Linear stability analysis of a time-divergent slamming flow

When a liquid slams into a solid, the intermediate gas is squeezed out at a speed that diverges when approaching the moment of impact. Although there is mounting experimental evidence that instabilities form on the liquid interface during such an event, understanding of the nature of these instabilities is limited. This study therefore addresses the stability of a liquid–gas interface with surface tension, subject to a diverging flow in the gas phase, where the liquid and the gas phase are both represented as potential fluids. We perform a Kelvin–Helmholtz-type linear modal stability analysis of the surface to obtain an amplitude equation that is subsequently analysed in detail and applied to two cases of interest for impact problems, namely, the parallel impact of a wave onto a vertical wall, and the impact of a horizontal plate onto a liquid surface. In both cases we find that long wavelengths are stabilised considerably in comparison with what may be expected based upon classical knowledge of the stability of interfaces subject to a constant gas flow. In the former case, this leads to the prediction of a marginally stable wavelength that is completely absent in the classical analysis. For the latter we find much resemblance to the classical case, with the connotation that the instability is suppressed for smaller disk sizes. The study ends with a discussion of the influence of gas viscosity and gas compressibility on the respective stability diagrams.

Answering Fuzzy Queries over Fuzzy DL-Lite Ontologies

A prominent problem in knowledge representation is how to answer queries taking into account also the implicit consequences of an ontology representing domain knowledge. While this problem has been widely studied within the realm of description logic ontologies, it has been surprisingly neglected within the context of vague or imprecise knowledge, particularly from the point of view of mathematical fuzzy logic. In this paper, we study the problem of answering conjunctive queries and threshold queries w.r.t. ontologies in fuzzy DL-Lite. Specifically, we show through a rewriting approach that threshold query answering w.r.t. consistent ontologies remains in ${AC}^{0}$ in data complexity, but that conjunctive query answering is highly dependent on the selected triangular norm, which has an impact on the underlying semantics. For the idempotent Gödel t-norm, we provide an effective method based on a reduction to the classical case.

Monte Carlo study of transport in low-dimensional quantum disorder systems at finite temperature

Using the quantum generalized Langevin equation and the path integral Monte Carlo approach, we study the transport dynamics of low-dimensional quantum disorder systems at finite temperature. Motivated by the nature of the classical-to-quantum transformation in fluctuations in the time domain, we extend the treatment to the spatial domain and propose a quantum random-correlated potential, describing specifically quantum disorder. For understanding the Anderson localization from the particle transport perspective, we present an intuitive treatment using a classical analogy in which the particle moves through a flat periodic crystal lattice corrugated by classical or quantum disorder. We emphasize an effective classical disorder potential in studying the quantum effects on the transport dynamics. Compared with the classical case, we find that the quantum escape rate from a disordered metastable potential is larger. Moreover, the diffusion enhancement of a quantum system moving in a weak, biased, periodic disorder potential is more significant compared with the classical case; for an effective rock-ratcheted disorder potential, quantum effects increase the directed current with decreasing temperature. For the classical case, we explore surface diffusion on a two-dimensional biased disorder potential at finite temperature; surprisingly, the optimal angle of the external bias force is found to enhance diffusion in the biased disorder surface. Furthermore, to explain the quantum transport dynamics in a disorder potential, we adopt the barrier-crossing mechanism and the mean first passage time theory to establish the probability distribution function.

Quantum absentminded driver problem revisited

The aim of the paper is to study the problem of absentminded driver in the quantum domain. In the classical case, it is a well-known example of a decision problem with imperfect recall that exhibits lack of equivalence between mixed and behavioral strategies. The optimal payoff outcome is significantly lower than the maximum payoff appearing in the game. This raises the question whether a quantum approach to the problem can increase the strategic position of the decision maker. The results that we present in the paper clearly reveal the benefits from playing the absentminded problem with the aid of quantum objects. Through appropriately chosen initial quantum state, the unitary strategies enable the decision maker to obtain the maximum possible payoff. At the same time, our scheme comes down to the classical problem with a suitable restriction of unitary strategies.

Fractal–Fractional Michaelis–Menten Enzymatic Reaction Model via Different Kernels

In this paper, three new models of fractal–fractional Michaelis–Menten enzymatic reaction (FFMMER) are studied. We present these models based on three different kernels, namely, power law, exponential decay, and Mittag-Leffler kernels. We construct three schema of successive approximations according to the theory of fractional calculus and with the help of Lagrange polynomials. The approximate solutions are compared with the resulting numerical solutions using the finite difference method (FDM). Because the approximate solutions in the classical case of the three models are very close to each other and almost matches, it is sufficient to compare one model, and the results were good. We investigate the effects of the fractal order and fractional order for all models. All calculations were performed using Mathematica software.

SURFACE LAYER THICKNESS AND ANISOTROPY OF THE SURFACE ENERGY OF CUBIC RUTHENIUM CRYSTALS

В работе рассмотрены вопросы анизотропии поверхностного слоя и анизотропии поверхностной энергии кубических кристаллов рутения. В основе этого рассмотрения лежит эмпирическая модель атомарно-гладких кристаллов, толщина поверхностного слоя которых зависит от одного фундаментального параметра -атомного объема элемента. Расчеты кристаллов рутения показали, что толщина поверхностного слоя кристаллов рутения во всех направлениях не превышает d (I) < 10 нм и они представляют собой наноструктуру. Кристаллы рутенийалюминий, рутенийгафний, рутенийтитан, рутенийцирконий имеют ơ > 3 Дж/м в направлении (100) . Нами рассмотрена задача о диффузии газа в нанометровой пластине рутения. В отличие от классической задачи в полученном уравнении появляется логарифмический член. Это приводит к расходимости в начале координат. Поэтому граничные условия нужно задавать не при x = 0, а при x = d (0) - длине де Бройлевской волны электронов. Только в этом случае имеют смысл классические уравнения диффузии. Существенно также, что, согласно полученному уравнению, диффузии нанопластины зависит как от материала пластины через коэффициент диффузии массивного образца, так и от размерного фактора. В классическом случае такой зависимости нет. Для описания фазовых переходов в наноструктурах предложены различные модели, среди которых можно отметить метод среднего поля Ландау, в котором используется параметр порядка. Мы воспользуемся теорией Ландау, заменяя температуру T на координату h . The paper deals with the anisotropy of the surface layer and the anisotropy of the free surface energy of cubic ruthenium crystals. This consideration is based on an empirical model of atomically smooth crystals, the thickness of the surface layer of which depends on single fundamental parameter - the atomic volume of an element. Calculations of ruthenium crystals showed that the thickness of the surface layer of ruthenium crystals in all directions does not exceed d(I)< 10 nm and they represent a nanostructure. Crystals of ruthenium aluminum, ruthenium hafnium, ruthenium titanium, ruthenium zirconium have ơ > 3 J/m in the (100) direction. We have considered the problem of gas diffusion in a nanometer ruthenium plate. In contrast to the classical problem, a logarithmic term appears in the resulting equation. This leads to divergence at the origin. Therefore, the boundary conditions must be specified not at x = 0, but at x = d (0) - the de Broglie wavelength of electrons. Only in this case the classical diffusion equations are meaningful. It is also important that, according to the obtained equation, the diffusion of the nanoplate depends both on the material of the plate through the diffusion coefficient of the bulk sample and on the size factor. In the classical case, there is no such dependence. Various models have been proposed to describe phase transitions in nanostructures, among which we can mention the Landau mean field method, in which the order parameter is used. We will use Landau's theory, replacing the temperature T with the coordinate h.

Divergence-Based Segmentation Algorithm for Heavy-Tailed Acoustic Signals with Time-Varying Characteristics

Many real-world systems change their parameters during the operation. Thus, before the analysis of the data, there is a need to divide the raw signal into parts that can be considered as homogeneous segments. In this paper, we propose a segmentation procedure that can be applied for the signal with time-varying characteristics. Moreover, we assume that the examined signal exhibits impulsive behavior, thus it corresponds to the so-called heavy-tailed class of distributions. Due to the specific behavior of the data, classical algorithms known from the literature cannot be used directly in the segmentation procedure. In the considered case, the transition between parts corresponding to homogeneous segments is smooth and non-linear. This causes that the segmentation algorithm is more complex than in the classical case. We propose to apply the divergence measures that are based on the distance between the probability density functions for the two examined distributions. The novel segmentation algorithm is applied to real acoustic signals acquired during coffee grinding. Justification of the methodology has been performed experimentally and using Monte-Carlo simulations for data from the model with heavy-tailed distribution (here the stable distribution) with time-varying parameters. Although the methodology is demonstrated for a specific case, it can be extended to any process with time-changing characteristics.

The de Almeida–Thouless Line in Hierarchical Quantum Spin Glasses

We determine explicitly and discuss in detail the effects of the joint presence of a longitudinal and a transversal (random) magnetic field on the phases of the Random Energy Model and its hierarchical generalization, the GREM. Our results extent known results both in the classical case of vanishing transversal field and in the quantum case for vanishing longitudinal field. Following Derrida and Gardner, we argue that the longitudinal field has to be implemented hierarchically also in the Quantum GREM. We show that this ensures the shrinking of the spin glass phase in the presence of the magnetic fields as is also expected for the Quantum Sherrington–Kirkpatrick model.

Einstein's Elevator: World Lines, Michelson-Morley Experiment and Relativistic Paradox

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation, and for the first time the worldlines equations are given. We consider a uniformly accelerated reference frame in rectilinear translation, and we show that the trajectories of the particles are semi-ellipses with the center on the event horizon. The frame of reference is non-inertial, the space-time is flat, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, especially the experiment with the accelerated Michelson-Morley interferometer is solved, and we described an experiment where a new relativistic paradox appears --- a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical. The concepts of metric, coordinated velocity and horizon are discussed, and the analogy with the black hole is made.

FINITE ELEMENT ANALYSIS OF THE DIFFUSION MODEL OF THE BIOCLOGGING OF THE GEOBARRIER

The distribution of an organic chemical and the filtration process in the soil which contains a thin geochemical barrier are considered. Microorganism colonies develop in the presence of organic chemicals in the soil which leads to the so-called phenomenon of bioclogging of the pore space. As a result, the conductivity characteristics of both the soil as a whole and the geochemical barrier change. Conjugation conditions as a component of the mathematical model of chemical filtration in the case of inhomogeneity of porous media and the presence of fine inclusions were modified for the case of bioclogging. The numerical solution of the corresponding nonlinear boundary value problem with modified conjugation conditions was found by the finite element method. The conditions of the existence of a generalized solution of the corresponding boundary value problem are indicated. The results on the theoretical accuracy of finite element solutions are presented. Differences in the value of pressure jumps at a thin geochemical barrier were analyzed for the case considered in the article and the classical case on a model example of filtration consolidation of the soil in the base of solid waste storage. The excess pressure in 600 days after the start of the process reaches 25 % of the initial value when taking into account the effect of bioclogging, while is only 6 % for the test case disregarding the specified effect.