Numerical study of Bingham flow in macrosopic two dimensional heterogenous porous media

The flow of non-Newtonian fluids is ubiquitous in many applications in the geological and industrial context. We focus here on yield stress fluids (YSF), i.e. a material that requires minimal stress to flow. We study numerically the flow of yield stress fluids in 2D porous media on a macroscopic scale in the presence of local heterogeneities. As with the microscopic problem, heterogeneities are of crucial importance because some regions will flow more easily than others. As a result, the flow is characterized by preferential flow paths with fractal features. These fractal properties are characterized by different scale exponents that will be determined and analyzed. One of the salient features of these results is that these exponents seem to be independent of the amplitude of heterogeneities for a log-normal distribution. In addition, these exponents appear to differ from those at the microscopic level, illustrating the fact that, although similar, the two scales are governed by different sets of equations

Long-Time Asymptotics for the Camassa-Holm Equation

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Camassa-Holm equation for decaying initial data, completing previous results by A. Boutet de Monvel and D. Shepelsky.Comment: 30 page

Method of modeling the cognitive radio using Opnet Modeler

This article is a review of the first wireless standard based on cognitive radio networks. The necessity of wireless networks based on the technology of cognitive radio. An example of the use of standard IEEE 802.22 in Wimax network through which was implemented in the simulation software environment Opnet Modeler. Schedules to check the performance of HTTP and FTP protocols CR network. Simulation results justify the use of standard IEEE 802.22 in wireless networks.Ця стаття являє собою огляд першого бездротового стандарту, заснованого на мережах когнітивного радіо. У роботі були розглянуті основні елементи стандарту IEEE 802.22, такі як структура фізичного і канального рівнів, топологія системи, ємність системи і задане покриття системи. Також були визначені головні переваги та проблеми стандарту 802.22.Використовуючи пакетOpnetModeler, було промодульовано сегмент CR мережі через Wimax, використовуючи RIPng протокол

Abstract kinetic equations with positive collision operators

We consider "forward-backward" parabolic equations in the abstract form $Jd \psi / d x + L \psi = 0$, $0< x < \tau \leq \infty$, where $J$ and $L$ are operators in a Hilbert space $H$ such that $J=J^*=J^{-1}$, $L=L^* \geq 0$, and $\ker L = 0$. The following theorem is proved: if the operator $B=JL$ is similar to a self-adjoint operator, then associated half-range boundary problems have unique solutions. We apply this theorem to corresponding nonhomogeneous equations, to the time-independent Fokker-Plank equation $\mu \frac {\partial \psi}{\partial x} (x,\mu) = b(\mu) \frac {\partial^2 \psi}{\partial \mu^2} (x, \mu)$, $0<x<\tau$, $\mu \in \R$, as well as to other parabolic equations of the "forward-backward" type. The abstract kinetic equation $T d \psi/dx = - A \psi (x) + f(x)$, where $T=T^*$ is injective and $A$ satisfies a certain positivity assumption, is considered also.Comment: 20 pages, LaTeX2e, version 2, references have been added, changes in the introductio

Spectral Asymptotics for Perturbed Spherical Schr\"odinger Operators and Applications to Quantum Scattering

We find the high energy asymptotics for the singular Weyl--Titchmarsh m-functions and the associated spectral measures of perturbed spherical Schr\"odinger operators (also known as Bessel operators). We apply this result to establish an improved local Borg-Marchenko theorem for Bessel operators as well as uniqueness theorems for the radial quantum scattering problem with nontrivial angular momentum.Comment: 20 page

Management of communication technologies as the basis of ensuring sustainable competitive advantages of service field enterprise

Метою статті є обґрунтування методологічного підходу до формування конкурентних переваг підприємства сфери послуг на засадах управління комунікативними технологіями. На основі аналізу ринку клінінгових послуг міста Одеси та області побудовано карту стратегічних груп та визначено основні підприємства-конкуренти ТОВ «Об’єкт Сервіс». У статті проведено оцінювання конкурентоспроможності досліджуваного підприємства на основі розрахунку інтегрального показника. За результатами опитування клієнтів підприємства встановлено недоліки процесу обслуговування. З використанням функціонального моделювання, а саме нотації Activity diagram, побудовано бізнес-процес «управління заявками», встановлено причини ускладнення комунікаційного процесу та можливі шляхи його покращення. У результаті перепланування бізнес-процесу «управління заявками» за допомогою впровадження інноваційних комунікативних технологій скорочено кількість операцій з восьми до семи та скорочено кількість часу, що витрачається на опрацювання однієї заявки. Доведено економічну доцільність впровадження цих технологій за результатами розрахунку показника ROI.The article substantiates the methodological approach to the formation of competitive advantages of the enterprise in the field of services based on the principles of management of communication technologies. Based on the research of the cleaning services market of Ukraine, it was established that due to the introduction of quarantine measures in connection with the COVID-19 pandemic, and then the introduction of martial law as a result of the armed aggression of the Russian Federation, the problem of uninterrupted operation of the enterprise in a remote format is urgent. Based on the analysis of the market of cleaning services in the city of Odesa and the region, a map of strategic groups was built and the main competing companies of Object Service LLC were identified. The article evaluates the competitiveness of Object Service LLC with its closest competitors based on the calculation of the integral indicator. A survey of clients of "Object Service" LLC was conducted, according to the results of which it was determined that the process of processing one application is not fast enough, therefore, it is necessary to develop tools for its optimization. The business process of "application management" was considered based on functional modeling in the Activity diagram notation, which helped to study in detail the operations in it, namely their number and how much time each operation takes separately. Based on the analysis of this business process, the reasons for the complication of the communication process and possible ways to improve it were determined. As a result of re-planning the business process "application management" with the help of introducing innovative communication technologies into this process, the number of operations was reduced from eight to seven and the amount of time spent on processing one application was reduced by more than one hour. The economic feasibility of the implementation of these technologies is proven using the ROI indicator

Prototyping X-ray tomographic reconstruction pipelines with FleXbox

Computer Tomography (CT) scanners for research applications are often designed to facilitate flexible acquisition geometries. Making full use of such CT scanners requires advanced reconstruction software that can (i) deal with a broad range of geometrical scanning settings, (ii) allows for customization of processing algorithms, and (iii) has the capability to process large amounts of data. FleXbox is a Python-based tomographic reconstruction toolbox focused on these three functionalities. It is built to bridge the gap between low-level tomographic reconstruction packages (e.g. ASTRA toolbox) and high-level distributed systems (e.g. Livermore Tomography Tools). FleXbox allows to model arbitrary source, detector and object trajectories. The modular architecture of FleXbox allows to design an optimal reconstruction approach for a single CT dataset. When multiple datasets of an object are acquired (either different spatial regions or different snapshots in time), they can be combined into a larger high resolution volume or a time series of volumes. The software allows to then create a computational reconstruction pipeline that can run without user interaction and enables efficient computation on large-scale 3D volumes on a single workstation

X-ray variation statistics and wind clumping in Vela X-1

We investigate the structure of the wind in the neutron star X-ray binary system Vela X-1 by analyzing its flaring behavior. Vela X-1 shows constant flaring, with some flares reaching fluxes of more than 3.0 Crab between 20-60 keV for several 100 seconds, while the average flux is around 250 mCrab. We analyzed all archival INTEGRAL data, calculating the brightness distribution in the 20-60 keV band, which, as we show, closely follows a log-normal distribution. Orbital resolved analysis shows that the structure is strongly variable, explainable by shocks and a fluctuating accretion wake. Analysis of RXTE ASM data suggests a strong orbital change of N_H. Accreted clump masses derived from the INTEGRAL data are on the order of 5 x 10^19 -10^21 g. We show that the lightcurve can be described with a model of multiplicative random numbers. In the course of the simulation we calculate the power spectral density of the system in the 20-100 keV energy band and show that it follows a red-noise power law. We suggest that a mixture of a clumpy wind, shocks, and turbulence can explain the measured mass distribution. As the recently discovered class of supergiant fast X-ray transients (SFXT) seems to show the same parameters for the wind, the link between persistent HMXB like Vela X-1 and SFXT is further strengthened.Comment: 8 pages, 6 figures, accepted for publication in A&

Transmutations and spectral parameter power series in eigenvalue problems

We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibility to write down the dispersion (characteristic) equations corresponding to a variety of spectral problems related to Sturm-Liouville equations in an analytic form is an attractive feature of the SPPS method. It is based on a computation of certain systems of recursive integrals. Considered as families of functions these systems are complete in the $L_{2}$-space and result to be the images of the nonnegative integer powers of the independent variable under the action of a corresponding transmutation operator. This recently revealed property of the Delsarte transmutations opens the way to apply the transmutation operator even when its integral kernel is unknown and gives the possibility to obtain further interesting properties concerning the Darboux transformed Schr\"{o}dinger operators. We introduce the systems of recursive integrals and the SPPS approach, explain some of its applications to spectral problems with numerical illustrations, give the definition and basic properties of transmutation operators, introduce a parametrized family of transmutation operators, study their mapping properties and construct the transmutation operators for Darboux transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with arXiv:1111.444

Adipose saturation reduces lipotoxic systemic inflammation and explains the obesity paradox

Obesity sometimes seems protective in disease. This obesity paradox is predominantly described in reports from the Western Hemisphere during acute illnesses. Since adipose triglyceride composition corresponds to long-term dietary patterns, we performed a meta-analysis modeling the effect of obesity on severity of acute pancreatitis, in the context of dietary patterns of the countries from which the studies originated. Increased severity was noted in leaner populations with a higher proportion of unsaturated fat intake. In mice, greater hydrolysis of unsaturated visceral triglyceride caused worse organ failure during pancreatitis, even when the mice were leaner than those having saturated triglyceride. Saturation interfered with triglyceride\u27s interaction and lipolysis by pancreatic triglyceride lipase, which mediates organ failure. Unsaturation increased fatty acid monomers in vivo and aqueous media, resulting in greater lipotoxic cellular responses and organ failure. Therefore, visceral triglyceride saturation reduces the ensuing lipotoxicity despite higher adiposity, thus explaining the obesity paradox