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The paper presents results of a theoretical study on the properties of a supersonic boundary layer and its linear stability under conditions of surface material sublimation. Calculations were performed for an adiabatic-wall boundary layer over a camphor coated flat-plate model at a free-stream Mach number of M=2. In the boundary layer, surface sublimation generates a binary mixture flow of air and foreign vapors. This flow is studied using boundary layer equations in approximation of local self-similarity. It is shown that increase of the flow stagnation temperature leads to the wall material sublimation. Increasing evaporation causes significant wall cooling and an increase in the near-wall density of the binary mixture. Such modification of the boundary layer profiles leads to a decrease of the amplification rates of the first mode perturbations, which were computed by means of the linear stability theory. It is concluded that application of a camphor coating facilitates the supersonic adiabatic-wall boundary-layer stabilization with increasing flow stagnation temperature.

In this paper we present a numerical study of two streamwise supersonic vortices interaction. A pair of vortices was generated by two coaxial straight wings with sharp leading and trailing edges. Mach number of incoming flow was M∞ = 3. Two configurations are considered: a pair of co-rotating vortices and a pair of counter-rotating vortices. In the case of counter-rotating vortices the wings attack angle was 10 degrees. In the case of co-rotating vortices the attack angle of one of the wings was 10 degrees, the attack angle of other one was -10 degrees. Numerical data were obtained in the domain of 10 wing chords downstream from a wings axis by a computational model based on the URANS equations with SA turbulence model. Numerical simulations were performed on the hybrid supercomputing system K-60 at the Keldysh Institute of Applied Mathematics RAS using the developed software package ARES for 3D turbulent flows modeling on high performance computing systems. This work is a continuation of the series of author’s works dedicated to the supersonic wingtip vortices.

Laser contact opening (LCO) and Ni/Cu light induced plating is an established front side metallization process which provides the possibility of thinner contacts with high aspect ratios and inherently low contact resistances. In this study, we work towards the development of an optical system which combines the speed of state-of-the-art scanner systems and the high numerical apertures lenses used to create small structures. We successfully demonstrate the feasibility of cylindrical lens as the focusing lens for laser ablation. The lens generates elliptical openings with a major diameter of 2.6 mm and a minor diameter of 3.1 μm with a single pulse. Successful formation of contacts is achieved in this study with a contact opening of 3 μm and plated finger width of 15 μm. Lifetime measurements after LCO for an open area percentage of 2-3% using the conventional scanner systems and cylindrical lens shows that increase in J0e due to lasering with cylindrical lens is almost half as compared to LCO with state-of-the-art galvanometer scanner and f-theta lens setup at a similar opened area percentage and laser fluence. The optimum laser parameters and plating generate contacts with Rc values that are comparable to the ones achieved using standard LCO despite having smaller contacts. Thermal annealing after LCO is included as the standard protocol as it demonstrates the best performance for this setup. These results provide a proof-of-concept for the feasibility of using cylindrical lenses as the focusing lens. Our study lays the foundation for further experimentation on hybrid systems, where the high throughput of the scanner system is combined with the high numerical aperture (NA) of cylindrical lens.

The theoretical and experimental investigation of the effect of the heavy gas (sulfur hexafluoride) blowing into the boundary layer on the hydrodynamic stability to controlled perturbations of the supersonic flat-plate boundary layer at Mach number 2 have been carried out. Artificial perturbations have been entered in the model’s boundary layer by using a harmonic point glow discharge perturbation source. It is obtained that heavy gas blowing stabilizes the supersonic boundary layer. In experiments at the excitation frequency f = 14 kHz, unit Reynolds number Re1 = 3×106 m−1 and streamwise coordinate x = 90 mm, it was obtained that for gas injection rate Q = 0.12 g/cm2 there is a stabilization of perturbations for all spanwise wave numbers, i.e. the complete stabilization of perturbations – for all wave numbers, the spatial disturbance amplification rates are less than zero.

The paper presents the results of the assessment of the applicability of structured laser illumination in combination with Rayleigh scattering or spontaneous Raman scattering methods for evaluating the local density and temperature distribution in a premixed methane flame. The examples presented in this paper show that the use of structured laser illumination makes it possible to obtain a signal free of background and reflected light by registering the scattering signal only at one S-polarization of the laser. The best quality of image reconstruction was obtained using a grating with a line spacing of 0.5 mm. Gratings with a larger step gave a strong blurring and loss in spatial resolution, a grating with a smaller line spacing during reconstruction led to the formation of secondary structures with lines.

This paper presents the method of estimating the spatial thickness of a stationary or flowing liquid film by the optical method based on the estimation of the monochromatic light beam attenuation when it propagates in an absorption medium, better known as the Beer–Lambert–Bouguer Law, which is also used in infrared spectroscopy method. The results of the test experiments show that the Beer–Lambert–Bouguer Law is correct if the light intensity is replaced by the value of the brightness component. An estimate of the brightness component is easy to obtain based on the analysis of digital photographs or video recording, namely, by tuples of the value of gray gradation (brightness) calculated using one of the mathematical models for the color representation. For unsteady flows of a liquid film, analyzing the extremum of the autocorrelation function from the displacement of the local area between two adjacent video frames, it is possible to estimate the volume-average value of the flow velocity.

A distinctive feature of the aviation technology development in recent years is the quantitative and qualitative complication of on-board equipment, which increases the problem of the cockpit thermal condition. The need to reduce sharply increased volumes of full-scale work related to the assessment and assurance of the cockpit thermal state caused an increase in the role of the cockpit systems thermophysical parameters estimation, which include air flow rates in air conditioning and ventilation systems, the characteristics of electrothermal and jet protection against fogging of the cockpit window, as well as the thickness of the insulation in the cockpit. In this work, a mathematical simulation of the thermal state of a pressurized thermally insulated compartment with honeycomb structures was proposed when solving direct and inverse problems of heat exchange. To solve the direct problem, the Galerkin method with the use of a piecewise linear basis, a second-order approximation Rosenbrock-type numerical scheme for non-autonomous systems, a combined walk-on-the-spheres method, and the Euler method were used. The inverse heat transfer problem solution is carried out by the quasi-Newton method of Broyden – Fletcher – Goldfarb – Shanno in combination with the Newton method. Confidence intervals of parametric identification estimates are determined using the covariance matrix of parameters estimate errors and quantile χ2 - probability distribution 1-α. The evaluation of required values of the air flow in the air conditioning and ventilation systems, the characteristics of the electrothermal and jet protection against fogging of the cockpit window, as well as the thickness of the insulation in the cockpit of a passenger aircraft was carried out.

The paper presents the results of an experimental study of the thermal modes of a supersonic combustion chamber at Mach numbers at the channel inlet 3-4, operating on hydrogen. Model is made in the form of a rectangular channel with a combined flame holder with a backward-facing step and wedge-shaped injectors. The experiments were carried out in the mode of a connected pipeline under conditions close to flight ones. It was found that the maximum level of heat flux is reached in the region where the ignition of the mixture is initiated, and this value is achieved during the non-stationary ignition of the combustion chamber. The position of this region shifts upstream with a decrease in the Mach number, which depends on the change in the position of the separation region of shock waves interaction with the boundary layer. With an increase in the Mach number to 4, intense combustion does not occur due to the displacement of this region downstream into the diverging channel and is accompanied by a significant increase in the flow rate. The data obtained show that when developing systems for thermal protection of the combustion chamber, it is necessary to take into account the uneven distribution of heat fluxes along the combustor length in order to prevent local destruction of the walls and possible saving of the coolant resource.

This study was initiated to reduce the production cost which is affected mostly by the amount of glue spread. The least and suitable glue consumption was investigated by determining mechanical and physical properties of Laminated Veneer Lumber (LVL) using different amounts of glue spread which were 150 g/m2, 200 g/m2, 250 g/m2 and 300 g/m2. The adhesive used was Phenol Resorcinol Formaldehyde (PRF) and the test methods were done according to JAS 233:2003 and ASTM D734. Modulus of Elasticity (MOE) and Modulus of Rupture (MOR) increased steadily along the increase amount of glue spread. MOE and MOR obtained were from 300 g/m2 glue spread which were 5701.71 N/mm2 and 44.45 N/mm2 respectively. The tensile shear strength also increased and the highest was 300 g/m2 glue spread with 10.74 N/mm2. As for physical properties, only density had increase along the glue amount with highest value of 439.73 kg/m3 by 300 g/m2 whereas water absorption and delamination decreased along increasing of glue spread with lowest value of 101.99 % and 0.92 %. Thickness swelling had an irregular trend with lowest value of 0.76 % for 250 g/m2 glue spread amount. Overall, the insignificance ranges from 200 g/m2 until 300 g/m2 thus can be suggested that glue spread amount can be reduced until 200 g/m2 to reduce production cost and prevent wastage.

In the present paper, source identification problem for the elliptic-telegraph equation is investigated. The second order of accuracy absolute stable difference scheme for the numerical solution of the one-dimensional identification problem for the elliptic-telegraph equation with the Dirichlet condition is presented. Some numerical results are provided.

Numerical simulation of self-induced pitch oscillations of a segmental-conical body at Mach number M = 2.0 is performed using the mathematical model of the pitching moment, which includes an ordinary linear differential equation of the first order. The parameters of the mathematical model were determined from the condition of the best agreement between the calculated and experimental transient processes pitch angle in time. Numerical modeling of self-induced oscillations was also carried out using the time-lag hypothesis and concepts of aerodynamic derivatives. It is shown that the proposed mathematical model is not only satisfactory describes the experimental transient process like the other two, but also explains the known experimental effects.

The Riemann-Hilbert problem for the first order elliptic system is considered in the Hardy-Smirnov space. This system is reduced to an equivalent Fredholm integral system on the boundary in the space Lp.

Thin films of zinc oxide doped with ITO (indium tin oxide) on anodic aluminum oxide substrates are surrounded in vacuum during high-repeat dully beat laser affirmation. The morphology of motion pictures on porous and non- penetrable surfaces of substrates was focused by atomic force microscopy. The optical properties of the motion pictures in the self-evident, close, and focus IR areas of the electromagnetic radiation extend, the Raman spectra, and besides the features of the photoluminescence characteristics have been probably inquired about. Zinc oxide motion pictures can be used in optoelectronic transducers, as luminescent material, as clear cathodes, tricky layers of gas and natural sensors, driving forces, X-ray and gamma-radiation identifiers.

The atomic emission spectroscopy from the expanding plasma plume produced during the laser-matter interaction is called the Laser-Induced Breakdown Spectroscopy (LIBS). This technique offers valuable information on the target materials composition. In this analysis, the plasma created by high fluence interaction Nd: YAG laser at 1064 nm wavelength with the target of copper and iron in the air. The laser-induced plasma emitted at various laser energies was characterized, which was studied using optical emission spectroscopy. We measured the plasma temperature Te (k) using the Boltzmann plot method, and the plasma density ne(cm−3) is determined by the Stark broadening profile corresponding to wavelength 653 nm of Cu II and Fe I. The identification of transition lines from the spectrum was performed by comparing spectral lines with the NIST atomic database.

Results of a numerical simulation of the unsteady axisymmetric flow forming in joint process of starting an impulse wind tunnel equipped with a plenum chamber and a throttling device as well as starting an axisymmetric inlet tested in this tunnel are reported. An impulse wind tunnel schematizing the hot-shot wind tunnel IT-302M based at ITAM and an operating flow regime of Mach number M = 8 obtained with a contoured nozzle were under consideration. There was applied a Reynolds-averaged Navier–Stokes code including the k-ω SST turbulence model. The starting process was initiated in accordance with the Riemann problem. The computed data showed a complicated starting shock-wave system forming in the nozzle and in front of the tested inlet, it included the primary shock wave, contact discontinuity transforming into a contact layer, inverse shock wave, expansion wave. This system determined the lasting of the processes of starting the nozzle and the inlet proper. As it was identified, a chain of changing inlet flow modes occurred in the starting process which began from the starting inlet mode when the flow in the inlet duct is supersonic and culminated in the eventual unstarting inlet mode with a bow shock in front of the inlet and with the subsonic flow in its duct.

The effect of the local surface heating on the stability of the boundary layer of the contoured nozzle M6 has been studied numerically for the hypersonic wind tunnel Transit-M ITAM SB RAS. Boundary layer profiles on the nozzle surface are found by the numerical simulation. Disturbance stability in the boundary layer is calculated in the context of the linear stability theory. It is shown that the local heating results in the slow-down of Goertler vortices amplification and Mack first mode in respect to the basic case; the stronger the heating, the stronger the effect. The second mode stabilizes at the local surface heating up to the temperature approaching to the stagnation temperature and de-stabilizes at further temperature rise. The optimal temperature of the local surface heating has been determined for the contoured nozzle M6 to stabilize disturbances in the boundary layer.

An experiment related to biodiesel transesterification was successfully done. The chemical reaction of transesterification was conducted at 65 °C during 14 h of reaction time involving the ratio of methanol and used cooking oil was 70 : 1. An additional catalyst is required upon 10 % of HPA (Heteropoly Acid) as an organic catalyst. The maximum conversion (yield) was achieved by 88.68 % with activation energy (Ea) was 53.99 kJ/mole with Pre-Exponential Factor (A) was obtained 2.9 x 107. Based on those experiments, s-curve modeling was designed. The s-curve was generated through three different selected temperature reactions as follows: 60, 65, and 70 °C (333, 338, and 343 K) with various reaction times 0.5, 1.0, and 2 h respectively. The mechanism to build the s-curve model through three stages starting by determination of reaction rate constant (k’) through linear regression equation continued with the curve formation between ln k’ with 1/T to produce a value of Ea and A. To produce the s-curve model was observed through numerical processes, interpreted and analyzed by applying the Avrami equation to determine reaction and temperature time is required by trans esterification reaction between methanol and used cooking oil. Referring to the curve was obtained several results which are the optimum temperature to obtain the best yield, time to obtain a 100 % yield, and time to obtain a determining yield. According to the s-curve model was formed, the time reaction 46.95 h and 22.79 h is able to achieve 100 % and 96.5 % of yield product by plotting reaction of temperature and time. This simulation can be applied to other biodiesel reaction which has different raw materials and types of a catalyst by keeping the same method to be applied through the transesterification method.

The results of numerical simulation of the interaction between a shock and the laminar boundary layer on a flat plate in motion in supersonic perfect-gas flow at Mach numbers M∞ = 2.3 and M∞ = 3 are considered. The shock is preassigned using the Rankine-Hugoniot boundary conditions, which corresponds to a shock wave produced by a wedge with a given semi-vertex angle in an inviscid gas flow. The simulation is based on the numerical solution of the time-dependent, two-dimensional Navier-Stokes equations by time marching to steady state. The numerical data are used to investigate the effect of the plate velocity of the separation flow structure and the basic laws governing the problem. It is shown that the motion of the plate downstream diminishes the separation zone length, whereas the opposite motion leads to its increase.

In order to make the quantum mechanics a closed theory one has to derive the Born rule from the first principles, like the Schroedinger equation, rather than postulate it. The Born rule was in certain sense derived in several articles, e.g. in [D. Deutsch, Proc. R. Soc. Lond. A455, 3129 (1999)] and [W. H. Zurek, Phys. Rev. Lett. 90, 120404 (2003)]. In this work some arguments of previous authors are simplified and made more "physical". It is shown how to derive the Born rule using the conservation of quantum state norm $\langle\Psi|\Psi\rangle$ that is the unitary evolution property determined by the Schroedinger equation. It is this property that makes the probability equal to the square of the amplitude modulus. We also present arguments in the spirit of the Many-World Interpretation to explain the origin of probabilistic behavior. Simply speaking, the randomness appears as a result of representing the wave function by using a detector of discrete nature that is found only in one state at a time, out of two or more possible states.

The work proposes the method to design high-rate axisymmetric air intakes through the flow reverse in a respective isoentropic nozzle. Calculation of the flow configuration and parameters in the isoentropic nozzle with the straight characteristic and preset exit Mach number is carried out by the method of characteristics. Then it is suggested that as the flow direction is reversed in the built nozzle contour, flow parameters do not change, but a compression flow appears which corresponds to the flow in the air intake. For comparison, the numerical simulation of the flow in the reversed air intake was made for the enter Mach number M = 6 and in the similar air Busemann intake. The calculations of the non-viscous flow, the total pressure recovery factor in the reversed air intake is 0.996, whereas in the air Busemann intake it is 0.985. The calculations involving the viscosity show that the presence of the boundary layer causes higher losses and reduction of the recovery factor to 0.869 in the the reversed air intake and to 0.832 for the Busemann air intake.

Hybridization of filler in polymer composites is one technique of combining different properties of filler for making unique composites. Carbon nanotubes (CNTs) can be used as filler to enhance the mechanical properties of polymer composites. However, CNTs are difficult to disperse in a polymer matrix. The hybridization of CNTs and inorganic fillers can combine their properties and improve the dispersion in polymer composites. This research was focused on the fabrication and characterization of CNTs-dolomite filled with epoxy composites. The CNTs-dolomite hybrid fillers were prepared by physically mixing method and Chemical Vapor Deposition (CVD) method. The CNTs-dolomite hybrid compound filled epoxy composites with different filler loading were characterized by tensile test, Rockwell hardness test and scanning electron microscopy (SEM). The Epoxy/CVD composites showed higher mechanical properties than the Epoxy/PHY composites. This increase was associated with the homogenous dispersion of CNTs-dolomite hybrid compound as observed using SEM. It was demonstrated that the Epoxy/5CVD composites are capable of increasing tensile strength by up to 67 %, and tensile modulus of 28 %, when compared to a pure epoxy composite.

We adopt methods of symplectic tomography and discrete phase space for the description of states of discrete variable quantum systems (qudits). The proposed tomographic functions are constructed as generalized analogs of the center-of-mass and the cluster tomograms and associated with finite linear manifolds in the discrete phase space. Hilbert spaces of considered qudits must have the power of a prime dimension, so the corresponding phase spaces are the vector spaces over finite fields. We find conditions for the nonnegativity of the constructed functions and obtain formulae for the density matrix restoration.

One of the few goals of statistical modeling is to see and analyze the probability of an event which can be represented with data. A probability distribution that is used for modeling data should have some abilities such as flexibility for modeling different kinds of data. Therefore, modeling data is of great importance. Furthermore, insurance companies also need to model data, which in this case is called modeling claim data. Modeling the claims distribution has its own challenge (e.g. skewed and heavy tailed) since most of the claim distributions are different from any classical distributions, therefore researchers are trying to find new models that can fit insurance data better. In this paper, a composite Exponential-Pareto distribution was proposed and introduced. This distribution is equal, but not equivalent to, an exponential density up to a certain threshold value, and a Pareto type-I density for the rest of the model. When being compared with the exponential distribution, the emerging density has a similar shape and a larger tail, and while being compared with the Pareto distribution, the emerging density has a smaller tail. A method to develop a composite distribution is called as composite parametric modeling, which introduced by Cooray and Ananda (2005). In this model, both the exponential distribution and the Pareto type-I distribution have the same weight. Based on the result, composite Exponential-Pareto distribution has some limitations, which are likely to severely diminish its potential for practical applications to real world insurance data. In order to address these issues, there are two different composite Exponential-Pareto distributions based on exponential and Pareto type-I distributions in order to address these concerns. These two different composite Exponential-Pareto distributions are based on the two-component mixture model introduced by Scollnik (2007). The first distribution, which is a reinterpreted composite Exponential-Pareto distribution from the first composite Exponential-Pareto distribution based on the two-component mixture model, has a fixed mixing weight. Meanwhile, the second distribution is a composite Exponential-Pareto distribution with a mixing weight that is not fixed so the distribution can be more flexible and can model different kinds of data. These three composite Exponential-Pareto distributions has k-th raw-moment that only defined for some k > 0. Therefore, this distribution can be categorized as a heavy-tail distribution. The result of this research is a composite distribution that could model a lot of data with characteristics such as unimodal, right-skewed, and heavy-tail because the composite distribution has similar characteristics. A data illustration was presented as a demonstration for how to implement the composite Exponential-Pareto distribution.

A two-qubit register is simulated using a graph of four quantum dots, each of which has a point contact. One-qubit Pauli gates and two-qubit gates CNOT CZ and CP(π) were implemented, the effect of dephasing created by point contacts on the accuracy of two-qubit gates was calculated numerically, and this system was calculated using the model potential.

The conceptual design of the hydrogen-fueled detonation ramjet (DR) of a new type for a cruising flight speed of Mach 2 at sea level is developed using 3D numerical simulations of the operation process. The calculated effective thrust of such a DR is shown to become positive at M = 1.3, i.e., the startup Mach number for such a DR can be lower than M ≈ 2.0, which is typical for ramjets operating on continuous-deflagration combustion. A DR demonstrator is designed and manufactured. Its test fires are performed in a blowdown wind tunnel (WT) at free air jet Mach numbers M = 2.0, 1.5, and 0.9. The result of test fires is the experimental proof of the possibility of arranging stable continuous-detonation combustion of hydrogen in the DR of the developed design at both Mach numbers exceeding 1.0. The maximum measured values of the fuel-based specific impulse and total thrust were 1610 s and 650 N for the tests with M = 1.5 and 1630 s and 860 N for the tests with M = 2.0.

In this article the solvability of the problem of optimal control of oscillatory processes described by the integro- differential equation with the Fredholm operator, with given control limitation is investigated.It is established that the desired control is among the solutions of the nonlinear Fredholm integral equation of the first kind. Sufficient conditions for the existence of a solution of nonlinear optimization problem are found.

The study of the lifetime of an organism, devices, etc., is very important in the field of health, biology, and industry. We need a distribution that can model the data with certain characteristics. The lifetime distribution with a decreasing hazard rate has been discussed in the new literature. In this research, a new distribution with a decreasing hazard rate is presented with three parameters that match real data that has no zero observation, namely the Exponential Conway Maxwell Poisson distribution (ECOMP). The ECOMP distribution can be used to model the minimum lifetime of an exponential random variable. In this research, we explain how to construct ECOMP distribution and discuss its properties. The parameter estimation is performed using the maximum likelihood method. The application of earthquake data shows that the ECOMP distribution is more suitable in modeling data than the Exponential Poisson (EP) distribution.

We estimate the Lebesgue constants of interpolation by rational functions on one or several intervals with fixed poles having accumulation points on the interval(s). To prove it we use an analogue of the inverse polynomial image method for rational functions with fixed poles.

The generators of the quasi-regular representation of the group SO(3,2) are obtained for parabolic coordinates. By the generators, the expression of the quadratic Casimir operator is presented. From the relation between the Casimir operator and Hamiltonian, the corresponding physical system is expressed, and its exact solution is given.

The most commonly used time series model is the discrete time series which assumes the variables being tested are continuous and produce continuous values. Whereas in many applications, a discrete time series model is needed to handle discrete variables and produce discrete values as well. The time series model that handles count or non-negative integer data is the Integer-valued Autoregressive model with the pth-order or INAR(p). This model is built with binomial thinning operator which implements probabilistic operations with discrete distribution that are suitable to model count data such as Poisson and Binomial. Model parameters will be estimated using the Yule-Walker method. In this research, we will discuss and describe the characteristics of the INAR(p) model using the binomial thinning operator. The INAR(p) specification follows the Autoregressive model with the pth order, AR(p). Forecasting in INAR(p) uses median forecasting by calculating the conditional probability of each possible non-negative integer value, then selecting a forecast value with a cumulative conditional probability greater than 0.5. The INAR(p) time series model will be applied to the 115 simulated data with non-negative integer values.

A series of computational experiments is discussed where a submerged round jet is subjected to different ways of active flow control to achieve the effect of jet splitting. The first method is to superimpose axial and helical excitations onto the velocity profile at the jet inlet. The second one consists of mechanical vibration of the jet inlet nozzle added to axial forcing. Both methods result in jet splitting at Reynolds numbers Re above 1000. At lower Re, the splitting is not guaranteed and requires pinpointing the optimal forcing frequencies and amplitudes to produce a meaningful effect.

Energy is the main driving force of an economy. Due to which many advancements in renewable energy technology have been witnessed over the decade. However, not all countries have efforts in the same direction and have continued using coal-based technology. These old technologies have a sizable energy wastage in the form of fuel thermal energy (Kinetic Energy). The said wastage can be harnessed by using a specifically designed recovery turbine deployed in the industrial stack. Keeping in mind the same, this research focuses on a mathematical model to develop the best-suited design for the utmost augmentation of the kinetic energy. A Convergent-Divergent nozzle with varying ratios of entry to the throat area (Aent/A*) and exit to the throat area (Ae/A*) were subjected to mathematical formulations. The combinations of Aent/A* and Ae/A* tested were (a)1.489 and 1.256 (b) 1.78 and 1.97 respectively. The results indicate that the combination “b” is a better option owing to the largest velocity augmentation. The maximum velocity at the throat was noted at 3.9 times the inlet velocity, which would result in a larger power output by the turbine positioned there. Post analysis of the Mach number (Ma), it was also concluded that the flow is incompressible, and no shockwaves were seen. The development of such a novel technology would result not only in financial saving for the industries but also reducing the environmental impact due to non-renewable sources of energy.

Quantile regression is a regression method that modelling a relationship between quantile of variable response and one or more variable predictors. Quantile regression has advantages that linear regression does not have; it is robust against outliers and can model heteroscedasticity data. The parameters of quantile regression can be estimated using the Bayesian method. The Bayesian method is a data analysis tool derived based on the Bayesian inference principle. Bayesian inference is the process of studying data analysis inductively with the Bayes theorem. To estimate regression parameters with Bayesian inference, it is necessary to find the posterior distribution of the regression parameters where the posterior distribution is proportional to the product of the prior distribution and its likelihood function. Since the calculation of the posterior distribution analytically is difficult to do if more parameters are estimated, the Markov Chain Monte Carlo (MCMC) method is proposed. The use of the Bayesian method in quantile regression has advantages, namely the use of MCMC has the advantages of obtaining sample parameter values from an unknown posterior distribution, using computationally efficient, and easy to implement. Yu and Moyeed (2001) introduced Bayesian quantile regression using the likelihood function of errors with an Asymmetric Laplace Distribution (ALD) and found that minimizing parameter estimates in quantile regression is the same as maximizing the likelihood function of errors with an Asymmetric Laplace Distribution (ALD). The method used to estimate quantile regression parameters is Gibbs sampling from the ALD, which is a combination of the exponential and normal distributions. To find the parameters of the regression model by sampling the posterior distribution found in this thesis. The results obtained from Gibbs sampling are a sample sequence of estimated parameters. After obtaining the sample sequences, the sample lines are averaged to obtain an estimated regression parameter. The case study in this thesis discusses the effect of risk factors from motor vehicle insurance customers on the size of claims submitted by customers.

The mechanism of intensification for the supersonic round jet mixing by a pulse-periodic energy deposition is studied numerically using the unsteady Reynolds averaged Navier-Stokes equations. A round low-density air jet at different Mach numbers (Mj = 1.05, 1.76, 3.00) is parallelly injected into a coflowing air stream of Mach number M = 2.5, interacting with the oblique shock generated by a compression ramp of 20 degree. The pulse-periodic energy deposition with 50 mJ/pulse at 20 kHz is initiated inside the jet for jet mixing control. The jet mixing enhancement is achieved through the large-scale vortices, initiated by the energy deposition zone interacting with oblique shock. The positive effects with the doubled increased jet cross section area and the strengthened turbulent kinetic energy are achieved, accompanied by a slightly decrease about 0.3% of the total pressure recovery coefficient downstream at the outlet.

During horizontal flight the propellers of quadcopter is working in oblique flow conditions. This case not studied enough for fixed pitch propellers especially at low Reynolds numbers, which are implemented on propellers of small quadcopters. The experimental investigation of characteristics of three-blade propeller for quadcopter in different conditions (including oblique blowing) was carried out. The effect of oblique flow mode on the dimensionless characteristics of the propeller was investigated. The unsteady component of the force generated by the propeller was estimated on the basis of numerical simulation.

The effects of the surface undulation on the development of boundary layer instabilities are studied in the supersonic boundary layer. The direct numerical simulations are performed for the boundary layer on a flat plate at flow Mach number M = 6. The surface undulation is considered as the means of passive flow control of the laminar-turbulent transition. It has been found that a wavy portion of the surface located at some distance from the leading edge can significantly reduce the amplitude of fluctuations downstream. The effect of suppressing disturbances significantly increases with increasing both the number of waves on the surface (i.e., the length of the wavy portion), and their depth.

The paper provides a brief overview of recent computational studies of flow and heat transfer control by rotary oscillations of an infinite circular cylinder at a relatively broad set of imposed frequencies and amplitudes [1, 2]. A study for a previously unreachable high subcritical Reynolds number Re = 1.4 × 105 showed that the efficiency of this control method increases with Re concerning the issue of drag and lift reduction. High-frequency oscillations even lead to around 90 % reduction of the drag. However, the benefits for heat transfer enhancement is not that obvious as the bulk Nusselt number shows only small variations. At the same time its angular distribution around the cylinder becomes much more homogeneous due to oscillations which practically can prevent local overheats.

The flow in 2D channels of variable cross-section was studied numerically. The channels contain bodies that split the channels into narrow ones. Solutions of Euler’s equations are obtained using the finite-volume solver of the Ansys CFX software package. A set of solutions is found. These solutions depend on the input Mach number and on the initial condition. Numerical simulations show a significant hysteresis in the drag coefficient of bodies in the channel relative to the supersonic Mach number set at the inlet. In a certain range of the inlet Mach number, there are asymmetric solutions of the equations.