On Mass Spectra of Primordial Black Holes

Evidence for the primordial black holes (PBH) presence in the early Universe renews permanently. New limits on their mass spectrum challenge existing models of PBH formation. One of the known models is based on the closed walls collapse after the inflationary epoch. Its intrinsic feature is the multiple production of small mass PBH which might contradict observations in the nearest future. We show that the mechanism of walls collapse can be applied to produce substantially different PBH mass spectra if one takes into account the classical motion of scalar fields together with their quantum fluctuations at the inflationary stage. Analytical formulas have been developed that contain both quantum and classical contributions.

PARTICLE TRAJECTORIES AND THE PERCEPTION OF CLASSICAL MOTION IN THE FREE PROPAGATION OF WAVE PACKETS.

The free propagation in time of a normalisable wave packet is the oldest problem of continuum quantum mechanics. Its motion from microscopic to macroscopic distance is the way in which most quantum systems are detected experimentally. Although much studied and analysed since 1927 and presented in many text books, here the problem is re-appraised from the standpoint of semi-classical mechanics. Particular aspects are the emergence of deterministic trajectories of particles emanating from a region of atomic dimensions and the interpretation of the wave function as describing a single particle or an ensemble of identical particles. Of possible wave packets, that of gaussian form is most studied due to the simple exact form of the time-dependent solution in real and in momentum space. Furthermore, this form is important in laser optics. Here the equivalence of the time-dependent Schroedinger equation to the paraxial equation for the propagation of light is demonstrated explicitly. This parallel helps to understand the relevance of trajectory concepts and the conditions necessary for the perception of motion as classical.

The hydrogen atom

The hydrogen atom is described by quantum mechanics. Radial wave functions are displayed, including those for large n (Rydberg atom). Emphasis is placed on the limits of classical motion, as giving a good indication of the atom's size. Positronium has the same size as hydrogen.

Usage of composite kernel in the SPH method for simulating the movement of granular materials

В работе для моделирования движения сыпучей среды используется метод сглаженных частиц. Для аппроксимации искомых функций предложено новое составное ядро малой связности. Основой для разработки ядра послужило требование к условию о сохранении плотности единичной SPH-частицы. Выполнение данного условия позволяет правильно моделировать поле плотности на границах расчетной области, а также в случаях структурных изменений каркаса гранулированных частиц сыпучей среды. Из анализа решения задачи гидростатики методом SPH получена оценка значения масштаба сглаживающей длины ядра для двумерного случая. Выполнен расчет процесса обрушения гранулированного “столба” и проведено сравнение полученных численных результатов моделирования с экспериментальными данными. The purpose of the study is to improve the practice of the SPH methodology which is applied for modelling of movement in the various media. The basis of the SPH-approximation of the function fields is formed by the forms of the smoothing kernel and its derivatives. Popular forms of smoothing kernels are characterized by the presence of significant fatal approximation errors when modelling granular media. Methodology. The state of granular medium is described by the classical motion and mass conservation equations. Each granule of the medium corresponds to a separate SPH particle. To approximate the density and pressure fields in the SPH particle, a new combination of the smoothing core and its first derivative forms is proposed. Results. The proposed new composite core fulfills the conditions of mass conservation and density recovery in the particle during SPH modeling. It is shown that the new composite core is characterized by a minimum error of pressure gradient approximation - about 2%. A new estimate for the velocity of propagation of an elastic wave in a medium, sufficient to obtain a correct numerical solution, is proposed. A comparative analysis of the obtained solutions with experimental data is made. Findings. The proposed composite shape of the smoothing kernel allows correct simulation of the motion of a granular medium by the SPH method. Its compactness (unit smoothing radius and unit smoothing length) makes it possible to correctly reconstruct the density field at the boundaries of the computational domain and in cases of structural changes in the framework of the granular medium. The numerical solution of the problem of the collapse of a column of granules obtained using the proposed composite core shows good agreement with experimental data.

Oscillating multiple giants

We propose a new example of the AdS/CFT correspondence between the system of multiple giant gravitons in AdS5× S5 and the operators with O(Nc) dimensions in $$ \mathcal{N} $$ N = 4 super Yang-Mills. We first extend the mixing of huge operators on the Gauss graph basis in the $$ \mathfrak{su}(2) $$ su 2 sector to all loops of the ’t Hooft coupling, by demanding the commutation of perturbative Hamiltonians in an effective U(p) theory, where p corresponds to the number of giant gravitons. The all-loop dispersion relation remains gapless at any λ, which suggests that harmonic oscillators of the effective U(p) theory should correspond to the classical motion of the D3-brane that is continuously connected to non-maximal giant gravitons.

Pair-production of cusps on a string in AdS3

The classical motion of a Nambu-Goto string in AdS3 spacetime is governed by the generalized sinh-Gordon equation. It can locally be reduced to the sinh-Gordon (shG), cosh-Gordon (chG), or Liouville equation, depending on the value of the scalar curvature of the induced metric. In this paper, I examine solutions that contain both shG-type and chG-type regions. The boundary between these regions moves with the speed of light. I show that near such boundaries (generalized) solitons can be classically pair-produced. The solitons move subluminally (superluminally) in the shG (chG) region on the worldsheet, and they correspond to cusps on the string. A direct energy cascade is observed at the moment of pair-creation.For the calculations, I use an exact discretization of the equation of motion. The solutions are segmented strings. In this discrete system, pair-production leads to a complete evaporation of the shG region. The final state is a gas of cusps in a chG environment.

The discomfort of riding shotgun – Why many people don’t like to be co-driver

This work investigates which conditions lead to co-driver discomfort aside from classical motion sickness, what characterizes uncomfortable situations and why these conditions lead to discomfort.The automobile is called a “passenger vehicle” as its main purpose is the transportation of people. However, passengers in the car are rarely considered in research about driving discomfort. The few studies in this area focus on driver discomfort, automated vehicles, and on driver assistant systems. An earlier public survey indicated that discomfort is also a relevant problem for co-drivers.An online questionnaire with N = 119 participants and a detailed follow up interview study with N = 24 participants were conducted.The results of the online questionnaire show that co-driver discomfort is a widespread problem (88 %). The results of the interviews indicate that the driving style is the only reason rated as very influential. Frequently mentioned reasons for discomfort are close following or fast driving. Uncomfortable situations were often perceived as safety critical. Participants also felt exposed to these situations. A model for possible cognitive origins of discomfort in co-drivers is proposed based on the study results.Co-driver discomfort is a common problem, highlighting the relevance of further research on supporting co-drivers. The reported correlations and the extension of theories from the areas of stress and self-regulation can help to explain the origin of this discomfort. The results provide a foundation for future design of interventions like human machine interfaces aiming at reducing co-driver discomfort.

Photodetachment of the H– ion in a forced harmonic potential

The photodetachment of a H– ion in a forced harmonic potential driven by a general time-dependent oscillating electric field has been investigated in the semi-classical closed orbit theory for the first time. It is found that the driven electric field frequency can affect the photodetachment cross-section of this system greatly. If the frequency of the driving electric field is equal to the harmonic frequency, a resonance phenomenon occurs in the classical motion of the detached electron. The interference effect between the returning electron wave travelling along the closed orbit with the initial outgoing wave gets stronger, causing the photodetachment cross-section to oscillate in a complicated manner. When the frequency of the driving electric field is unequal to the harmonic frequency, the driving electric field can weaken or strengthen the oscillatory structure in the photodetachment cross-section. In addition, the strength and initial phase in the driving electric field can also influence the photodetachment dynamics of the system. Our work provides a new method for controlling the photodetachment of negative ions in a harmonic potential and may guide future experimental research for cavity dynamics or in the ion trap.