A pseudodifferential equation with damping for one-way wave propagation in inhomogeneous acoustic media

A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential one-way wave equation for an inhomogeneous acoustic medium using a known factorization argument. We give explicitly the two highest order terms, that are necessary for approximating the solution. A wave front (singularity) whose propagation velocity has non-zero component in the special direction is correctly described. The equation can't describe singularities propagating along turning rays, i.e. rays along which the velocity component in the special direction changes sign. We show that incorrectly propagated singularities are suppressed if a suitable dissipative term is added to the equation.Comment: 15 page

A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory

We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a discrete operator to be applied to the source and the wavefields are constructed. Their coefficients are piecewise polynomial functions of $hk$, chosen such that phase and amplitude errors are minimal. The phase errors of the scheme are very small, approximately as small as those of the 2-D quasi-stabilized FEM method and substantially smaller than those of alternatives in 3-D, assuming the same number of gridpoints per wavelength is used. In numerical experiments, accurate solutions are obtained in constant and smoothly varying media using meshes with only five to six points per wavelength and wave propagation over hundreds of wavelengths. When used as a coarse level discretization in a multigrid method the scheme can even be used with downto three points per wavelength. Tests on 3-D examples with up to $10^8$ degrees of freedom show that with a recently developed hybrid solver, the use of coarser meshes can lead to corresponding savings in computation time, resulting in good simulation times compared to the literature.Comment: 33 pages, 12 figures, 6 table

Dative by genitive replacement in the Greek language of the papyri: a diachronic account of case semantics

Semantic analysis of the prenominal first person singular genitive pronoun (μου) in the Greek of the documentary papyri shows that the pronoun is typically found in the position between a verbal form and an alienable possessum which functions as the patient of the predicate. When the event expressed by the predicate is patient-affecting, the possessor is indirectly also affected. Hence the semantic role of this affected alienable possessor might be interpreted as a benefactive or malefactive in genitive possession constructions. By semantic extension the meaning of the genitive case in this position is extended into goal-oriented roles, such as addressee and recipient, which are commonly denoted by the dative case in Ancient Greek. The semantic similarity of the genitive and dative cases in these constructions might have provided the basis for the merger of the cases in the Greek language

Kinematic artifacts in prestack depth migration.

Strong refraction of waves in the migration velocity model introduces kinematic artifacts¿coherent events not corresponding to actual reflectors¿into the image volumes produced by prestack depth migration applied to individual data bins. Because individual bins are migrated independently, the migration has no access to the bin component of slowness. This loss of slowness information permits events to migrate along multiple incident-reflected ray pairs, thus introducing spurious coherent events into the image volume. This pathology occurs for all common binning strategies, including common-source, common-offset, and common-scattering angle. Since the artifacts move out with bin parameter, their effect on the final stacked image is minimal, provided that the migration velocity model is kinematically correct. However, common-image gathers may exhibit energetic primary events with substantial residual moveout, even with the kinematically accurate migration velocity model

Only in the standard representation the Dirac theory is a quantum theory of a single fermion

It is shown that the relativistic quantum mechanics of a single fermion can be developed only on the basis of the standard representation of the Dirac bispinor. As in the nonrelativistic quantum mechanics, the arbitrariness in defining the bispinor, as a four-component wave function, is restricted by its multiplication by an arbitrary phase factor. We reveal the role of the large and small components of the bispinor, establish their link in the nonrelativistic limit with the Pauli spinor, as well as explain the role of states with negative energies. The Klein tunneling is treated here as a physical phenomenon analogous to the propagation of the electromagnetic wave in a medium with negative dielectric permittivity and permeability. For the case of localized stationary states we define the effective one-particle operators which act in the space of the large component but contain the contributions of both components. The effective operator of energy is presented in a compact analytical form.Comment: 15 pages, 3 figures, thoroughly rewritte

Linguistic variation in Greek papyri: towards a new tool for quantitative study

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Semiclassical analysis for the Kramers-Fokker-Planck equation

We study some accurate semiclassical resolvent estimates for operators that are neither selfadjoint nor elliptic, and applications to the Cauchy problem. In particular we get a precise description of the spectrum near the imaginary axis and precise resolvent estimates inside the pseudo-spectrum. We apply our results to the Kramers-Fokker-Planck operator