On the propagation of nonlinear acoustic waves in viscous and thermoviscous fluids

Jordan, P.M.; Norton, Guy V.; Chin‐Bing, Stanley A.; Warn-Varnas, A.

doi:10.1016/j.euromechflu.2012.01.016

Cited by 20 publications

(31 citation statements)

References 12 publications

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“…As an illustration, consider the potential (7) with α 2 = 121/128. In this case, (18) takes the form…”

Section: T I C < T < T Ii Cmentioning

confidence: 99%

“…The study of kinks (also known as topological solitons [13]) and domain walls in classical and quantum field theories [14,15], in theories of gravity and cosmology [16,17] and even in the nonlinear field theories of fluid * Electronic address: khare@iiserpune.ac.in † Electronic address: christov@lanl.gov ‡ Electronic address: avadh@lanl.gov mechanics [18] remains a topic of active research. Similarly, Ginzburg-Landau theories [19,20] have been very successful in explaining superconducting, superfluid and many other transitions as well as in modeling topological defects (e.g., vortices and domain walls) in a variety of functional materials, through the inclusion of the gradient of the relevant order parameter in the free energy.…”

Section: Introductionmentioning

confidence: 99%

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Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

2014

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We obtain exact solutions for kinks in φ 8 , φ 10 and φ 12 field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically-decaying tails and also asymmetric cases with mixed exponentialalgebraic tail decay, unlike the lower-order φ 4 and φ 6 theories. Additionally, we construct distinct kinks with equal energies in all three field theories considered, and we show the co-existence of up to three distinct kinks (for a φ 12 potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the φ 10 field theory, which is a quasi-exactly solvable (QES) model akin to φ 6 , we are also able to obtain three analytical solutions for the classical free energy as well as the probability distribution function in the thermodynamic limit.

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“…As an illustration, consider the potential (7) with α 2 = 121/128. In this case, (18) takes the form…”

Section: T I C < T < T Ii Cmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

2014

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“…differences between the traveling wave solutions of the original and the approximate equations. Here, we follow the approach in [43] and find the associated ODE of (A.1) to be…”

Section: Resultsmentioning

confidence: 99%

Nonlinear waves in electromigration dispersion in a capillary

Christov

2017

Wave Motion

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We construct exact solutions to an unusual nonlinear advection-diffusion equation arising in the study of Taylor-Aris (also known as shear) dispersion due to electroosmotic flow during electromigration in a capillary. An exact reduction to a Darboux equation is found under a traveling-wave anzats. The equilibria of this ordinary differential equation are analyzed, showing that their stability is determined solely by the (dimensionless) wave speed without regard to any (dimensionless) physical parameters. Integral curves, connecting the appropriate equilibria of the Darboux equation that governs traveling waves, are constructed, which in turn are shown to be asymmetric kink solutions (i.e., non-Taylor shocks). Furthermore, it is shown that the governing Darboux equation exhibits bistability, which leads to two coexisting non-negative kink solutions for (dimensionless) wave speeds greater than unity. Finally, we give some remarks on other types of traveling-wave solutions and a discussion of some approximations of the governing partial differential equation of electromigration dispersion.

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“…Taking the limit a 1 → 0, (4.9) reduces to 10) which is the special case of the Blackstock-Lesser-Seebass-Crighton model corresponding to classical lossless fluids; see Jordan et al (2012) and the references therein.…”

Section: (A) Bidirectional Equation Of Motionmentioning

confidence: 99%

“…If we now divide (4.9) by [1 − 2e(b − 1)f t ], which can never be zero, expand each occurrence of the reciprocal of this quantity in a binomial series (recall e 1) and then simplify and neglect terms O(e 2 ), our equation of motion becomes 11) which in the limit a 1 → 0 reduces to the lossless version of Kuznetsov's equation; again, see Jordan et al (2012) and the references therein. Because we have confined our attention to only right-running waves, let us now replace 3 the wave operator and the 'small' term (f t ) 2 in (4.11) with 2v t (v t + v x ) and (f x ) 2 , respectively.…”

Section: (B) Right-running Approximation: a Travelling Wave Solution mentioning

confidence: 99%

Compact acoustic travelling waves in a class of fluids with nonlinear material dispersion

Jordan

Saccomandi

2012

Proc. R. Soc. A.

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We apply a phenomenological theory of continua put forth by Rubin, Rosenau and Gottlieb in 1995 to an important class of compressible media. Regarding the material characteristic length coefficient, a, not as constant, but instead as a quadratic function of the velocity gradient, we carry out an in-depth analysis of one-dimensional acoustic travelling waves in inviscid, non-thermally conducting fluids. Analytical and numerical methods are employed to study the resulting waveforms, a special case of which exhibits compact support. In particular, a phase plane analysis is performed; simplified approximate/asymptotic expressions are presented; and a weakly nonlinear, KdV-like model that admits compact travelling wave solutions (TWSs), but which is not of the class K (m, n), is derived and analysed. Most significantly, our formulation allows for compact, pulse-type, acoustic waveforms in both gases and liquids.

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On the propagation of nonlinear acoustic waves in viscous and thermoviscous fluids

Cited by 20 publications

References 12 publications

Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

Nonlinear waves in electromigration dispersion in a capillary

Compact acoustic travelling waves in a class of fluids with nonlinear material dispersion

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