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Ray and wave chaos in ocean acoustics [[electronic resource] ] : chaos in waveguides / / Denis Makarov ... [et al.]
| Ray and wave chaos in ocean acoustics [[electronic resource] ] : chaos in waveguides / / Denis Makarov ... [et al.] |
| Autore | Makarov Denis |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2010 |
| Descrizione fisica | 1 online resource (412 p.) |
| Disciplina | 534.23 |
| Collana | Series on complexity, nonlinearity and chaos |
| Soggetto topico |
Underwater acoustics
Waves Chaotic behavior in systems |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-75805-5
9786612758058 981-4273-18-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 1. Ray and Wave Propagation; 1.1 Underwater Sound Channel; 1.2 Basic Equations; 1.2.1 Helmholtz equation; 1.2.2 Parabolic equation; 1.3 Geometrical Optics Approximations and Optical- Mechanical Analogy. The Hamiltonian Formalism; 1.3.1 Eikonal and transport equations; 1.3.2 Momentum-position variables; 1.3.3 Action-angle variables in a range-independent waveguide; 1.3.3.1 Canonical transformation; 1.3.3.2 Ray path in the unperturbed waveguide; 1.3.3.3 Canonical transformation in the form of Fourier series; 1.3.4 Action-angle variables in a range-dependent waveguide
1.3.4.1 Slow range variation of the sound speed field1.3.4.2 Weak variation of the sound speed field; 1.3.5 Geometrical optics for the Helmholtz equation; 1.3.5.1 Eikonal and transport equations; 1.3.5.2 Momentum-position variables; 1.3.5.3 Action-angle variables; 1.4 Ray Travel Times; 1.4.1 Timefront; 1.4.2 Travel time as a function of starting momentum; 1.5 Range-Dependent Environments; 1.5.1 Internal waves; 1.5.2 Rossby waves; 1.5.3 Currents; 1.5.4 Eddies; 1.6 Acoustic Ocean Tomography; 1.7 Experiments on Long-Range Sound Propagation; 1.7.1 The Heard Island Feasibility Test 1.7.2 Experiments with bottom-mounted sources1.7.2.1 Downsloped bathymetry near a source; 1.7.3 Acoustic Engineering Test; 1.7.4 Alternate Source Test; 1.7.5 Acoustic Thermometry of Ocean Climate; 1.8 Summary; 2. Ray Chaos; 2.1 Hamiltonian Chaos; 2.1.1 Dynamics of Hamiltonian systems; 2.1.2 Statistical description of Hamiltonian chaos; 2.2 Lyapunov Instability; 2.3 Ray-Medium Resonance; 2.4 Overlapping of Resonances; 2.5 Vertical Resonance; 2.5.1 Adiabatic approximation; 2.5.2 Passage through a resonance; 2.5.2.1 Scattering on a resonance; 2.5.2.2 Capturing into a resonance 2.5.3 Vertical resonance versus ray-medium resonance2.5.4 Resonance-induced chaotic layer; 2.5.5 Influence of vertical resonance on a timefront of a received pulse; 2.6 Manifestation of Regular and Chaotic Ray Motion in Distributions of Ray Travel Times; 2.6.1 Perturbed waveguide; 2.6.2 Timefront; 2.6.3 Amplitude of a pulse signal in plane "travel time-depth"; 2.6.4 Gap between travel times of chaotic and regular rays; 2.6.5 "Focusing" of ray travel times; 2.6.6 Role of stickiness and chaotic jets in "focusing" of ray travel times; 2.6.7 Smoothed intensity of pulse signal; 2.7 Summary 3. Wave Chaos3.1 The Problem of Wave Chaos; 3.1.1 Ehrenfest time; 3.1.2 Semiclassical propagator; 3.1.3 Fidelity or overlap of wave fields; 3.1.4 Dynamical localization; 3.2 Normal Modes; 3.2.1 Range-independent waveguide; 3.2.1.1 Eigenfunctions and eigenvalues in the WKB approximation; 3.2.1.2 Mode amplitudes; 3.2.1.3 Brillouin waves; 3.2.1.4 Matrix elements; 3.2.1.5 Ray-mode relations; 3.2.2 Range-dependent waveguide; 3.2.2.1 Coupled mode equations: slow and strong range dependence; 3.2.2.2 Coupled mode equations: weak range dependence 3.2.3 Normal modes corresponding to the Helmholtz equation |
| Record Nr. | UNINA-9910455587203321 |
Makarov Denis
|
||
| Hackensack, N.J., : World Scientific, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Ray and wave chaos in ocean acoustics [[electronic resource] ] : chaos in waveguides / / Denis Makarov ... [et al.]
| Ray and wave chaos in ocean acoustics [[electronic resource] ] : chaos in waveguides / / Denis Makarov ... [et al.] |
| Autore | Makarov Denis |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2010 |
| Descrizione fisica | 1 online resource (412 p.) |
| Disciplina | 534.23 |
| Altri autori (Persone) | MakarovDenis |
| Collana | Series on complexity, nonlinearity and chaos |
| Soggetto topico |
Underwater acoustics
Waves Chaotic behavior in systems |
| ISBN |
1-282-75805-5
9786612758058 981-4273-18-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 1. Ray and Wave Propagation; 1.1 Underwater Sound Channel; 1.2 Basic Equations; 1.2.1 Helmholtz equation; 1.2.2 Parabolic equation; 1.3 Geometrical Optics Approximations and Optical- Mechanical Analogy. The Hamiltonian Formalism; 1.3.1 Eikonal and transport equations; 1.3.2 Momentum-position variables; 1.3.3 Action-angle variables in a range-independent waveguide; 1.3.3.1 Canonical transformation; 1.3.3.2 Ray path in the unperturbed waveguide; 1.3.3.3 Canonical transformation in the form of Fourier series; 1.3.4 Action-angle variables in a range-dependent waveguide
1.3.4.1 Slow range variation of the sound speed field1.3.4.2 Weak variation of the sound speed field; 1.3.5 Geometrical optics for the Helmholtz equation; 1.3.5.1 Eikonal and transport equations; 1.3.5.2 Momentum-position variables; 1.3.5.3 Action-angle variables; 1.4 Ray Travel Times; 1.4.1 Timefront; 1.4.2 Travel time as a function of starting momentum; 1.5 Range-Dependent Environments; 1.5.1 Internal waves; 1.5.2 Rossby waves; 1.5.3 Currents; 1.5.4 Eddies; 1.6 Acoustic Ocean Tomography; 1.7 Experiments on Long-Range Sound Propagation; 1.7.1 The Heard Island Feasibility Test 1.7.2 Experiments with bottom-mounted sources1.7.2.1 Downsloped bathymetry near a source; 1.7.3 Acoustic Engineering Test; 1.7.4 Alternate Source Test; 1.7.5 Acoustic Thermometry of Ocean Climate; 1.8 Summary; 2. Ray Chaos; 2.1 Hamiltonian Chaos; 2.1.1 Dynamics of Hamiltonian systems; 2.1.2 Statistical description of Hamiltonian chaos; 2.2 Lyapunov Instability; 2.3 Ray-Medium Resonance; 2.4 Overlapping of Resonances; 2.5 Vertical Resonance; 2.5.1 Adiabatic approximation; 2.5.2 Passage through a resonance; 2.5.2.1 Scattering on a resonance; 2.5.2.2 Capturing into a resonance 2.5.3 Vertical resonance versus ray-medium resonance2.5.4 Resonance-induced chaotic layer; 2.5.5 Influence of vertical resonance on a timefront of a received pulse; 2.6 Manifestation of Regular and Chaotic Ray Motion in Distributions of Ray Travel Times; 2.6.1 Perturbed waveguide; 2.6.2 Timefront; 2.6.3 Amplitude of a pulse signal in plane "travel time-depth"; 2.6.4 Gap between travel times of chaotic and regular rays; 2.6.5 "Focusing" of ray travel times; 2.6.6 Role of stickiness and chaotic jets in "focusing" of ray travel times; 2.6.7 Smoothed intensity of pulse signal; 2.7 Summary 3. Wave Chaos3.1 The Problem of Wave Chaos; 3.1.1 Ehrenfest time; 3.1.2 Semiclassical propagator; 3.1.3 Fidelity or overlap of wave fields; 3.1.4 Dynamical localization; 3.2 Normal Modes; 3.2.1 Range-independent waveguide; 3.2.1.1 Eigenfunctions and eigenvalues in the WKB approximation; 3.2.1.2 Mode amplitudes; 3.2.1.3 Brillouin waves; 3.2.1.4 Matrix elements; 3.2.1.5 Ray-mode relations; 3.2.2 Range-dependent waveguide; 3.2.2.1 Coupled mode equations: slow and strong range dependence; 3.2.2.2 Coupled mode equations: weak range dependence 3.2.3 Normal modes corresponding to the Helmholtz equation |
| Record Nr. | UNINA-9910780894803321 |
|
Makarov Denis
|
||
| Hackensack, N.J., : World Scientific, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Ray and wave chaos in ocean acoustics : chaos in waveguides / / Denis Makarov ... [et al.]
| Ray and wave chaos in ocean acoustics : chaos in waveguides / / Denis Makarov ... [et al.] |
| Autore | Makarov Denis |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2010 |
| Descrizione fisica | 1 online resource (412 p.) |
| Disciplina | 534.23 |
| Altri autori (Persone) | MakarovDenis |
| Collana | Series on complexity, nonlinearity and chaos |
| Soggetto topico |
Underwater acoustics
Waves Chaotic behavior in systems |
| ISBN |
9786612758058
9781282758056 1282758055 9789814273183 981427318X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 1. Ray and Wave Propagation; 1.1 Underwater Sound Channel; 1.2 Basic Equations; 1.2.1 Helmholtz equation; 1.2.2 Parabolic equation; 1.3 Geometrical Optics Approximations and Optical- Mechanical Analogy. The Hamiltonian Formalism; 1.3.1 Eikonal and transport equations; 1.3.2 Momentum-position variables; 1.3.3 Action-angle variables in a range-independent waveguide; 1.3.3.1 Canonical transformation; 1.3.3.2 Ray path in the unperturbed waveguide; 1.3.3.3 Canonical transformation in the form of Fourier series; 1.3.4 Action-angle variables in a range-dependent waveguide
1.3.4.1 Slow range variation of the sound speed field1.3.4.2 Weak variation of the sound speed field; 1.3.5 Geometrical optics for the Helmholtz equation; 1.3.5.1 Eikonal and transport equations; 1.3.5.2 Momentum-position variables; 1.3.5.3 Action-angle variables; 1.4 Ray Travel Times; 1.4.1 Timefront; 1.4.2 Travel time as a function of starting momentum; 1.5 Range-Dependent Environments; 1.5.1 Internal waves; 1.5.2 Rossby waves; 1.5.3 Currents; 1.5.4 Eddies; 1.6 Acoustic Ocean Tomography; 1.7 Experiments on Long-Range Sound Propagation; 1.7.1 The Heard Island Feasibility Test 1.7.2 Experiments with bottom-mounted sources1.7.2.1 Downsloped bathymetry near a source; 1.7.3 Acoustic Engineering Test; 1.7.4 Alternate Source Test; 1.7.5 Acoustic Thermometry of Ocean Climate; 1.8 Summary; 2. Ray Chaos; 2.1 Hamiltonian Chaos; 2.1.1 Dynamics of Hamiltonian systems; 2.1.2 Statistical description of Hamiltonian chaos; 2.2 Lyapunov Instability; 2.3 Ray-Medium Resonance; 2.4 Overlapping of Resonances; 2.5 Vertical Resonance; 2.5.1 Adiabatic approximation; 2.5.2 Passage through a resonance; 2.5.2.1 Scattering on a resonance; 2.5.2.2 Capturing into a resonance 2.5.3 Vertical resonance versus ray-medium resonance2.5.4 Resonance-induced chaotic layer; 2.5.5 Influence of vertical resonance on a timefront of a received pulse; 2.6 Manifestation of Regular and Chaotic Ray Motion in Distributions of Ray Travel Times; 2.6.1 Perturbed waveguide; 2.6.2 Timefront; 2.6.3 Amplitude of a pulse signal in plane "travel time-depth"; 2.6.4 Gap between travel times of chaotic and regular rays; 2.6.5 "Focusing" of ray travel times; 2.6.6 Role of stickiness and chaotic jets in "focusing" of ray travel times; 2.6.7 Smoothed intensity of pulse signal; 2.7 Summary 3. Wave Chaos3.1 The Problem of Wave Chaos; 3.1.1 Ehrenfest time; 3.1.2 Semiclassical propagator; 3.1.3 Fidelity or overlap of wave fields; 3.1.4 Dynamical localization; 3.2 Normal Modes; 3.2.1 Range-independent waveguide; 3.2.1.1 Eigenfunctions and eigenvalues in the WKB approximation; 3.2.1.2 Mode amplitudes; 3.2.1.3 Brillouin waves; 3.2.1.4 Matrix elements; 3.2.1.5 Ray-mode relations; 3.2.2 Range-dependent waveguide; 3.2.2.1 Coupled mode equations: slow and strong range dependence; 3.2.2.2 Coupled mode equations: weak range dependence 3.2.3 Normal modes corresponding to the Helmholtz equation |
| Record Nr. | UNINA-9911095019703321 |
|
Makarov Denis
|
||
| Hackensack, N.J., : World Scientific, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Ray and wave chaos in ocean acoustics : chaos in waveguides / / Denis Makarov ... [et al.]
| Ray and wave chaos in ocean acoustics : chaos in waveguides / / Denis Makarov ... [et al.] |
| Autore | Makarov Denis |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2010 |
| Descrizione fisica | 1 online resource (412 p.) |
| Disciplina | 534.23 |
| Altri autori (Persone) | MakarovDenis |
| Collana | Series on complexity, nonlinearity and chaos |
| Soggetto topico |
Underwater acoustics
Waves Chaotic behavior in systems |
| ISBN |
9786612758058
9781282758056 1282758055 9789814273183 981427318X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 1. Ray and Wave Propagation; 1.1 Underwater Sound Channel; 1.2 Basic Equations; 1.2.1 Helmholtz equation; 1.2.2 Parabolic equation; 1.3 Geometrical Optics Approximations and Optical- Mechanical Analogy. The Hamiltonian Formalism; 1.3.1 Eikonal and transport equations; 1.3.2 Momentum-position variables; 1.3.3 Action-angle variables in a range-independent waveguide; 1.3.3.1 Canonical transformation; 1.3.3.2 Ray path in the unperturbed waveguide; 1.3.3.3 Canonical transformation in the form of Fourier series; 1.3.4 Action-angle variables in a range-dependent waveguide
1.3.4.1 Slow range variation of the sound speed field1.3.4.2 Weak variation of the sound speed field; 1.3.5 Geometrical optics for the Helmholtz equation; 1.3.5.1 Eikonal and transport equations; 1.3.5.2 Momentum-position variables; 1.3.5.3 Action-angle variables; 1.4 Ray Travel Times; 1.4.1 Timefront; 1.4.2 Travel time as a function of starting momentum; 1.5 Range-Dependent Environments; 1.5.1 Internal waves; 1.5.2 Rossby waves; 1.5.3 Currents; 1.5.4 Eddies; 1.6 Acoustic Ocean Tomography; 1.7 Experiments on Long-Range Sound Propagation; 1.7.1 The Heard Island Feasibility Test 1.7.2 Experiments with bottom-mounted sources1.7.2.1 Downsloped bathymetry near a source; 1.7.3 Acoustic Engineering Test; 1.7.4 Alternate Source Test; 1.7.5 Acoustic Thermometry of Ocean Climate; 1.8 Summary; 2. Ray Chaos; 2.1 Hamiltonian Chaos; 2.1.1 Dynamics of Hamiltonian systems; 2.1.2 Statistical description of Hamiltonian chaos; 2.2 Lyapunov Instability; 2.3 Ray-Medium Resonance; 2.4 Overlapping of Resonances; 2.5 Vertical Resonance; 2.5.1 Adiabatic approximation; 2.5.2 Passage through a resonance; 2.5.2.1 Scattering on a resonance; 2.5.2.2 Capturing into a resonance 2.5.3 Vertical resonance versus ray-medium resonance2.5.4 Resonance-induced chaotic layer; 2.5.5 Influence of vertical resonance on a timefront of a received pulse; 2.6 Manifestation of Regular and Chaotic Ray Motion in Distributions of Ray Travel Times; 2.6.1 Perturbed waveguide; 2.6.2 Timefront; 2.6.3 Amplitude of a pulse signal in plane "travel time-depth"; 2.6.4 Gap between travel times of chaotic and regular rays; 2.6.5 "Focusing" of ray travel times; 2.6.6 Role of stickiness and chaotic jets in "focusing" of ray travel times; 2.6.7 Smoothed intensity of pulse signal; 2.7 Summary 3. Wave Chaos3.1 The Problem of Wave Chaos; 3.1.1 Ehrenfest time; 3.1.2 Semiclassical propagator; 3.1.3 Fidelity or overlap of wave fields; 3.1.4 Dynamical localization; 3.2 Normal Modes; 3.2.1 Range-independent waveguide; 3.2.1.1 Eigenfunctions and eigenvalues in the WKB approximation; 3.2.1.2 Mode amplitudes; 3.2.1.3 Brillouin waves; 3.2.1.4 Matrix elements; 3.2.1.5 Ray-mode relations; 3.2.2 Range-dependent waveguide; 3.2.2.1 Coupled mode equations: slow and strong range dependence; 3.2.2.2 Coupled mode equations: weak range dependence 3.2.3 Normal modes corresponding to the Helmholtz equation |
| Record Nr. | UNINA-9911150319603321 |
| Makarov Denis | ||
| Hackensack, N.J., : World Scientific, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||