A numerical prediction using the Direct Simulation Monte Carlo method (DSMC)has been performed on low speed gas flows through a short parallel plate microchannel(L/Dh=6). Computations were carried out for nitrogen, argon, and helium gas. Micro pressure driven flows are simulated with the inlet value of the Knudsen numbers ranging from 0.09 to 0.2. The effects of varying pressure, wall temperature, inlet flow and gas transport properties on the wall heat transfer, pressure and velocity distribution were examined. Friction factors and heat transfer from the channel were also calculated and compared with those of previous studies. Finally, the averaged Nusselt number was correlated in a simple form of the averaged Peclet number and Knudsen number in the transition flow regime.

In this work, statistical techniques were employed to study the modeling of a hypersonic shock with the Direct Simulation Monte Carlo (DSMC) method, and to gain insight into how the model interacts with a set of physical parameters. Direct Simulation Monte Carlo (DSMC) is a particle based method which is useful for simulating gas dynamics in rarefied and/or highly non-equilibrium flowfields. A DSMC code was written and optimized for use in this research. The code was developed with shock tube simulations in mind, and it includes a number of improvements which allow for the efficient simulation of 1D, hypersonic shocks. Most importantly, a moving sampling region is used to obtain an accurate steady shock profile from an unsteady, moving shock wave. The code is MPI parallel and an adaptive load balancing scheme ensures that the workload is distributed properly between processors over the course of a simulation. Global, Monte Carlo based sensitivity analyses were performed in order to determine which of the parameters examined in this work most strongly affect the simulation results for two scenarios: a 0D relaxation from an initial high temperature state and a hypersonic shock. The 0D relaxation scenario was included in order to examine whether, with appropriate initial conditions, it can be viewed in some regards as a substitute for the 1D shock in a statistical sensitivity analysis. In both analyses sensitivities were calculated based on both the square of the Pearson correlation coefficient and the mutual information. The quantity of interest (QoI) chosen for these analyses was the NO density profile. This vector QoI was broken into a set of scalar QoIs, each representing the density of NO at a specific point in time (for the relaxation) or a specific streamwise location (for the shock), and sensitivities were calculated for each scalar QoI based on both measures of sensitivity. The sensitivities were then integrated over the set of scalar QoIs to determine an overall sensitivity for each parameter. A weighting function was used in the integration in order to emphasize sensitivities in the region of greatest thermal and chemical non-equilibrium. The six parameters which most strongly affect the NO density profile were found to be the same for both scenarios, which provides justification for the claim that a 0D relaxation can in some situations be used as a substitute model for a hypersonic shock. These six parameters are the pre-exponential constants in the Arrhenius rate equations for the N2 dissociation reaction N2 + N ⇄ 3N, the O2 dissociation reaction O2 + O ⇄ 3O, the NO dissociation reactions NO + N ⇄ 2N + O and NO + O ⇄ N + 2O, and the exchange reactions N2 + O ⇄ NO + N and NO + O ⇄ O2 + N. After identification of the most sensitive parameters, a synthetic data calibration was performed to demonstrate that the statistical inverse problem could be solved for the 0D relaxation scenario. The calibration was performed using the QUESO code, developed at the PECOS center at UT Austin, which employs the Delayed Rejection Adaptive Metropolis (DRAM) algorithm. The six parameters identified by the sensitivity analysis were calibrated successfully with respect to a group of synthetic datasets. / text

"This dissertation is devoted to the computational investigation of supersonic gas flows in rectangular nanochannels with scales between 100 nm and 1000 nm, using an unstructured three-dimensional Direct Simulation Monte Carlo (U3DSMC) methodology. This dissertation also contributes to the computational mathematics background of the U3DSMC method with validations and verifications at the micronscale and nanoscale, as well as with the investigation of the statistical fluctuations and errors associated with U3DSMC simulations at the nanoscale. The U3DSMC code is validated by comparisons with previous two dimensional DSMC simulations of flows in micron-scale rectangular channels. The simulation involves the supersonic flow of nitrogen into a microchannel with height of 1.2 m and width of 6 m. The free stream conditions correspond to a pressure of 72,450 Pa, Mach number , Knudsen number and mean free path nm. The U3DSMC centerline temperature, heat flux to the wall, and mean velocity as a function of the transverse direction are in very good agreement with previous 2D results. Statistical fluctuations and errors in U3DSMC have added significance in nanoscale domains because the number of real particles can be very small inside a computational cell. The effect of the number of samples, the number of computational particles in a Delaunay cell, and the Mach number on the fractional errors of density, velocity and temperature are investigated for uniform and pressure-driven nanoscale flows. The uniform nanoflow is implemented by applying a and free stream boundary condition with m-3, K, nm in a domain that requires resolution of a characteristic length scale nm. The pressure-driven flows consider a nanochannel of 500 nm height, 100 nm width and 4 m length. Subsonic boundary conditions are applied with inlet pressure 101,325 Pa and outlet pressure of 10132.5 Pa. The analysis shows that U3DSMC simulations at nanoscales featuring 10-30 particles per Delaunay cell result in statistical errors that are consistent with theoretical estimates. The rarefied flow of nitrogen with speed ratio of 2, 5, and 10, pressure of 10.132 kPa into rectangular nanochannels with height of 100, 500 and 1000 nm is investigated using U3DSMC. The investigation considers rarefaction effects with =0.481, 0.962, 4.81, geometric effects with nanochannel aspect ratios of (L/H) from AR=1, 10, 100 and back-pressure effects with imposed pressures from 0 to 200 kPa. The computational domain features a buffer region upstream of the inlet and the nanochannel walls are assumed to be diffusively reflecting at the free stream temperature of 273 K. The analysis is based on the phase space distributions as well as macroscopic flow variables sampled in cells along the centerline. The phase space distributions show the formation of a disturbance region ahead of the inlet due to slow particles backstreaming through the inlet and the formation of a density enhancement with its maximum inside the nanochannel. The velocity phase-space distributions show a low-speed particle population generated inside the nanochannel due to wall collisions which is superimposed with the free stream high-speed population. The mean velocity decreases, while the number density increases in the buffer region. The translational temperature increases in the buffer region and reaches its maximum near the inlet. For AR=10 and 100 nanochannels the gas reaches near equilibrium with the wall temperature. The heat transfer rate is largest near the inlet region where non-equilibrium effects are dominant. For =0.481, 0.962, 4.81, vacuum back pressure, and AR=1, the nanoflow is supersonic throughout the nanochannel, while for AR=10 and 100, the nanoflow is subsonic at the inlet and becomes sonic at the outlet. For =0.962, AR=1, and imposed back pressure of 120 kPa and 200 kPa, the nanoflow becomes subsonic at the outlet. For =0.962 and AR=10, the outlet pressure nearly matches the imposed back pressure with the nanoflow becoming sonic at 40 kPa and subsonic at 100 kPa. Heat transfer rates at the inlet and mass flow rates at the outlet are in good agreement with those obtained from theoretical free-molecular models. The flows in these nanochannels share qualitative characteristics found in microchannels ad well as continuum compressible flows in channels with friction and heat loss. The rarefied flow of nitrogen with speed ratio of 2, 5, 10, at an atmospheric pressure of 101.32 kPa into rectangular nanochannels with height of 100 and 500 nm is investigated using U3DSMC. The investigation considers rarefaction effects with =0.0962 and 4.81, geometric effects with nanochannel aspect ratios of (L/H) of AR=1 and 10 and vacuum back-pressure. Phase plots and sample-averaged macroscopic parameters are used in the analysis. Under vacuum back pressure the centerline velocity decreases in the buffer region from its free stream value. For 0.481, 0.0962 and AR=1 the Mach number is supersonic at the inlet and remains supersonic throughout the nanochannel. For 0.481, 0.0962 and AR=10, the flow becomes subsonic at the inlet and shows a sharp increase in pressure. The Mach number, subsequently, increases and reaches the sonic point at the outlet. For 0.481, 0.0962 and AR=1 the translational temperature reaches a maximum near the inlet and decreases monotonically up to the outlet. For 0.481, 0.0962 and AR=10, the translational temperature reaches a maximum near the inlet and then decreases to come in near equilibration with the wall temperature of 273 K. "

This work is part of an effort to develop an unstructured, three-dimensional, direct simulation Monte Carlo/particle-in-cell (DSMC/PIC) code for the simulation of non-ionized, fully ionized and partially-ionized flows in micropropulsion devices. Flows in microthrusters are often in the transitional to rarefied regimes, requiring numerical techniques based on the kinetic description of the gaseous or plasma propellants. The code is implemented on unstructured tetrahedral grids to allow discretization of arbitrary surface geometries and includes an adaptation capability. In this study, an existing 3D DSMC code for rarefied gasdynamics is improved with the addition of the variable hard sphere model for elastic collisions and a vibrational relaxation model based on discrete harmonic oscillators. In addition the existing unstructured grid generation module of the code is enhanced with grid-quality algorithms. The unstructured DSMC code is validated with simulation of several gaseous micronozzles and comparisons with previous experimental and numerical results. Rothe s 5-mm diameter micronozzle operating at 80 Pa is simulated and results are compared favorably with the experiments. The Gravity Probe-B micronozzle is simulated in a domain that includes the injection chamber and plume region. Stagnation conditions include a pressure of 7 Pa and mass flow rate of 0.012 mg/s. The simulation examines the role of injection conditions in micronozzle simulations and results are compared with previous Monte Carlo simulations. The code is also applied to the simulation of a parabolic planar micronozzle with a 15.4-micron throat and results are compared with previous 2D Monte Carlo simulations. Finally, the code is applied to the simulation of a 34-micron throat MEMS-fabricated micronozzle. The micronozzle is planar in profile with sidewalls binding the upper and lower surfaces. The stagnation pressure is set at 3.447 kPa and represents an order of magnitude lower pressure than used in previous experiments. The simulation demonstrates the formation of large viscous boundary layers in the sidewalls. A particle-in-cell model for the simulation of electrostatic plasmas is added to the DSMC code. Solution to Poisson's equation on unstructured grids is obtained with a finite volume implementation. The Poisson solver is validated by comparing results with analytic solutions. The integration of the ionized particle equations of motion is performed via the leapfrog method. Particle gather and scatter operations use volume weighting with linear Lagrange polynomial to obtain an acceptable level of accuracy. Several methods are investigated and implemented to calculate the electric field on unstructured meshes. Boundary conditions are discussed and include a formulation of plasma in bounded domains with external circuits. The unstructured PIC code is validated with the simulation of a high voltage sheath formation.

In this thesis, a numerical and theoretical investigation of the Pulsed Pressure Chemical Vapour Deposition (PP-CVD) progress is presented. This process is a novel method for the deposition of thin films of materials from either liquid or gaseous precursors. PP-CVD operates in an unsteady manner whereby timed pulsed of the precursor are injected into a continuously evacuated reactor volume. A non-dimensional parameter indicating the extent of continuum breakdown under strong temporal gradients is developed. Experimental measurements, supplemented by basic continuum simulations, reveal that spatio-temporal breakdown of the continuum condition occurs within the reactor volume. This means that the use of continuum equation based solvers for modelling the flow field is inappropriate. In this thesis, appropriate methods are developed for modelling unsteady non-continuum flows, centred on the particle-based Direct Simulation Monte Carlo (DSMC) method. As a first step, a basic particle tracking method and single processor DSMC code are used to investigate the physical mechanisms for the high precursor conversion efficiency and deposition uniformity observed in experimental reactors. This investigation reveals that at soon after the completion of the PP-CVD injection phase, the precursor particles have an approximately uniform distribution within the reactor volume. The particles then simply diffuse to the substrate during the pump-down phase, during which the rate of diffusion greatly exceeds the rate at which particles can be removed from the reactor. Higher precursor conversion efficiency was found to correlate with smaller size carrier gas molecules and moderate reactor peak pressure. An unsteady sampling routine for a general parallel DSMC method called PDSC, allowing the simulation of time-dependent flow problems in the near continuum range, is then developed in detail. Nearest neighbour collision routines are also implemented and verified for this code. A post-processing procedure called DSMC Rapid Ensemble Averaging Method (DREAM) is developed to improve the statistical scatter in the results while minimising both memory and simulation time. This method builds an ensemble average of repeated runs over small number of sampling intervals prior to the sampling point of interest by restarting the flow using either xi a Maxwellian distribution based on macroscopic properties for near equilibrium flows (DREAM-I) or output instantaneous particle data obtained by the original unsteady sampling of PDSC for strongly non-equilibrium flows (DREAM-II). The method is validated by simulating shock tube flow and the development of simple Couette flow. Unsteady PDSC is found to accurately predict the flow field in both cases with significantly reduced run-times over single processor code and DREAM greatly reduces the statistical scatter in the results while maintaining accurate particle velocity distributions. Verification simulations are conducted involving the interaction of shocks over wedges and a benchmark study against other DSMC code is conducted. The unsteady PDSC routines are then used to simulate the PP-CVD injection phase. These simulations reveal the complex flow phenomena present during this stage. The initial expansion is highly unsteady; however a quasi-steady jet structure forms within the reactor after this initial stage. The simulations give additional evidence that the collapse of the jet at the end of the injection phase results in an approximately uniform distribution of precursor throughout the reactor volume. Advanced modelling methods and the future work required for development of the PP-CVD method are then proposed. These methods will allow all configurations of reactor to be modelled while reducing the computational expense of the simulations.

The modeling of Micro- and NanoElectroMechanical Systems (MEMS and NEMS) requires new computational techniques that can deal efficiently with geometric complexity and scale dependent effects that may arise. Reduced feature sizes increase the coupling of physical phenomena and noncontinuum behavior, often requiring models based on molecular descriptions and/or first principles. Furthermore, noncontinuum effects are often localized to small regions of (relatively) large systemsprecluding the global application of microscale models due to computational expense. Multiscale modeling couples efficient continuum solvers with detailed microscale models to providing accurate and efficient models of complete systems. This thesis presents the development of multiscale modeling techniques for nonequilibrium microscale gas phase phenomena, especially thermally driven microflows. Much of this focuses on improving the ability of the Information Preserving DSMC (IP-DSMC) to model thermally driven flows. The IP-DSMC is a recent technique that seeks to accelerate the solution of direct simulation Monte Carlo (DSMC) simulations by preserving and transporting certain macroscopic quantities within each simulation molecules. The primary contribution of this work is the development of the Octant Splitting IP-DSMC (OSIP-DSMC) which recovers previously unavailable information from the preserved quantities and the microscopic velocities. The OSIP-DSMC can efficiently simulate flow fields induced by nonequilibrium systems, including phenomena such as thermal transpiration. The OSIP-DSMC provides an efficient method to explore rarefied gas transport phenomena which may lead to a greater understanding of these phenomena and new concepts for how these may be utilized in practical engineering systems. Multiscale modeling is demonstrated utilizing the OSIP-DSMC and a 2D BEM solver for the continuum (heat transfer) model coupled with a modified Alternating Schwarz coupling scheme. An interesting application for this modeling technique is Thermal Sensing Atomic Force Microscopy (TSAFM). TSAFM relies on gas phase heat transfer between heated cantilever probes and the scanned surface to determine the scan height, and thus the surface topography. Accurate models of the heat transfer phenomena are required to correctly interpret scan data. This thesis presents results demonstrating the effect of subcontinuum heat transfer on TSAFM operation and explores the mechanical effects of the Knudsen Force on the heated cantilevers.

In dieser Arbeit werden verschiedene Prozesse zur Atomlagenabscheidung (ALD) von TiO2 und HfO2 experimentell untersucht. Die Untersuchungen schließen eine experimentelle Charakterisierung des Schichtwachstums sowie eine massenspektrometrische Analyse der Reaktionsprodukte ein. Im Detail wurden der ALD-Prozess mit Cp*Ti(OMe)3 und Ozon zur Abscheidung von TiO2 sowie der ALD-Prozess mit TEMAHf und Ozon zur Abscheidung von HfO2 untersucht. Der theoretische Teil der Arbeit beginnt mit einer Methode zur Bestimmung des absoluten Haftkoeffizienten. Anschließend werden numerische Modelle entwickelt, welche die Adsorption von Präkursormolekülen durch strukturierte Substrate beschreiben. Diese Modelle enthalten die Substratstruktur und den absoluten Haftkoeffizienten. Es wird eine statistische numerische Methode entwickelt, mit der der Gastransport in dem ALD-Reaktor statistisch beschrieben wird. Die statistischen Größen, welche die Gasdynamik im Reaktor beschreiben, werden mit der Discrete Simulation Monte Carlo (DSMC) Methode bestimmt. Mit dieser Methode und den Modellen der Adsorption kann der komplette ALD-Prozess simuliert werden. Die neu entwickelte Methode wird verwendet um die Effizienz verschiedener ALD-Reaktoren in Abhängigkeit des absoluten Haftkoeffizienten, der Substratstruktur sowie der Prozessbedingungen zu untersuchen. Die Geometrie des Reaktors wird variiert und mit der Referenzgeometrie verglichen. / This dissertation is divided into an experimental part and a theoretical part. The experimental part describes the atomic layer deposition (ALD) of TiO2 and HfO2. TDMAT and Cp*Ti(OMe)3 were used as titanium precursors, while TEMAHf was used as the hafnium precursor. Ozone was used as the oxygen source. The self limiting film growth and the temperature window of these ALD processes were investigated. The reaction by-products of the Cp*Ti(OMe)3/O3 process were identified by quadrupol mass spectrometry (QMS). The QMS analysis of the TEMAHf/O3 process revealed that water is formed during the metal precursor pulse. The theoretical part of this thesis describes the development of models and numerical methods to simulate the ALD as a whole. First of all, a model for the adsorption of precursor molecules by planar substrates was developed. This model was extended to describe the adsorption of precursor molecules inside a cylindrical hole with an aspect ratio of 20, 40 and 80. The adsorption of precursor molecules is dominated by the absolute sticking coefficient (SC), i.e., the reactivity of the precursor molecules. From the numerical model the saturation profiles along the wall of a cylindrical hole can be determined. From the comparison of the simulated profile with an experimentally determined thickness profile the SC can be determined. This method was used to determine the SC of the precursors examined in the experimental part. The SC of TEMAHf increases exponentially with the substrate temperature. A discrete particle method (DSMC) was used to derive a statistical description of the gas kinetics inside an ALD reactor. Combining the statistical description of the gas transport and the numerical models of the adsorption, it is possible to simulate the ALD for any combination of reactor, substrate and SC. It is possible to distinguish the contribution of the reactor geometry, the process parameters and the process chemistry (SC) to the process efficiency. Therefore, the ALD reactor geometry can be optimized independently of the process chemistry. This method was used to study a shower head ALD reactor. The reactor geometry, the composition of the gas at the inlet and the position of the inlet nozzles was varied in order to find more efficient ALD reactors. The efficiency of the reference geometry is limited by the inlet nozzles close to the exhaust and the decrease of the pressure on the substrate near the exhaust. The efficiency of ALD processes with different SCs was simulated for planar and structured substrates with a diameter of 300 mm and 450 mm.

The primary purpose of this study is to model the water vapor flow produced by a comet impact on the Moon using the Direct Simulation Monte Carlo (DSMC) method. Toward that end, our DSMC solver was modified in order to model the cometary water from the time of impact until it is either destroyed due to escape or photodestruction processes or captured inside one of the lunar polar cold traps. In order to model the complex flow induced by a comet impact, a 3D spherical parallel version of the DSMC method was implemented. The DSMC solver was also modified to take as input the solution from the SOVA hydrocode for the impact event at a fixed interface. An unsteady multi-domain approach and a collision limiting scheme were also added to the previous implementation in order to follow the water from the continuum regions near the point of impact to the much later rarefied atmospheric flow around the Moon. The present implementation was tested on a simple unsteady hemispherical expansion flow into a vacuum. For these simulations, the data at the interface were provided by a 1D analytical model instead of the SOVA solution. Good results were obtained downstream of the interface for density, temperature and radial velocity. Freezing of the vibrational modes was also observed in the transitional regime as the flow became collisionless. The 45° oblique impact of a 1 km radius ice sphere at 30 km/s was simulated up to several months after impact. Most of the water crosses the interface under 5 s moving mostly directly downstream of the interface. Most of the water escapes the gravity well of the Moon within the first few hours after impact. For such a comet impact, only ~3% of the comet mass remains on the Moon after impact. As the Moon rotates, the molecules begin to migrate until they are destroyed or captured in a cold trap. Of the 3% of the water remaining on the Moon after impact, only a small fraction, ~0.14% of the comet mass, actually reaches the cold traps; nearly all of the rest is photo-destroyed. Based on the surface area of the cold traps used in the present simulations, ~1 mm of ice would have accumulated in the polar cold traps after such an impact. Estimates for the total mass of water accumulated in the polar cold traps over one billion years are consistent with recent observations. / text

It is well established that rarefied flows cannot be properly described by traditional hydrodynamics, namely the Navier-Stokes equations for gas flows, and the Fourier’s law for heat transfer. Considering the significant advancement in miniaturization of electronic devices, where dimensions become comparable with the mean free path of the flow, the It is well established that rarefied flows cannot be properly described by traditional hydrodynamics, namely the Navier-Stokes equations for gas flows, and the Fourier's law for heat transfer. Considering the significant advancement in miniaturization of electronic devices, where dimensions become comparable with the mean free path of the flow, the study of rarefied flows is extremely important. This dissertation includes two main parts. First, we look into the heat transport in solids when the mean free path for phonons are comparable with the length scale of the flow. A set of macroscopic moment equations for heat transport in solids are derived to extend the validity of Fourier's law beyond the hydrodynamics regime. These equations are derived such that they remain valid at room temperature, where the MEMS devices usually work. The system of moment equations for heat transport is then employed to model the thermal grating experiment, recently conducted on a silicon wafer. It turns out that at room temperature, where the experiment was conducted, phonons with high mean free path significantly contribute to the heat transport. These low frequency phonons are not considered in the classical theory, which leads to failure of the Fourier's law in describing the thermal grating experiment. In contrast, the system of moment equations successfully predict the deviation from the classical theory in the experiment, and suggest the importance of considering both low and high frequency phonons at room temperature to capture the experimental results. In the second part of this study, we look into the gas-surface interactions for conventional gas dynamics when the gas flow is rarefied. An extension to the well-known Maxwell boundary conditions for gas-surface interactions are obtained by considering velocity dependency in the reflection kernel from the surface. This extension improves the Maxwell boundary conditions by providing an extra free parameter that can be fitted to the experimental data for thermal transpiration effect in non-equilibrium flows. The velocity dependent Maxwell boundary conditions are derived for the Direct Simulation Monte Carlo (DSMC) method and the regularized 13-moment (R13) equations for conventional gas dynamics. Then, a thermal cavity is considered to test and study the effect of these boundary conditions on the flow formation in the slip and early transition regime. It turns out that using velocity dependent boundary conditions allows us to change the size and direction of the thermal transpiration force, which leads to marked changes in the balance of transpiration forces and thermal stresses in the flow. / Graduate

Orientador: José Paulo Fernandes Garcia / Banca: Laurence Duarte Colvara / Banca: Ivan Nunes da Silva / Resumo: O enfoque principal do trabalho foi dado ao Controle Discreto com Modos Deslizantes(CDMD) aplicado em sistemas que possuem atraso no processamento do sinal de controle e acesso somente à saída do sistema. A estratégia de controle tem por objetivo a utilização de técnicas de controle com modos deslizantes para a elaboração de uma lei de controle simples e robusta às incertezas da planta e ao atraso. O observador de estados apresentado possui características de modo deslizante, o qual realiza a estimação robusta do vetor de estados que na maioria dos casos práticos não é totalmente acessível. Os métodos de projetos propostos podem ser aplicados no controle de plantas estáveis ou instáveis com atraso no sinal de controle e acesso somente à saída da planta. Para comprovar a eficiência dos projetos apresentados neste trabalho, analisou-se o controlador atuando com acesso a todos estados e o controlador atuando juntamente com o observador robusto para a estimação dos estados. Os resultados foram obtidos através de simulações no Sistema Bola e Viga, Sistema Pêndulo Invertido Linear e Sistema Pêndulo Invertido Rotacional que são exemplos de plantas de natureza instável. / Abstract: The main focus was placed on the Discrete Sliding Mode Control (DSMC) applied to systems that have a delay in the processing of the control signal and access to the system output only. The control strategy is intended to use control techniques of sliding modes to elaborate a simple and robust control law against the uncertainties of the plant and the delay. The states observer presented has the characteristics of a sliding mode, which performs the robust estimation of the states vector that, in most practical cases, is not fully accessible. The design methods proposed may be applied to the control of stable or unstable plants with delay on the control signal and access to the plant output only. In order to attest the efficiency of the design presented in this work, the controller was analyzed at work with access to all states and jointly with the robust observer to estimate the states. The results were obtained by means of simulations in the Ball and Beam System, Linear Inverted Pendulum System, and Rotational Inverted Pendulum System, which are examples of plants of unstable nature. / Mestre