Browsing by Author "Wu, JS"

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Adhesion, permeability, and mechanical properties of multilayered blown films using maleated low-density polyethylene blends as adhesion-promoting layers
(2003)
Huang, CH
;
Wu, JS
;
Huang, CC
;
Lin, LS
;
應用化學系
We have fabricated three-layer films, comprising a varying content of ethylene-vinyl alcohol copolymer (EVOH) as the internal layer and blends of low-density polyethylene (LDPE) and low-density ethylene grafted with maleic anhydride (LDPE-g-MAH) as the external layers, by a coextrusion blown-film process. We chose to use blends to promote the adhesion between EVOH and LDPE and to reduce the number of layers in the coextrusion system. The peel strength increased sharply when the amount of LDPE-g-MAH was greater than 12.5 wt% and we associate it with the promotion of adhesion between layers brought about by specific interactions between EVOH and LDPE-g-MAH. FT-IR spectroscopic analysis showed an increase in the intensity of the absorbance of the ester band upon increasing the content of LDPE-g-MAH, which indicates that a chemical reaction occurs that promotes adhesion at the interface. The tensile strength did not change significantly with increasing LDPE-g-MAH content, which had a small effect on elongation and modulus in both the machine direction (MD) and transverse direction (TD). Tear strength decreased continuously with increasing LDPE-g-MAH content, in both the MD and TD, as a result of the greater ease of crack propagation in the EVOH layer. The oxygen permeability of the three-layer films remained almost constant upon varying the amount of LDPE-g-MAH. These three-layer films all followed the theoretical prediction made by the inverse additivity rule. The water vapor permeabilities of the three-layer films, however, were affected by the degree of hydrogen bonding, which was analyzed by FT-IR spectroscopy. The effects of this hydrogen bonding resulted in a discrepancy between the experimental findings and the theoretical predictions, especially when the EVOH content was increased.
Analysis of internal micro-scale gas flows with pressure boundaries using the DSMC method
(2001)
Wu, JS
;
Tseng, KC
;
機械工程學系
;
Department of Mechanical Engineering
The development and applications of a two-dimensional DSMC (Direct Simulation Monte Carlo) program for pressure boundaries using unstructured cells and its applications to typical internal micro-scale gas flows, including a micro-manifold, a micro-nozzle and a slider air bearing of computer hard disk, are described. This is aimed to further teat the treatment of pressure boundaries by particle flux conservation, especially at subsonic speed, to gas flows involving many exits, more complicated geometry and moving boundaries. Firstly, results of a T-shaped micro-manifold with inlet Knudsen number of 0.2 show that excellent mass flow conservation between the inlet and two exits is obtained at low subsonic gas flows. Secondly, a micro-nozzle with the fixed inlet Knudsen number of 0.067 is simulated. For higher specified pressure ratio (exit to inlet), the location of maximum Mach number moves further downstream as the pressure ratio decreases; while, for lower specified pressure ratio, the Mach number increases all the way through the nozzle to the exit. Eventually, supersonic speed is observed at the exit for pressure ratio equal to or less than 0.143. Thirdly, for the gas flows of a slider air bearing of computer hard drive, the results agree very well with those of Alexander et al. (Phys. Fluids, 1994) for all the simulated conditions. In summary, the particle flux conservation concept has been proved successfully at multiple (more than two) pressure boundaries with complicated geometries and moving solid boundaries.
Analysis of micro-scale gas flows with pressure boundaries using direct simulation Monte Carlo method
(2001-07-01)
Wu, JS
;
Tseng, KC
;
機械工程學系
;
Department of Mechanical Engineering
The development of a two-dimensional direct simulation Monte Carlo program for pressure boundaries using unstructured cells and its applications to typical micro-scale gas flows are described. For the molecular collision kinetics, variable hard sphere molecular model and no time counter collision sampling scheme are used, while the cell-by-cell particle tracing technique is implemented for particle movement. The program has been verified by comparison of simulated equilibrium collision frequency with theoretical value and by comparison of simulated non-equilibrium profiles of one-dimensional normal shock with previous reported work. Applications to micro-scale gas flows includes micro-manifold, micro-nozzle and slider air bearing. The aim is to further test the treatment of pressure boundaries, developed previously by the first author, by particle flux conservation for gas flows involving many exits, complicated geometries and moving boundaries. For micro-manifold gas flows, excellent mass flow conservation between the inlet and two exits is obtained at low subsonic flows. For micro-nozzle gas flows, with fixed inlet pressure, the mass flow rate increases with decreasing pressure ratio (exit to inlet), but remains essentially the same at pressure ratios much lower than that obtained by continuum inviscid analysis. For higher specified pressure ratios, the locations of maximum Mach number moves further downstream as the pressure ratio decreases; while, for lower specified pressure ratios, the Mach number increases all the way through the nozzle to the exit. Eventually, supersonic speed is observed at the exit for pressure ratios equal to or less than 0.143. Finally, for slider air bearing gas flows of the computer hard drive, the simulated gas pressures, at different rotating speeds, agree very well with previous studies. However, there exists strong translational nonequilibrium in the gas flows at the high rotating speeds. The applicability of the treatment of pressure boundaries using the equilibrium Maxwell-Boltzmann distribution function is discussed in terms of the magnitude of the local Knudsen number at the pressure boundary for micro-nozzles and slider air bearing applications. (C) 2001 Elsevier Science Ltd. All rights reserved.
Application of local mesh refinement in the DSMC method
(2001)
Wu, JS
;
Tseng, KC
;
Kuo, CH
;
機械工程學系
;
Department of Mechanical Engineering
The implementation of an adaptive mesh embedding (h-refinement) schemes using unstructured grid in two-dimensional Direct Simulation Monte Carlo (DSMC) method is reported. In this technique, local isotropic refinement is used to introduce new meshes where local cell Knudsen number is less than some preset value. This simple scheme, however, has several severe consequences affecting the performance of the DSMC method. Thus, we have applied a technique to remove the hanging mode, by introducing anisotropic refinement in the interfacial cells. This is completed by simply connect the hanging node(s) with the other non-hanging node(s) in the non-refined, interfacial cells. In contrast, this remedy increases negligible amount of work; however, it removes all the difficulties presented in the first scheme with hanging nodes. We have tested the proposed scheme for Argon gas using different types of mesh, such as triangular and quadrilateral or mixed, to high-speed driven cavity flow. The results show an improved flow resolution as compared with that of unadaptive mesh. Finally, we have triangular adaptive mesh to compute two near-continuum gas flows, including a supersonic flow over a cylinder and a supersonic flow over a 35 degrees compression ramp. The results show fairly good agreement with previous studies. In summary, the computational penalties by the proposed adaptive schemes are found to be small as compared with the DSMC computation itself. Nevertheless, we have concluded that the proposed scheme is superior to the original unadaptive scheme considering the accuracy of the solution.
Assessment of conservative weighting scheme in simulating chemical vapour deposition with trace species
(2003-09-10)
Wu, JS
;
Hsiao, WJ
;
Lian, YY
;
Tseng, KC
;
機械工程學系
Low-pressure or ultra-high vacuum chemical vapour deposition often involves important trace species in both gas-phase and surface reactions. The conservative weighting scheme (J. Thermophys. Heat Transfer 1996; 10(4):579) has been used to deal with the trace species often involved in some non-reactive physical processes, which is otherwise considered computationally impossible using the conventional DSMC method. This conservative weighting scheme (CWS) improves greatly the statistical uncertainties by decreasing the weighting factors of trace-species particles and ensures the conservation of both momentum and energy between two colliding particles with large difference of weighting factors. This CWS is further extended to treat reactive processes for gas-phase and surface reactions with trace species, which is called extended conservative weighting scheme (ECWS). A single-cell equilibrium simulation is performed for verifying both the CWS and ECWS in treating trace species. The results of using CWS show that it is most efficient and accurate for weight ratio (trace to non-trace) equal to or less than 0.01 for flows with two and three species. The results of a single-cell simulation using ECWS for gas-phase reaction and surface reactions show that only ECWS can produce acceptable results with reasonable computational time. Copyright (C) 2003 John Wiley Sons, Ltd.
Blends of poly(propylene) and polyacetal compatibilized by ethylene vinyl alcohol copolymers
(2003-08-08)
Huang, JM
;
Cheng, HJ
;
Wu, JS
;
Chang, FC
;
應用化學系
Polymer blends of poly(propylene) (PP) and polyacetal (polyoxymethylene, POM) with ethylene vinyl alcohol (EVOH) copolymers were investigated by differential scanning calorimetry (DSC), rheological, tensile, and impact measurements, Fourier transform infrared spectroscopy (FTIR), and scanning electron microscopy (SEM). The PP-POM-EVOH blends were extruded with a co-rotating twin-screw extruder. The ethylene group in the EVOH is partially miscible with PP, whereas the hydroxyl group in the EVOH can form hydrogen bonding with POM. The EVOH tends to reside along the interface, acting as a surfactant to reduce the interfacial tension and to increase the interfacial adhesion between the blends. Results from SEM and mechanical tests indicate that a small quantity of the EVOH copolymer or a smaller vinyl alcohol content in the EVOH copolymer results in a better compatibilized blend in terms of finer phase domains and better mechanical properties. (C) 2003 Wiley Periodicals, Inc.
Concurrent DSMC method using dynamic domain decomposition
(2003)
Wu, JS
;
Tseng, KC
;
機械工程學系
;
Department of Mechanical Engineering
In the current study, a parallel two-dimensional direct simulation Monte Carlo method is reported, which incorporates a multi-level graph-partitioning technique to dynamically decompose the computational domain. The current DSMC method is implemented on an unstructured mesh using particle ray-tracing technique, which takes the advantages of the cell connectivity information. Standard Message Passage Interface (MPI) is used to communicate data between processors. In addition, different strategies applying the Stop at Rise (SAR) [7] scheme is utilized to determine when to adapt the workload distribution among processors. Corresponding analysis of parallel performance is reported using the results of a high-speed driven cavity flow on IBM-SP2 parallel machines (memory-distributed, CPU 160 MHz, RAM 256 MM each) up to 64 processors. Small, medium and large problems, based on the number of particles and cells, are simulated. Results, applying SAR scheme every two time steps, show that parallel efficiency is 57%, 90% and 107% for small, medium and large problems, respectively, at 64 processors. In general, benefits,of applying SAR scheme at larger periods decrease gradually with increasing problem size. Detailed time analysis shows that degree of imbalance levels off very rapidly at a relatively low value (30%-40%) with increasing number of processors applying dynamic load balancing, while it, at a value of 5similar to6 times larger, increases with increasing number of processors without dynamic load balancing. At the end, the completed code is applied to compute a near-continuum gas flow to demonstrate its superior computational capability.
Derivation of variable soft sphere model parameters in direct-simulation Monte Carlo method using quantum chemistry computation
(2003-12-01)
Wu, JS
;
Hsu, YL
;
機械工程學系
;
Department of Mechanical Engineering
A practical procedure for deriving parameters of the variable soft sphere (VSS) molecular model for the Lennard-Jones potential of gas species in the direct-simulation Monte Carlo (DSMC) method is introduced. Intermolecular potential energy is fitted through the Lennard-Jones (L-J) potential, which is obtained by quantum chemistry computation. Computed L-J potentials are then used to compute viscosity and diffusivity coefficients for like and unlike molecules, respectively, based on gas kinetics theory. Related parameters of the VSS molecular model are derived by fitting these computed coefficients to those derived from the VSS model. Test results for O-2-H-2 Mixtures using this procedure are in good agreement with existing data. VSS parameters for silicon-based species frequently encountered in the chemical vapor deposition process are derived as an example to illustrate the importance of this procedure in extending the applicability of the DSMC computation to gas species other than air-related species.
Development of a general parallel three-dimensional Direct Simulation Monte Carlo Code
(2005)
Wu, JS
;
Tseng, KC
;
Lee, UM
;
Lian, YY
;
機械工程學系
Development of a general parallel three-dimensional direct Simulation Monte Carlo Code, termed as PDSC, is reported in this paper. The PDSC is implemented on the memory-distributed parallel machine (e.g., PC-cluster system) using message passing interface (MPI) with several important features, including tetrahedral unstructured mesh, solution-based adaptive mesh refinement, variable time-step method, dynamic load balancing technique, extended conservative weighting scheme for trace species, very low-speed flows, iterative pressure boundary treatment method and hybrid NS-DSMC method. In addition, a graphic user interface (GUI) using VTK (Visualization Toolkit) library and Qt is developed to ease the settings of boundary conditions and domain decomposition for parallel processing and to preserve future possibility of including more features into the code.
Development of a parallel Poisson's equation solver with adaptive mesh refinement and its application in field emission prediction
(2006-06-15)
Hsu, KH
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Chen, PY
;
Hung, CT
;
Chen, LH
;
Wu, JS
A parallel electrostatic Poisson's equation solver coupled with parallel adaptive mesh refinement (PAMR) is developed in this paper. The three-dimensional Poisson's equation is discretized using the Galerkin finite element method using a tetrahedral mesh. The resulting matrix equation is then solved through the parallel conjugate gradient method using the non-overlapping subdomain-by-subdomain scheme. A PAMR module is coupled with this parallel Poisson's equation solver to adaptively refine the mesh where the variation of potentials is large. The parallel performance of the parallel Poisson's equation is studied by simulating the potential distribution of a CNT-based triode-type field emitter. Results with similar to 100 000 nodes show that a parallel efficiency of 84.2% is achieved in 32 processors of a PC-cluster system. The field emission properties of a single CNT triode- and tetrode-type field emitter in a periodic cell are computed to demonstrate their potential application in field emission prediction. (c) 2006 Elsevier B.V. All rights reserved.
Effects of ambient turbulence and fuel properties on the evaporation rate of single droplets
(2001-12-01)
Wu, JS
;
Liu, YJ
;
Sheen, HJ
;
機械工程學系
;
Department of Mechanical Engineering
Results of the evaporation of a single liquid fuel droplet in various free-stream turbulence intensities and scales are reported. Experiments are carried out at room temperature by using n-heptane and n-decane, fuels at Re-d = 100. A low-speed vertical wind tunnel with different turbulence intensities and scales, controlled by using different sizes of disk, is constructed. The free-stream turbulence intensities are varied in the range from 1% to 60% and the. integral length scales are from 2.5 to 20 times of the initial droplet diameter. Results show that the time history of droplet diameter follows the d(2)-law in turbulent environments with generally higher evaporation rates as compared with those in quasi-laminar cases. Combined effects of liquid fuel properties and ambient turbulence properties on the evaporation rate can be reasonably well explained by the correlation of normalized evaporation rate with the effective vaporization Damkohler number, Da(v). (C) 2001 Elsevier Science Ltd. All rights reserved.
Evaporation model of a single hydrocarbon fuel droplet due to ambient turbulence at intermediate Reynolds numbers
(2003-11-01)
Wu, JS
;
Hsu, KH
;
Kuo, PM
;
Sheen, HJ
;
機械工程學系
A general evaporation model of a single liquid fuel droplet under various ambient turbulence conditions at intermediate droplet Reynolds numbers is proposed combining the current and previous experimental results. Extensive evaporation experiments of single fuel droplets are conducted at room temperature in quasi-laminar and turbulent environments at Reynolds numbers in the range of 72-333. Tested hydrocarbon fuels include by pentane, hexane, heptane, octane and decane. Flow fields, behind a perforated plate or a circular disk in a vertical low-speed wind tunnel, provide the required ambient turbulent environments for droplet evaporation experiments. The ambient turbulence intensities vary in the range of 1-60% and the integral length scales in the range of 0.5-20 times of the initial droplet diameter. Results show that normalized evaporation rate (K/K-L) decreases with increasing effective Damkohler number (0.0001 < Da(v) < 0.1) and is approximately equal to unity with further increasing Damkohler number (0.1 < Da(v) < 1). (C) 2003 Elsevier Ltd. All rights reserved.
Mixed-metal oxide films via a heterobimetallic complex as an MOCVD single-source precursor
(1996-10-07)
Shyu, SG
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Wu, JS
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Chuang, SH
;
Chi, KM
;
Sung, YS
A single-phase polycrystalline mixed-metal oxide WCoO4 film on Si(100) can be prepared by MOCVD with the use of [(eta-C5H5)(CO)(3)WCo(CO)(4)] as a single-source precursor.
Morphological, thermal, barrier and mechanical properties of LDPE/EVOH blends in extruded blown films
(2004-03-01)
Huang, CH
;
Wu, JS
;
Huang, CC
;
Lin, LS
;
應用化學系
We have investigated the morphological, thermal, barrier, and mechanical properties of low-density polyethylene/ethylenevinyl alcohol blend (LDPE/EVOH; 85/15 wt%) in highly and biaxially oriented blown films. Maleic anhydride-grafted linear low-density polyethylene (LDPE-g-MAH) in various concentrations (from 0 to 10 phr) was used as the compatibilizer for the immiscible system. Thermal analysis of the blend films shows that their melting temperatures, crystallization temperatures, and heats of fusion stay almost constant upon varying the amount of compatibilizer. The addition of the compatibilizer did not adversely affect the inherent properties of the blends, especially their barrier properties, through constraint effects of the grafted EVOH (EVOH-g-LD). The heat of fusion of EVOH obtained during the first heating is much higher than that of the second as a result of stress-induced crystallization during the blown film process. Oxygen permeation measurements show that the oxygen barrier properties of both highly and biaxially oriented blown films decrease upon increasing the amount of compatibilizer. although morphological analysis showed that the blends exhibit better laminar dispersion of the EVOH phase in the LDPE matrix when LDPE-g-MAH is added. The increase in oxygen permeability results from the presence of microvoids at the interface between the two phases during the process. Mechanical measurements showed that there exists an optimal amount of LDPE-g-MAH for maximizing both the tensile and tear properties in both the machine and transverse directions.
Parallel DSMC method using dynamic domain decomposition
(2005-05-07)
Wu, JS
;
Tseng, KC
;
機械工程學系
;
Department of Mechanical Engineering
A general parallel direct simulation Monte Carlo method using unstructured mesh is introduced, which incorporates a multi-level graph-partitioning technique to dynamically decompose the computational domain. The current DSMC method is implemented on an unstructured mesh using particle ray-tracing technique, which takes the advantages of the cell connectivity information. In addition, various strategies applying the stop at rise (SAR) (IEEE Trans Comput 1988; 39:1073-1087) scheme is studied to determine how frequent the domain should be re-decomposed. A high-speed, bottom-driven cavity flow, including small, medium and large problems, based on the number of particles and cells, are simulated. Corresponding analysis of parallel performance is reported on IBM-SP2 parallel machine up to 64 processors. Analysis shows that degree of imbalance among processors with dynamic load balancing is about 1/6 - 1/2 of that without dynamic load balancing. Detailed time analysis shows that degree of imbalance levels off very rapidly at a relatively low value with increasing number of processors when applying dynamic load balancing, which makes the large problem size fairly scalable for processors more than 64. In general, optimal frequency of activating SAR scheme decreases with problem size. At the end, the method is applied to compute two two-dimensional hypersonic flows, a three-dimensional hypersonic flow and a three-dimensional near-continuum twin-jet gas flow to demonstrate its superior computational capability and compare with experimental data and previous simulation data wherever available. Copyright (c) 2005 John Wiley A Sons, Ltd.
Parallel DSMC simulation of a single under-expanded free orifice jet from transition to near-continuum regime
(2005-11-01)
Wu, JS
;
Chou, SY
;
Lee, UM
;
Shao, YL
;
Lian, YY
This paper describes the numerical analysis of the flow structure of a single underexpanded argon free jet issuing into a lower-pressure or vacuum environment using the parallel three-dimensional direct simulation Monte Carlo (DSMC) method employing dynamic domain decomposition. Unstructured and tetrahedral solution-based refined mesh depending on the local mean free path is used to improve the resolution of solution. Simulated Knudsen numbers of the stagnation conditions based on orifice diameter, Reynolds numbers based on the conditions at the orifice exit, and stagnation-to-background pressure ratios are in the range of 0.0005-0.1, 7-1472, and 5-infinity, respectively, where "infinity" represents vacuum condition in the background environment. Results shou, that centerline density decays in a rate proportional to the inverse of the square of the axial distance (z(-2)) from the orifice for all ranges of flow in the current stud's The more rarefied the background condition is, the longer the z(-2)-regime is. In addition, a distinct flow structure, including barrel shock, Mach disk and jet boundary, is clearly identified as the Knudsen number reaches as low as 0.001. Predicted location and size of Mach disk in the near-continuun limit (Kn = 0.001, 0.0005) are found to be in reasonable agreement with experimental results in the continuum regime.
Parallel implementation of DSMC using unstructured mesh
(2003-09-01)
Wu, JS
;
Tseng, KC
;
Yang, TJ
;
機械工程學系
;
Department of Mechanical Engineering
The parallel implementation of the Direct Simulation Monte Carlo (DSMC) method on memory-distributed machines using unstructured mesh is reported. Physical domain decomposition is used to distribute the workload among multiple processors. A high-speed driven cavity flow is used as the benchmark problem for the validation of the parallel implementation. Three static partitioning techniques including simple coordinate partitioning, two-step partitioning (JOSTLE) and multi-level partitioning (METIS) are used for static domain decomposition, respectively. A cell renumbering technique is used to improve the memory management efficiency. Results of parallel efficiency show that two-step partitioning using JOSTLE performs the best, with 63% up to 25 processors, due to better load balancing among the processors. The powerful computational capability of the parallel implementation is demonstrated by computing a 2-D, near-continuum, hypersonic flow over a cylinder as well as a 3-D hypersonic flow over a sphere, respectively, both using 25 processors. Results compare reasonably well with previous simulated and experimental studies.
Parallel implementation of molecular dynamics simulation for short-ranged interaction
(2005-08-01)
Wu, JS
;
Hsu, YL
;
Lee, YM
;
機械工程學系
;
Department of Mechanical Engineering
A parallel molecular dynamics simulation method, designed for large-scale problems, employing dynamic spatial domain decomposition for short-ranged molecular interactions is proposed. In this parallel cellular molecular dynamics (PCMD) simulation method, the link-cell data structure is used to reduce the searching time required for forming the cut-off neighbor list as well as for domain decomposition, which utilizes the multi-level graph-partitioning technique. A simple threshold scheme (STS), in which workload imbalance is monitored and compared with some threshold value during the runtime, is proposed to decide the proper time for repartitioning the domain. The simulation code is implemented and tested on the memory-distributed parallel machine, e.g., PC-cluster system. Parallel performance is studied using approximately one million L-J atoms in the condensed, vaporized and supercritical states. Results show that fairly good parallel efficiency at 49 processors can be obtained for the condensed and supercritical states (similar to 60%), while it is comparably lower for the vaporized state (-40%). (c) 2005 Elsevier B.V. All rights reserved.
Parallel particle simulation of the near-continuum hypersonic flows over compression ramps
(2003-01-01)
Wu, JS
;
Tseng, KC
;
機械工程學系
;
Department of Mechanical Engineering
This paper describes the analysis of the near-continuum hypersonic flow over a compression ramp using the two-dimensional parallel direct simulation Monte Carlo (DSMC) method. Unstructured and triangular solution-based adaptive mesh depending on the local mean free path is used to improve the resolution of solution for the flow field with highly varying properties. In addition, a freestream parameter is defined to help reduced the cell numbers in the freestream area, resulting in appreciable decrease of the computational time (20-30%) without sacrificing the accuracy of the solution. The two-step multilevel graph partition technique is used for physical domain decomposition, employing estimated particle number distribution in each cell as the graph vertex weight. 32 IBM-SP2 processors are used throughout the study unless otherwise specified. The Effect of the outflow vacuum boundary condition, compression ramp angle, freestream condition, and length of the ramp to the flow field are investigated. Computational results are compared with previous numerical results whenever available.
Parallel three-dimensional direct simulation Monte Carlo method and its applications
(2003-09-01)
Wu, JS
;
Lian, YY
;
機械工程學系
;
Department of Mechanical Engineering
The development of a parallel three-dimensional direct simulation Monte Carlo (DSMC) method using unstructured cells is reported. Variable hard sphere molecular model and no time counter method are used for the molecular collision kinetics, while the cell-by-cell ray-tracing technique is implemented for particle movement. Developed serial code has been verified by comparing the results of a supersonic corner flow with those of Bird's three-dimensional structured DSMC code. In addition, a benchmark test is performed for an orifice expanding flow to verify the parallel implementation of DSMC method by comparing with available experimental data. Static physical domain decomposition is used to distribute the workload among multiple processors by considering the estimated particle weighting distribution. Two-step multi-level graph partitioning technique is used to perform the required domain decomposition. Completed code is then applied to compute a hypersonic flow over a sphere (external flow) and the flow field of a spiral drag pump (internal flow), respectively. Results of the former are in good agreement with previous numerical results using axisymmetric DSMC method and experimental data. Results of the latter also agree well with previous numerical results. (C) 2002 Elsevier Science Ltd. All rights reserved.