Derivation of Lighthill’s Eighth Power Law of an Aeroacoustic Quadrupole in Acoustic Spacetime

Acoustic spacetime is a four-dimensional manifold analogue to the relativistic spacetime with the reference speed of light replaced by the speed of sound. It has been established primarily for the indirect studies of relativistic phenomena by means of their better understood acoustic analogues. More recently, it has also been used for the analytical treatment of sound propagation in various uniform and non-uniform flows of the background fluid. In this paper the analogy is extended and utilized to derive Lighthill’s eight power law for sound generation of an aeroacoustic quadrupole. Adding to the existing analogue theory, propagating sound waves are described in terms of a weak perturbation of the background acoustic spacetime metric. The obtained result proves that the acoustic analogy can be extended to cover both weak perturbation of the fluid due to the sound waves and certain sound generation mechanisms, at least in incompressible low Mach number flows.

Modeling the Impact of Hamiltonian Perturbations on Expectation Value Dynamics

Evidently, some relaxation dynamics, e.g. exponential decays, are much more common in nature than others. Recently there have been attempts to explain this observation on the basis of “typicality of perturbations” with respect to their impact on expectation value dynamics. These theories suggest that a majority of the very numerous, possible Hamiltonian perturbations entail more or less the same type of alteration of the decay dynamics. Thus, in this paper, we study how the approach towards equilibrium in closed quantum systems is altered due to weak perturbations. To this end, we perform numerical experiments on a particular, exemplary spin system. We compare our numerical data to predictions from three particular theories. We find satisfying agreement in the weak perturbation regime for one of these approaches.

Application of Chaos Theory in the Assessment of Emotional Vulnerability and Emotion Dysregulation in Adults

In this work, we propose an interdisciplinary chaos analysis of emotion dysregulation (ED) and emotional vulnerability in adults. One of the main goals was the assessment of incongruences that occur in the evaluation of one’s own emotional dysregulation mechanisms in the presence of an extremely weak stimulus (Butterfly Effect). Thus, we considered a “flavor” of the Lyapunov Function method based on the assumption that the effort of answering to the test is itself a small perturbation. In this context, we calculated the “instability coefficient” Δ defined as the Euclidean distance between the pairs of vectors that include similar and reverted items of a test. The relationship between Δ, ED, and emotional characteristics as quality (positive/negative) and type (trait/state) was highlighted. We hypothesized that a higher level of Δ should be significantly related with a higher ED and with the type and the quality of emotions. The results suggest that Δ is significantly correlated with trait emotions (positively with negative emotions, and negatively with positive ones) and with ED. Moreover, Δ significantly predicts ED in adults. Thus, we consider that this approach is promising with respect to the evolution of emotional mechanisms across time. The presence of an initial instability to a weak perturbation might predict future abnormal emotional functioning, which could put at risk the mental or psychosomatic systems.

Shaping and processing the vortex spectra of singular beams with anomalous orbital angular momentum

The article examines physical mechanisms responsible for shaping the vortex avalanche induced by a weak perturbation of the holographic lattice of a combined vortex beam. For this, we have developed a new technique for measuring the degenerate spectra of optical vortices and orbital angular momentum of combined singular beams. The technique is based on measuring the intensity moments of higher orders of a beam containing vortices with both positive and negative topological charges. The appropriate choice of the mode amplitudes in the combined beam enables us to form orbital angular momentum anomalous spectral regions in the form of resonance dips and bursts. Since the intensity moments of a vortex mode with positive and negative topological charges are the same (the moments are degenerate) for an axially symmetric beam, the measurements are carried out in the plane of the double focus of a cylindrical lens. The calibration measurements show that the experimental error is not higher than 4.5 %. We also reveal that the dips and bursts in the orbital angular momentum spectrum are caused by the vortex avalanche induced by weak perturbations of the holographic grating relief responsible for the beam shaping. The appearance of the orbital angular momentum dips or bursts is controlled by the relation between the energy fluxes in the vortex avalanche with positive or negative topological charges.

Second-order sensitivity analysis for parametric equilibrium problems in set-valued optimization

In the paper, we first establish relationships between second-order contingent derivatives of a given set-valued map and that of the weak perturbation map. Then, these results are applied to sensitivity analysis for parametric equilibrium problems in set-valued optimization.

A weak perturbation theory for approximations of invariant measures in M/G/1 model

The calculation of the stationary distribution for a stochastic infinite matrix is generally difficult and does not have closed form solutions, it is desirable to have simple approximations converging rapidly to this distribution. In this paper, we use the weak perturbation theory to establish analytic error bounds for the M/G/1 model. Numerical examples are carried out to illustrate the quality of the obtained error bounds.

Breather wave, rogue wave and lump wave solutions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid

Under investigation in this paper is a (3[Formula: see text]+[Formula: see text]1)-dimensional generalized Kadomtsev–Petviashvili equation, which describes the long water waves and small-amplitude surface waves with the weak nonlinearity, weak dispersion and weak perturbation in a fluid. Via the Hirota method and symbolic computation, the lump wave, breather wave and rogue wave solutions are obtained. We graphically present the lump waves under the influence of the dispersion effect, nonlinearity effect, disturbed wave velocity effects and perturbed effects: Decreasing value of the dispersion effect can lead to the range of the lump wave decreases, but has no effect on the amplitude. When the value of the nonlinearity effect or disturbed wave velocity effects increases respectively, lump wave’s amplitude decreases but lump wave’s location keeps unchanged. Amplitudes of the lump waves are independent of the perturbed effects. Breather waves and rogue waves are displayed: Rogue waves emerge when the periods of the breather waves go to the infinity. When the value of the dispersion effect decreases, range of the rogue wave increases. When the value of the nonlinearity effect or disturbed wave velocity effects decreases respectively, rogue wave’s amplitude decreases. Value changes of the perturbed effects cannot influence the rogue wave.