolving into a late accelerated phase. We discuss the various representations of f ( R ) -gravity as an Ideal Fluid or a scalar–tensor gravity theory, taking into account conformal transformations. We point out that mathematical equivalence does not correspond, in several cases, to the physical equivalence of Jordan frame and Einstein frame. Finally, we show that wide classes of f ( R ) gravity models, including matter and accelerated phases, can be phenomenologically reconstructed by means of observational data. In principle, any popular quintessence models could be “reframed” as an f ( R ) -gravity model.
