The effect of inertia and vertical confinement on the flow past a circular cylinder in a Hele-Shaw configuration

The Poiseuille flow (centreline velocity $U_c$ ) of a fluid (kinematic viscosity $\nu$ ) past a circular cylinder (radius $R$ ) in a Hele-Shaw cell (height $2h$ ) is traditionally characterised by a Stokes flow ( $\varLambda =(U_cR/\nu )(h/R)^2 \ll 1$ ) through a thin gap ( $\epsilon =h/R \ll 1$ ). In this work we use asymptotic methods and direct numerical simulations to explore the parameter space $\varLambda$ – $\epsilon$ when these conditions are not met. Starting with the Navier–Stokes equations and increasing $\varLambda$ (which corresponds to increasing inertial effects), four successive regimes are identified, namely the linear regime, nonlinear regimes I and II in the boundary layer (the ‘ inner’ region) and a nonlinear regime III in both the inner and outer region. Flow phenomena are studied with extensive comparisons made between reduced calculations, direct numerical simulations and previous analytical work. For $\epsilon =0.01$ , the limiting condition for a steady flow as $\varLambda$ is increased is the instability of the Poiseuille flow. However, for larger $\epsilon$ , this limit is at a much higher $\varLambda$ , resulting in a laminar separation bubble, of size ${O}(h)$ , forming for a certain range of $\epsilon$ at the back of the cylinder, where the azimuthal location was dependent on $\epsilon$ . As $\epsilon$ is increased to approximately 0.5, the secondary flow becomes increasingly confined adjacent to the sidewalls. The results of the analysis and numerical simulations are summarised in a plot of the parameter space $\varLambda$ – $\epsilon$ .

A mathematical model of p62-ubiquitin aggregates in autophagy

Aggregation of ubiquitinated cargo by oligomers of the protein p62 is an important preparatory step in cellular autophagy. In this work a mathematical model for the dynamics of these heterogeneous aggregates in the form of a system of ordinary differential equations is derived and analyzed. Three different parameter regimes are identified, where either aggregates are unstable, or their size saturates at a finite value, or their size grows indefinitely as long as free particles are abundant. The boundaries of these regimes as well as the finite size in the second case can be computed explicitly. The growth in the third case (quadratic in time) can also be made explicit by formal asymptotic methods. In the absence of rigorous results the dynamic stability of these structures has been investigated by numerical simulations. A comparison with recent experimental results permits a partial parametrization of the model.

Development of Methods of Asymptotic Analysis of Transition Layers in Reaction–Diffusion–Advection Equations: Theory and Applications

This work presents a review and analysis of modern asymptotic methods for analysis of singularly perturbed problems with interior and boundary layers. The central part of the work is a review of the work of the author and his colleagues and disciples. It highlights boundary and initial-boundary value problems for nonlinear elliptic and parabolic partial differential equations, as well as periodic parabolic problems, which are widely used in applications and are called reaction–diffusion and reaction–diffusion–advection equations. These problems can be interpreted as models in chemical kinetics, synergetics, astrophysics, biology, and other fields. The solutions of these problems often have both narrow boundary regions of rapid change and inner layers of various types (contrasting structures, moving interior layers: fronts), which leads to the need to develop new asymptotic methods in order to study them both formally and rigorously. A general scheme for a rigorous study of contrast structures in singularly perturbed problems for partial differential equations, based on the use of the asymptotic method of differential inequalities, is presented and illustrated on relevant problems. The main achievements of this line of studies of partial differential equations are reflected, and the key directions of its development are indicated.

Comparing Optimization Criteria in Antibiotic Allocation Protocols

Clinicians prescribing antibiotics in a hospital context follow one of several possible "treatment protocols" - heuristic rules designed to balance the immediate needs of patients against the long term threat posed by the evolution of antibiotic resistance and multi-resistant bacteria. Several criteria have been proposed for assessing these protocols, unfortunately these criteria frequently conflict with one another, each providing a different recommendation as to which treatment protocol is best. Here we review and compare these optimization criteria. We are able to demonstrate that criteria focused primarily on slowing evolution of resistance are directly antagonistic to patient health both in the short and long term. We provide a new optimization criteria of our own, intended to more meaningfully balance the needs of the future and present. Asymptotic methods allow us to evaluate this criteria and provide insights not readily available through the numerical methods used previously in the literature. When cycling antibiotics, we find an antibiotic switching time which proves close to optimal across a wide range of modelling assumptions.

Modeling of the Scattering Field of an FGM-148 Javelin Anti-Tank Missile in Altair Feko

Introduction. Computer-aided design systems for microwave devices are an effective tool for assessing the backscattering characteristics of complex-shaped objects. However, these calculations are often associated with significant computational costs, especially at large values of the ratio of the characteristic dimensions of the object to the wavelength. The use of asymptotic methods in combination with the mesh coarsening of object partition can significantly reduce these costs. However, in each practical case, this leads to a deterioration in the accuracy of the estimates obtained, which is hard to predict.Aim. Comparative assessment of the results of modeling the scattering field in the CAD of microwave devices using various methods for calculating and detailing the object model in the decimeter and centimeter wavelength ranges.Materials and methods. The research object was an anti-tank guided missile FGM-148 Javelin. The scattering field of Altair FEKO microwave devices was modeled in CAD using the methods of moments and physical optics in the frequency range from 1 to 10 GHz and angles from 0 to 180°. A comparison of one-dimensional backscatter diagrams and radar images obtained using these methods was carried out.Results. For the class of objects under consideration, the method of physical optics provides acceptable accuracy at frequencies of 5 GHz and higher with a step of partitioning the model surface of the order of one centimeter and a total calculation duration of the order of several minutes (Intel Core i5-4460 PC / 3.2 GHz / 8 MB RAM). At lower frequencies, acceptable accuracy and a similar calculation duration are achieved when calculating by the method of moments and a partitioning step of about 20 cm. The possibility of using the Altair FEKO CAD system for modeling radar images of objects with a resolution of at least 20 cm is demonstrated.Conclusion. The results obtained complement the well-known studies in the field of comparative assessment of the time and accuracy characteristics of various methods for calculating the scattering field of objects in the CAD of microwave devices.

ASYMPTOTIC METHODS OF ANALYSIS IN ELECTRODYNAMICS

Рассматривается метод геометрической дифракции и физической оптики, который является одним из самых точных и эффективных для решения крупных электродинамических задач. Для анализа характеристик процесса приводится его математическое описание, а также для сравнения с ним приведено описание метода конечного интегрирования, который является наиболее популярным и эффективным для малых объектов. Так показано, что применение метода МКИ невозможно для крупных объектов, так как в процессе сеточного разбиения происходит создание слишком большого числа ячеек для расчета, что значительно усложняет процедуру анализа. Для оценки эффективности и точности метода было произведено моделирование антенного элемента, который установлен на корабле-носителе. Так, характеристики излучателя рассчитывались с использованием метода конечного интегрирования, после чего характеристики диаграмм направленности передавались в проект с кораблем, затем производилось моделирование с использованием метода SBR. Итоговые результаты моделирования показали высокую эффективность и точность метода, а возможность установки шага сканирования позволяет управлять временем моделирования, однако стоит учитывать, что слишком большой шаг приводит к снижению точности анализа The article discusses the method of geometric diffraction and physical optics, which is one of the most accurate and effective for solving large electrodynamic problems. To analyze the characteristics of the process, we give its mathematical description and, for comparison, a description of the final integration method, which is the most popular and effective for small objects. Thus, we show that the application of the MCI method is impossible for large objects since in the process of grid division, too many cells are created for the calculation, which significantly complicates the analysis procedure. To assess the effectiveness and accuracy of the method, we simulated the antenna element, which is installed on the carrier ship. We calculated the characteristics of the emitter using the method of finite integration, after which we transferred the characteristics of the radiation patterns to the project with the ship, then we carried out the simulation using the SBR method. The final results of modeling showed high efficiency and accuracy of the method, and the ability to set the scanning step allows you to control the simulation time, however, it should be borne in mind that too large a step leads to a decrease in the accuracy of the analysis.

Electromagnetic Insights Into Path Loss Modelling of IRS-Assisted SISO Links: Method-Of-Moment Based Analysis

In this paper, we demonstrate the usefulness of MoM (Method-of-Moments) based methods in efficient path-loss modelling for SISO (single-input single-output) communication links assisted by IRS (Intelligent Reflecting Surfaces). Being a full-wave computational electromagnetic tool, MoM is better equipped compared to high-frequency asymptotic methods like PO (Physical Optics), to handle the crucial electromagnetic (EM) effects like: mutual coupling between IRS unit-cells or interactions with spherical wave-front in antenna near-field. Furthermore, in terms of computational speed, accuracy and reproducibility, the MoM-based MATLAB Antenna Toolbox is significantly advantageous to emulate IRS-assisted wireless channels, as compared to the in-house FDTD (finite-difference time-domain) techniques. We consider a SISO system of two half-wavelength dipoles, and use a rectangular array of circular loops loaded with lumped circuit components as IRS. The lumped circuit loading enables us to control the reactance of individual unit-cells, resulting in alteration of IRS reflection coefficient and consequent changes in channel characteristics. Using numerous numerical simulations, we highlight the impacts of various IRS-parameters like: electrical size and number of unit-cells, distance of IRS from the transmitter/receiver as well as mutual coupling, on the path-loss models (both sub-6 GHz and mm-wave).

Dynamics of tilted atmospheric vortices under asymmetric diabatic heating

Päschke et al. (J Fluid Mech, 2012) studied the nonlinear dynamics of strongly tilted vortices subject to asymmetric diabatic heating by asymptotic methods. They found, inter alia, that an azimuthal Fourier mode 1 heating pattern can intensify or attenuate such a vortex depending on the relative orientation of the tilt and the heating asymmetries. The theory originally addressed the gradient wind regime which, asymptotically speaking, corresponds to vortex Rossby numbers of order unity in the limit. Formally, this restricts the applicability of the theory to rather weak vortices. It is shown below that said theory is, in contrast, uniformly valid for vanishing Coriolis parameter and thus applicable to vortices up to low hurricane strengths. An extended discussion of the asymptotics as regards their physical interpretation and their implications for the overall vortex dynamics is also provided in this context. The paper’s second contribution is a series of three-dimensional numerical simulations examining the effect of different orientations of dipolar diabatic heating on idealized tropical cyclones. Comparisons with numerical solutions of the asymptotic equations yield evidence that supports the original theoretical predictions of Päschke et al. In addition, the influence of asymmetric diabatic heating on the time evolution of the vortex centerline is further analyzed, and a steering mechanism that depends on the orientation of the heating dipole is revealed. Finally, the steering mechanism is traced back to the correlation of dipolar perturbations of potential temperature, induced by the vortex tilt, and vertical velocity, for which diabatic heating not necessarily needs to be responsible, but which may have other origins.

Study on free oscillations of a micromechanical gyroscope taking into account the nonorthogonality of the torsion axes

Introduction. The paper is devoted to the study on free oscillations of the sensing element of a micromechanical R-Rtype gyroscope of frame construction developed by the Kuznetsov Research Institute of Applied Mechanics, taking into account the nonorthogonality of the torsion axes. The influence of the instrumental manufacturing error on the accuracy of a gyroscope on a movable base in the case of free oscillations is studied. The work objective was to improve the device accuracy through developing a mathematical model of an R-R type micromechanical gyroscope, taking into account the nonorthogonality of the torsion axes, and to study the influence of this error on the device accuracy. The urgency of the problem of increasing the accuracy of micromechanical gyroscopes is associated with improving the accuracy of inertial navigation systems based on micromechanical sensors.Materials and Methods. A new mathematical model that describes the gyroscope dynamics, taking into account the instrumental error of manufacturing the device, and a formula for estimating the error of a gyroscope, are proposed. The dependences of the state variables obtained from the results of modeling and on the basis of the experiment are presented. Methods of theoretical mechanics and asymptotic methods, including the Lagrange formalism and the Krylov-Bogolyubov averaging method, were used in the research.Results. A new mathematical model of the gyroscope dynamics, taking into account the nonorthogonality of the torsion axes, is developed. The solution to the equations of small oscillations of the gyroscope sensing element and the estimate of the precession angle for the case of a movable base are obtained. A comparative analysis of the developed model and the experimental data obtained in the case of free oscillations of the gyroscope sensing element with a fixed base is carried out. The analysis has confirmed the adequacy of the constructed mathematical model. Analytical expressions are formed. They demonstrate the fact that the nonorthogonality of the torsion axes causes a cross-influence of the amplitudes of the primary vibrations on the amplitudes of the secondary vibrations of the sensing element, and the appearance of an additional error in the angular velocity readings when the gyroscope is operating in free mode.Discussion and Conclusions. The results obtained can be used to improve the device accuracy using the algorithm for analytical compensation of the gyroscope error and the method for identifying the mathematical model parameters.

Electromechanical Models of Micro and Nanoresonators

This work is devoted to numerical and partly experimental investigation of the electromechanical models of micro and nanoresonators. The main purpose of this resonators is detected the adherence of micro or nanoparticles and measurement its mass. The periodical oscillations of mono and many layers nanocapacitors, from which nanoresonator situated in electric field is constructed, are studied. The purpose of this work is creating of electromechanical models of MEMS and NEMS the aim of which is to identify the changes introduced into dynamic systems due to adhesion of micro or nanoparticles. It’s significant to note that the time of overcharge of the nano-capacitor is much less, then the period of excited oscillations. This fact gives the possibility to apply asymptotic methods in numerical investigation. Physical experiments similar in model to the electromechanical nanoresonators were carried out. This work is an extended review article based on the results of previous our works.