Methods and Models for Accelerating Dynamic Simulation of Fluid Power Circuits

The objective of this dissertation is to improve the dynamic simulation of fluid power circuits. A fluid power circuit is a typical way to implement power transmission in mobile working machines, e.g. cranes, excavators etc. Dynamic simulation is an essential tool in developing controllability and energy-efficient solutions for mobile machines. Efficient dynamic simulation is the basic requirement for the real-time simulation. In the real-time simulation of fluid power circuits there exist numerical problems due to the software and methods used for modelling and integration. A simulation model of a fluid power circuit is typically created using differential and algebraic equations. Efficient numerical methods are required since differential equations must be solved in real time. Unfortunately, simulation software packages offer only a limited selection of numerical solvers. Numerical problems cause noise to the results, which in many cases leads the simulation run to fail. Mathematically the fluid power circuit models are stiff systems of ordinary differential equations. Numerical solution of the stiff systems can be improved by two alternative approaches. The first is to develop numerical solvers suitable for solving stiff systems. The second is to decrease the model stiffness itself by introducing models and algorithms that either decrease the highest eigenvalues or neglect them by introducing steady-state solutions of the stiff parts of the models. The thesis proposes novel methods using the latter approach. The study aims to develop practical methods usable in dynamic simulation of fluid power circuits using explicit fixed-step integration algorithms. In this thesis, twomechanisms whichmake the systemstiff are studied. These are the pressure drop approaching zero in the turbulent orifice model and the volume approaching zero in the equation of pressure build-up. These are the critical areas to which alternative methods for modelling and numerical simulation are proposed. Generally, in hydraulic power transmission systems the orifice flow is clearly in the turbulent area. The flow becomes laminar as the pressure drop over the orifice approaches zero only in rare situations. These are e.g. when a valve is closed, or an actuator is driven against an end stopper, or external force makes actuator to switch its direction during operation. This means that in terms of accuracy, the description of laminar flow is not necessary. But, unfortunately, when a purely turbulent description of the orifice is used, numerical problems occur when the pressure drop comes close to zero since the first derivative of flow with respect to the pressure drop approaches infinity when the pressure drop approaches zero. Furthermore, the second derivative becomes discontinuous, which causes numerical noise and an infinitely small integration step when a variable step integrator is used. A numerically efficient model for the orifice flow is proposed using a cubic spline function to describe the flow in the laminar and transition areas. Parameters for the cubic spline function are selected such that its first derivative is equal to the first derivative of the pure turbulent orifice flow model in the boundary condition. In the dynamic simulation of fluid power circuits, a tradeoff exists between accuracy and calculation speed. This investigation is made for the two-regime flow orifice model. Especially inside of many types of valves, as well as between them, there exist very small volumes. The integration of pressures in small fluid volumes causes numerical problems in fluid power circuit simulation. Particularly in realtime simulation, these numerical problems are a great weakness. The system stiffness approaches infinity as the fluid volume approaches zero. If fixed step explicit algorithms for solving ordinary differential equations (ODE) are used, the system stability would easily be lost when integrating pressures in small volumes. To solve the problem caused by small fluid volumes, a pseudo-dynamic solver is proposed. Instead of integration of the pressure in a small volume, the pressure is solved as a steady-state pressure created in a separate cascade loop by numerical integration. The hydraulic capacitance V/Be of the parts of the circuit whose pressures are solved by the pseudo-dynamic method should be orders of magnitude smaller than that of those partswhose pressures are integrated. The key advantage of this novel method is that the numerical problems caused by the small volumes are completely avoided. Also, the method is freely applicable regardless of the integration routine applied. The superiority of both above-mentioned methods is that they are suited for use together with the semi-empirical modelling method which necessarily does not require any geometrical data of the valves and actuators to be modelled. In this modelling method, most of the needed component information can be taken from the manufacturer’s nominal graphs. This thesis introduces the methods and shows several numerical examples to demonstrate how the proposed methods improve the dynamic simulation of various hydraulic circuits.

From Fluid Dynamics to Human Psychology.What Drives Financial Markets Towards Extreme Events

For decades researchers have been trying to build models that would help understand price performance in financial markets and, therefore, to be able to forecast future prices. However, any econometric approaches have notoriously failed in predicting extreme events in markets. At the end of 20th century, market specialists started to admit that the reasons for economy meltdowns may originate as much in rational actions of traders as in human psychology. The latter forces have been described as trading biases, also known as animal spirits. This study aims at expressing in mathematical form some of the basic trading biases as well as the idea of market momentum and, therefore, reconstructing the dynamics of prices in financial markets. It is proposed through a novel family of models originating in population and fluid dynamics, applied to an electricity spot price time series. The main goal of this work is to investigate via numerical solutions how well theequations succeed in reproducing the real market time series properties, especially those that seemingly contradict standard assumptions of neoclassical economic theory, in particular the Efficient Market Hypothesis. The results show that the proposed model is able to generate price realizations that closely reproduce the behaviour and statistics of the original electricity spot price. That is achieved in all price levels, from small and medium-range variations to price spikes. The latter were generated from price dynamics and market momentum, without superimposing jump processes in the model. In the light of the presented results, it seems that the latest assumptions about human psychology and market momentum ruling market dynamics may be true. Therefore, other commodity markets should be analyzed with this model as well.

Application of Computational Fluid Dynamics in Modeling Blood Flow in Human Thoracic Aorta

The aim of this study was to simulate blood flow in thoracic human aorta and understand the role of flow dynamics in the initialization and localization of atherosclerotic plaque in human thoracic aorta. The blood flow dynamics in idealized and realistic models of human thoracic aorta were numerically simulated in three idealized and two realistic thoracic aorta models. The idealized models of thoracic aorta were reconstructed with measurements available from literature, and the realistic models of thoracic aorta were constructed by image processing Computed Tomographic (CT) images. The CT images were made available by South Karelia Central Hospital in Lappeenranta. The reconstruction of thoracic aorta consisted of operations, such as contrast adjustment, image segmentations, and 3D surface rendering. Additional design operations were performed to make the aorta model compatible for the numerical method based computer code. The image processing and design operations were performed with specialized medical image processing software. Pulsatile pressure and velocity boundary conditions were deployed as inlet boundary conditions. The blood flow was assumed homogeneous and incompressible. The blood was assumed to be a Newtonian fluid. The simulations with idealized models of thoracic aorta were carried out with Finite Element Method based computer code, while the simulations with realistic models of thoracic aorta were carried out with Finite Volume Method based computer code. Simulations were carried out for four cardiac cycles. The distribution of flow, pressure and Wall Shear Stress (WSS) observed during the fourth cardiac cycle were extensively analyzed. The aim of carrying out the simulations with idealized model was to get an estimate of flow dynamics in a realistic aorta model. The motive behind the choice of three aorta models with distinct features was to understand the dependence of flow dynamics on aorta anatomy. Highly disturbed and nonuniform distribution of velocity and WSS was observed in aortic arch, near brachiocephalic, left common artery, and left subclavian artery. On the other hand, the WSS profiles at the roots of branches show significant differences with geometry variation of aorta and branches. The comparison of instantaneous WSS profiles revealed that the model with straight branching arteries had relatively lower WSS compared to that in the aorta model with curved branches. In addition to this, significant differences were observed in the spatial and temporal profiles of WSS, flow, and pressure. The study with idealized model was extended to study blood flow in thoracic aorta under the effects of hypertension and hypotension. One of the idealized aorta models was modified along with the boundary conditions to mimic the thoracic aorta under the effects of hypertension and hypotension. The results of simulations with realistic models extracted from CT scans demonstrated more realistic flow dynamics than that in the idealized models. During systole, the velocity in ascending aorta was skewed towards the outer wall of aortic arch. The flow develops secondary flow patterns as it moves downstream towards aortic arch. Unlike idealized models, the distribution of flow was nonplanar and heavily guided by the artery anatomy. Flow cavitation was observed in the aorta model which was imaged giving longer branches. This could not be properly observed in the model with imaging containing a shorter length for aortic branches. The flow circulation was also observed in the inner wall of the aortic arch. However, during the diastole, the flow profiles were almost flat and regular due the acceleration of flow at the inlet. The flow profiles were weakly turbulent during the flow reversal. The complex flow patterns caused a non-uniform distribution of WSS. High WSS was distributed at the junction of branches and aortic arch. Low WSS was distributed at the proximal part of the junction, while intermedium WSS was distributed in the distal part of the junction. The pulsatile nature of the inflow caused oscillating WSS at the branch entry region and inner curvature of aortic arch. Based on the WSS distribution in the realistic model, one of the aorta models was altered to induce artificial atherosclerotic plaque at the branch entry region and inner curvature of aortic arch. Atherosclerotic plaque causing 50% blockage of lumen was introduced in brachiocephalic artery, common carotid artery, left subclavian artery, and aortic arch. The aim of this part of the study was first to study the effect of stenosis on flow and WSS distribution, understand the effect of shape of atherosclerotic plaque on flow and WSS distribution, and finally to investigate the effect of lumen blockage severity on flow and WSS distributions. The results revealed that the distribution of WSS is significantly affected by plaque with mere 50% stenosis. The asymmetric shape of stenosis causes higher WSS in branching arteries than in the cases with symmetric plaque. The flow dynamics within thoracic aorta models has been extensively studied and reported here. The effects of pressure and arterial anatomy on the flow dynamic were investigated. The distribution of complex flow and WSS is correlated with the localization of atherosclerosis. With the available results we can conclude that the thoracic aorta, with complex anatomy is the most vulnerable artery for the localization and development of atherosclerosis. The flow dynamics and arterial anatomy play a role in the localization of atherosclerosis. The patient specific image based models can be used to diagnose the locations in the aorta vulnerable to the development of arterial diseases such as atherosclerosis.

Polycystic ovary syndrome: implications of metabolic dysfunction

OBJECTIVE: To determine the prevalence of metabolic syndrome (MS) and its clinical interrelations in polycystic ovary syndrome (PCOS).METHODS: This was a cross-sectional, prospective study with 100 patients with diagnosed PCOS based on the consensus of Rotterdam (2003). We investigated the interrelationships of MS, with intrinsic PCOS data. Dermatological profile was analyzed, in addition to acanthosis nigricans (AN) in the presence of hirsutism and acne. The use of HOMA-IR (homeostatic model assessment of insulin resistance) aimed at the correlation with MS in order to establish the metabolic dysfunction with the state of insulin resistance.RESULTS: The mean and standard deviations corresponding figures for age, body mass index and waist circumference were, respectively, 25.72 (± 4.87), 30.63 (± 9.31) and 92.09 (± 18.73). The prevalence of MS was 36% and significantly correlated with BMI, AN, and in 51% of patients the state of insulin resistance (HOMA-IR). Regarding skin profile, only AN significant correlation with MS.CONCLUSION: We propose the routine inspection of metabolic components related to severe PCOS. These parameters configure the cardiovascular risk and such conduct is of undoubted importance to public health.

Evaluation of common mental disorders in women with polycystic ovary syndrome and its relationship with body mass index

PURPOSE: To evaluate the prevalence of common mental disorders in women diagnosed with polycystic ovary syndrome as compared with paired controls without this syndrome. METHODS: Cross-sectional study with a Control Group examining women between the ages of 18 and 30 who did not use antidepressants and who sought the Gynecology Service of the researched sites. For every woman diagnosed with the polycystic ovary syndrome, another with the same age, educational status and presence or absence of sexual partners was sought without this diagnosis. In total, 166 patients agreed to participate, consisting of 95 diagnosed with polycystic ovary syndrome and 71 in the Control Group. The diagnosis of polycystic ovary syndrome was made by the presence of two from three criteria: oligomenorrhea or amenorrhea, clinical or biochemical hyperandrogenism and polycystic ovaries on transvaginal ultrasound, following exclusion of patients with Cushing's syndrome, congenital adrenal hyperplasia, and androgen-secreting tumors. Weight and height were measured to calculate the body mass index. The Self-Reporting Questionnaire, which evaluated 20 items, was used as an indicator of common mental disorders. A χ² analysis stratified by the category of body mass index was used to compare the prevalence of common mental disorders, between the groups of women with and without the polycystic ovary syndrome. RESULTS: There were no significant differences in age, education, presence of sexual partners, ethnicity, socioeconomic status, use of psychiatric medication, and search for consultation in mental health between the studied groups. The prevalence of obese women with indications of common mental disorders was significantly higher in women with polycystic ovary syndrome than in the Control Group. In the group with healthy body mass index, the incidence of common mental disorders was statistically significant different between women with polycystic ovary syndrome and normal controls (p=0.008). CONCLUSIONS: Women with diagnosis of this disease have an almost three-fold increased likelihood of common mental disorders as compared with those without polycystic ovary syndrome. Although obesity is often observed in polycystic ovary syndrome, even women with a healthy body mass index have an increased risk of psychiatric comorbidity.

Arterial hypertension and metabolic profile in patients with polycystic ovary syndrome

PURPOSE: To evaluate parameters related with arterial pressure and metabolic profile in women with polycystic ovary syndrome (POS). METHODS: This monocentric study at the University Hospital Endocrinology Section included 60 women aged 18-45 years, 42 being diagnosed with POS and acting as 18 controls. All women were subjected to transvaginal ultrasound and monitored for arterial pressure for 24 h in the ambulatory (MAP). Venous blood samples were taken between 07.00 and 09.00, after 12 h fasting. Basal (BG) and fasting glucose concentrations, total cholesterol and its fractions, triglycerides and insulin (to calculate the homeostatic assay insulin-resistance, HOMA-IR) were measured. Collected data were the mean arterial blood pressure (24-h awake/sleep cycle), arterial pressure nocturnal descensus, glycemia and fasting glucose for HOMA-IR, and lipid profile. The Student's t test was used to compare homogeneous variables; the Mann-Whitney test was used to compare non-homogeneous variables; the Pearson's correlation coefficient was used to search for correlation between the variables. The c² test was used for comparison of the absence of nocturnal descensus. Significance was taken as p<0.05. RESULTS: The mean age of the patients with POS was 27.4±5.5 (18-45 years, n=42) and the body mass index (BMI) was 30.2±6.5 kg/m² (18.3-54.9). In the Control Group, the mean age was 31.4±6.1 (18-45 years) and the BMI was 27.1±6.2 kg/m² (18.3-54.9, n=18). No difference in the metabolic parameters and insulin resistance was observed between the two groups. Comparison between these parameters and MAP showed that the only parameter with a correlation was the BMI, independent of the POS diagnosis. This was not seen in nocturnal descensus, which was uncorrelated with POS and any of the other studied parameters. CONCLUSION: POS women do not show higher arterial blood pressure, glycemia, HDL-col, TG, HOMA-IR and BMI compared to non-POS women. However, POS patients showed correlation between arterial pressure and BMI, suggesting that obesity is a primary factor involved in arterial pressure changes in these patients.

Predictors of fluid intravasation during operative hysteroscopy: a preplanned prospective observational study with 200 cases

PURPOSE: To verify the predictors of intravasation rate during hysteroscopy.METHODS: Prospective observational study (Canadian Task Force classification II-1). All cases (n=200 women; 22 to 86 years old) were treated in an operating room setting. Considering respective bag overfill to calculate water balance, we tested two multiple linear regression models: one for total intravasation (mL) and the other for absorption rate (mL.min-1). The predictors tested (independent variables) were energy (mono/bipolar), tube patency (with/without tubal ligation), hysterometry (cm), age≤50 years, body surface area (m2), surgical complexity (with/without myomectomy) and duration (min).RESULTS: Mean intravasation was significantly higher when myomectomy was performed (442±616 versus 223±332 mL; p<0.01). In the proposed multiple linear regression models for total intravasation (adjusted R2=0.44; p<0.01), the only significant predictors were myomectomy and duration (p<0.01).In the proposed model for intravasation rate (R2=0.39; p<0.01), only myomectomy and hysterometry were significant predictors (p=0.02 and p<0.01, respectively).CONCLUSIONS: Not only myomectomy but also hysterometry were significant predictors of intravasation rate during operative hysteroscopy.

Peritoneal fluid changes in horses subjected to small colon distension

Intestinal devitalization in cases of small colon obstruction may be difficult to detect based only in clinical signs. The purpose was to serially evaluate blood and peritoneal fluid of horses subjected to small colon distension. Seventeen adult horses were allotted in three groups. In the small colon-distended group (DG, n=7) a surgically-implanted latex balloon was inflated to promote intraluminal small colon distension. In the shamoperated group (SG, n=5), the balloon was implanted but not inflated, and no surgery was done in the control group (CG, n=5). Blood and peritoneal fluid were sampled before and after (6 samples with a 30-minute interval) intestinal obstruction for cytological and biochemical analyses. No significant changes in clinical signs occurred within groups or across time during the experimental period. There were no statistical differences among SG and SG groups in hematologic and blood chemistry variables. Although total protein concentration and lactate dehydrogenase (LDH) activity in peritoneal fluid remained most of the time within reference values during the experimental period in all groups, increases from baseline values were detected in SG and DG groups. Such increases occurred earlier, progressively and with greater magnitude in the DG when compared with the SG (P<0.05). Increases from baselines values were also observed in total nucleated cells and neutrophils counts in the DG (P<0.05). In conclusion, distension of the equine small colon induced progressive subtle increases in total protein and LDH concentrations in the peritoneal fluid during the first hours. Serial evaluation of these variables in peritoneal fluid may be useful for early detection of intestinal devitalization in clinical cases of equine small colon obstruction.

Progesterone and Follicle Stimulating Hormone interact and promote goat preantral follicles survival and development in vitro

We investigated the effects of progesterone and follicle stimulating hormone (FSH) on survival and growth of caprine preantral follicles. Pieces of ovarian tissue were cultured for 1 or 7 days in minimum essential medium (MEM) alone or containing progesterone (1, 2.5, 5, 10 or 20ng/mL), FSH (50ng/mL) or the interaction between progesterone and FSH. Fresh (non-cultured control) and cultured ovarian tissues were processed for histological and ultrastructural studies. After 7 days the addition of FSH to all progesterone concentrations maintained the percentage of normal follicles similar to fresh control. At day 7 of culture, a higher percentage of developing follicles was observed only in 2.5ng/ml of progesterone associated with FSH or 10ng/ml of progesterone alone when compared with control. From day 1 to day 7 of culture, a significant increase in the percentage of developing follicles was observed in MEM and 2.5ng/ml of progesterone + FSH. In addition, after 7 days, in all treatments, there was a significant increase in follicular diameter when compared with control, except for MEM alone and in 5ng/ml of progesterone + FSH or 10ng/ml of progesterone alone. Ultrastructural studies confirmed follicular integrity after 7 days of culture in 2.5ng/ml of progesterone with FSH. In conclusion, this study demonstrated that the interaction between progesterone and FSH maintains ultrastructural integrity, stimulates primordial follicles activation and further growth of cultured caprine preantral follicles.

Enteral fluid therapy through nasogastric tube in rumen cannulated goats

This paper reports the effects of fluid therapy in goats through nasogastric route with an electrolyte solution composed by concentrations of sodium, potassium and chloride similar to goat plasma (140mmol/L of Na+, 4.5mmol/L of K+, 110mmol/L of Cl-). Four Alpine Chamoisee goats, two of them with evident leakage of the rumen cannulas, were used in a crossover experimental design of two periods and two groups. In one group the two goats were submitted to a treatment protocol to induce dehydration before the fluid therapy, whereas the other group was not. Fluid therapy consisted supplying 10mL/kg/h of the electrolyte solution during 8 hours. No signs of discomfort or stress were observed. The dehydration model employed caused a mild dehydration indicated by decrease in feces humidity, body weight and abdominal circumference, and increase in plasma total solids concentration. During fluid therapy globular volume and plasma total solids decreased, whereas % body weight and abdominal circumference increased. No signs of hyperhydration were observed and serum electrolytes (Na+, Cl-, K+) presented no significant alterations in both groups. Fluid therapy proposed in this study was efficient to treat dehydration, even for rumen cannulated animals with evident leakage, and can be administrated safely with no electrolyte imbalance.

Lactated Ringer's solution or 0.9% sodium chloride as fluid therapy in pigeons (Columba livia) submitted to humerus osteosynthesis

The study aimed to compare the effects of intraosseous infusion of lactated Ringer's and 0.9% sodium chloride solutions on the electrolytes and acid-base balance in pigeons submitted to humerus osteosynthesis. Eighteen pigeons were undergoing to isoflurane anesthesia by an avalvular circuit system. They were randomly assigned into two groups (n=9) receiving lactated Ringer's solution (LR) or 0.9% sodium chloride (SC), in a continuous infusion rate of 20mL/kg/h, by using an intraosseous catheter into the tibiotarsus during 60-minute anesthetic procedure. Heart rate (HR), and respiratory rate (RR) were measured every 10 min. Venous blood samples were collected at 0, 30 and 60 minutes to analyze blood pH, PvCO2, HCO3 -, Na+ and K+. Blood gases and electrolytes showed respiratory acidosis in both groups during induction, under physical restraint. This acidosis was evidenced by a decrease of pH since 0 min, associated with a compensatory response, observed by increasing of HCO3 - concentration, at 30 and 60 min. It was not observed any changes on Na+ and K+ serum concentrations. According to the results, there is no reason for choosing one of the two solutions, and it could be concluded that both fluid therapy solutions do not promote any impact on acid-base balance and electrolyte concentrations in pigeons submitted to humerus osteosynthesis.

Follicle and corpus luteum size and vascularity as predictors of fertility at the time of artificial insemination and embryo transfer in beef cattle

Abstract:Two ultrasound based fertility prediction methods were tested prior to embryo transfer (ET) and artificial insemination (AI) in cattle. Female bovines were submitted to estrous synchronization prior to ET and AI. Animals were scanned immediately before ET and AI procedure to target follicle and corpus luteum (CL) size and vascularity. In addition, inseminated animals were also scanned eleven days after insemination to target CL size and vascularity. All data was compared with fertility by using gestational diagnosis 35 days after ovulation. Prior to ET, CL vascularity showed a positive correlation with fertility, and no pregnancy occurred in animals with less than 40% of CL vascularity. Prior to AI and also eleven days after AI, no relationship with fertility was seen in all parameters analyzed (follicle and CL size and vascularity), and contrary, cows with CL vascularity greater than 70% exhibit lower fertility. In inseminated animals, follicle size and vascularity was positive related with CL size and vascularity, as shown by the presence of greater CL size and vascularity originated from follicle with also greater size and vascularity. This is the first time that ultrasound based fertility prediction methods were tested prior to ET and AI and showed an application in ET, but not in AI programs. Further studies are needed including hormone profile evaluation to improve conclusion.

Fluid dynamic modelling and simulation of circulating fluidized bed reactors: importance of the interface turbulence transfer

The main objective of this work is to analyze the importance of the gas-solid interface transfer of the kinetic energy of the turbulent motion on the accuracy of prediction of the fluid dynamic of Circulating Fluidized Bed (CFB) reactors. CFB reactors are used in a variety of industrial applications related to combustion, incineration and catalytic cracking. In this work a two-dimensional fluid dynamic model for gas-particle flow has been used to compute the porosity, the pressure, and the velocity fields of both phases in 2-D axisymmetrical cylindrical co-ordinates. The fluid dynamic model is based on the two fluid model approach in which both phases are considered to be continuous and fully interpenetrating. CFB processes are essentially turbulent. The model of effective stress on each phase is that of a Newtonian fluid, where the effective gas viscosity was calculated from the standard k-epsilon turbulence model and the transport coefficients of the particulate phase were calculated from the kinetic theory of granular flow (KTGF). This work shows that the turbulence transfer between the phases is very important for a better representation of the fluid dynamics of CFB reactors, especially for systems with internal recirculation and high gradients of particle concentration. Two systems with different characteristics were analyzed. The results were compared with experimental data available in the literature. The results were obtained by using a computer code developed by the authors. The finite volume method with collocated grid, the hybrid interpolation scheme, the false time step strategy and SIMPLEC (Semi-Implicit Method for Pressure Linked Equations - Consistent) algorithm were used to obtain the numerical solution.

Modeling of the Fluid-Structure Interaction in Inelastic Piping Systems

In many engineering applications, compliant piping systems conveying liquids are subjected to inelastic deformations due to severe pressure surges such as plastic tubes in modern water supply transmission lines and metallic pipings in nuclear power plants. In these cases the design of such systems may require an adequate modeling of the interactions between the fluid dynamics and the inelastic structural pipe motions. The reliability of the prediction of fluid-pipe behavior depends mainly on the adequacy of the constitutive equations employed in the analysis. In this paper it is proposed a systematic and general approach to consistently incorporate different kinds of inelastic behaviors of the pipe material in a fluid-structure interaction analysis. The main feature of the constitutive equations considered in this work is that a very simple numerical technique can be used for solving the coupled equations describing the dynamics of the fluid and pipe wall. Numerical examples concerning the analysis of polyethylene and stainless steel pipe networks are presented to illustrate the versatility of the proposed approach.