A non-reflecting wave equation through directional wave-field suppression and its finite difference implementation

The acoustic wave equation describes wave propagation directly from basic physical laws, even in heterogeneous acoustic media. When numerically simulating waves with the wave equation, contrasts in the medium parameters automatically generate all scattering effects. For some applications - such as propagation analysis or certain wave-equation based imaging techniques - it is desirable to suppress these reflections, as we are only interested in the transmitted wave-field. To achieve this, a modification to the constitutive relations is proposed, yielding an extra term that suppresses waves with reference to a preferred direction. The scale-factor $$\alpha$$ α of this extra term can either be interpreted as a penetration depth or as a typical decay time. This modified theory is implemented using a staggered-grid, time-domain finite difference scheme, where the acoustic Poynting-vector is used to estimate the local propagation direction of the wave-field. The method was successfully used to suppress reflections in media with bone tissue (medical ultrasound) and geophysical subsurface structures, while introducing only minor perturbations to the transmitted wave-field and a small increase in computation time.

Manipulating the spectral collapse in two-photon Rabi model

We have investigated the eigenenergy spectrum of the two-photon Rabi model with a full quadratic coupling, particularly the special feature “spectral collapse”. The critical coupling strength is reduced by half from that of the two-photon Rabi model, implying that the spectral collapse can now occur at a more attainable value of the critical coupling. At the critical coupling some discrete eigenenergy levels still survive below the continuous energy spectrum, i.e. an incomplete spectral collapse, and the set of discrete eigenenergies has a one-to-one mapping with that of a particle of variable effective mass in a finite potential well. Since the energy difference between the two atomic levels specifies the depth of the potential well, the number of bound states available (or the extent of the “spectral collapse”) can be straightforwardly monitored. Obviously, this bears a great resemblance to the spectral collapse of the two-photon Rabi model, at least qualitatively. Moreover, since the full quadratic coupling includes an extra term proportional to the photon number operator only, our analysis indicates that one may manipulate the critical coupling of the two-photon Rabi model by incorporating an adjustable proportionality constant to this extra term.

Errata to Sound Hashing Modes of Arbitrary Functions, Permutations, and Block Ciphers

In ToSC 2018(4), Daemen et al. performed an in-depth investigation of sound hashing modes based on arbitrary functions, permutations, or block ciphers. However, for the case of invertible primitives, there is a glitch. In this errata, we formally fix this glitch by adding an extra term to the security bound, q/2b−n, where q is query complexity, b the width of the permutation or the block size of the block cipher, and n the size of the hash digest. For permutations that are wider than two times the chaining value this term is negligible. For block cipher based hashing modes where the block size is close to the digest size, the term degrades the security significantly.

Friedlander–Keller ray expansions and scalar wave reflection at canonically perturbed boundaries

This paper concerns the reflection of high-frequency, monochromatic linear waves of wavenumber k(≫ 1) from smooth boundaries which are O(k−1/2) perturbations away from either a specified near-planar boundary or else from a given smooth, two-dimensional curve of general O(1) curvature. For each class of perturbed boundary, we will consider separately plane and cylindrical wave incidence, with general amplitude profiles of each type of incident field. This interfacial perturbation scaling is canonical in the sense that a ray approach requires a modification to the standard WKBJ ‘ray ansatz’ which, in turn, leads to a leading-order amplitude (or ‘transport’) equation which includes an extra term absent in a standard application of the geometrical theory of diffraction. This extra term is unique to this scaling, and the afore-mentioned modification that is required is an application of a generalised type of ray expansion first posed by F. G. Friedlander and J. B. Keller (1955 Commun. Pure Appl. Math.6, 387–394).

Tenure in Office and Public Procurement

We study the impact of politicians' tenure in office on the outcomes of public procurement using a dataset on Italian municipal governments. To identify a causal relation, we first compare elections where the incumbent mayor barely won or barely lost another term. We then use the introduction of a two-term limit, which granted one potential extra term to mayors appointed before the reform. The main result is that an increase in tenure is associated with “worse” procurement outcomes. Our estimates are informative of the possibility that time in office progressively leads to collusion between government officials and local bidders. (JEL D72, H57, H76)

Irreversible work versus fidelity susceptibility for infinitesimal quenches

We compare the irreversible work produced in an infinitesimal sudden quench of a quantum system at zero temperature with its ground state fidelity susceptibility, giving an explicit relation between the two quantities. We find that the former is proportional to the latter but for an extra term appearing in the irreversible work which includes also contributions from the excited states. We calculate explicitly the two quantities in the case of the quantum Ising chain, showing that at criticality they exhibit different scaling behaviors. The irreversible work, rescaled by square of the quench’s amplitude, exhibits a divergence slower than that of the fidelity susceptibility. As a consequence, the two quantities obey also different finite-size scaling relations.

NEW MODEL FOR NUCLEON GENERALIZED PARTON DISTRIBUTIONS

We describe a new type of models for nucleon generalized parton distributions (GPDs) H and E. They are heavily based on the fact nucleon GPDs require to use two forms of double distribution (DD) representations. The outcome of the new treatment is that the usual "DD+D-term" construction should be amended by an extra term, [Formula: see text] which has the DD structure α/βe(β, α), with e(β, α) being the DD that generates GPD E(x, ξ). We found that this function, unlike the D-term, has support in the whole -1 ≤ x ≤ 1 region. Furthermore, it does not vanish at the border points |x| = ξ.

The Drift on Top of Waves

Wave particles move in circles, and for steep waves they also move with a drift in the wave direction. This drift can be found by second order Stokes theory. In this document it is questioned if Stokes’ theory gives reliable drift on the free surface, or if an extra term should be introduced in the equations. The CFD program COMFLOW is used to show that classic Stokes theory may be insufficient for calculating drift on the free surface.