950 resultados para Constant-pressure conditions


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Here, we report on the first application of high-pressure XPS (HP-XPS) to the surface catalyzed selective oxidation of a hydrocarbon over palladium, wherein the reactivity of metal and oxide surfaces in directing the oxidative dehydrogenation of crotyl alcohol (CrOH) to crotonaldehyde (CrHCO) is evaluated. Crotonaldehyde formation is disfavored over Pd(111) under all reaction conditions, with only crotyl alcohol decomposition observed. In contrast, 2D Pd5O4 and 3D PdO overlayers are able to selectively oxidize crotyl alcohol (1 mTorr) to crotonaldehyde in the presence of co-fed oxygen (140 mTorr) at temperatures as low as 40 °C. However, 2D Pd5O4 ultrathin films are unstable toward reduction by the alcohol at ambient temperature, whereas the 3D PdO oxide is able to sustain catalytic crotonaldehyde production even up to 150 °C. Co-fed oxygen is essential to stabilize palladium surface oxides toward in situ reduction by crotyl alcohol, with stability increasing with oxide film dimensionality.

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Clogging is the main operational problem associated with horizontal subsurface flow constructed wetlands (HSSF CWs). The measurement of saturated hydraulic conductivity has proven to be a suitable technique to assess clogging within HSSF CWs. The vertical and horizontal distribution of hydraulic conductivity was assessed in two full-scale HSSF CWs by using two different in situ permeameter methods (falling head (FH) and constant head (CH) methods). Horizontal hydraulic conductivity profiles showed that both methods are correlated by a power function (FH= CH 0.7821, r 2=0.76) within the recorded range of hydraulic conductivities (0-70 m/day). However, the FH method provided lower values of hydraulic conductivity than the CH method (one to three times lower). Despite discrepancies between the magnitudes of reported readings, the relative distribution of clogging obtained via both methods was similar. Therefore, both methods are useful when exploring the general distribution of clogging and, specially, the assessment of clogged areas originated from preferential flow paths within full-scale HSSF CWs. Discrepancy between methods (either in magnitude and pattern) aroused from the vertical hydraulic conductivity profiles under highly clogged conditions. It is believed this can be attributed to procedural differences between the methods, such as the method of permeameter insertion (twisting versus hammering). Results from both methods suggest that clogging develops along the shortest distance between water input and output. Results also evidence that the design and maintenance of inlet distributors and outlet collectors appear to have a great influence on the pattern of clogging, and hence the asset lifetime of HSSF CWs. © Springer Science+Business Media B.V. 2011.

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The selective liquid phase hydrogenation of furfural to furfuryl alcohol over Pt nanoparticles supported on SiO2, ZnO, γ-Al2O3, CeO2 is reported under extremely mild conditions. Ambient hydrogen pressure, and temperatures as low as 50 °C are shown sufficient to drive furfural hydrogenation with high conversion and >99% selectivity to furfuryl alcohol. Strong support and solvent dependencies are observed, with methanol and n-butanol proving excellent solvents for promoting high furfuryl alcohol yields over uniformly dispersed 4 nm Pt nanoparticles over MgO, CeO2 and γ-Al2O3. In contrast, non-polar solvents conferred poor furfural conversion, while ethanol favored acetal by-product formation. Furfural selective hydrogenation can be tuned through controlling the oxide support, reaction solvent and temperature.

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This study experimentally investigated methyl chloride (MeCl) purification method using an inhouse designed and built volumetric adsorption/desorption rig. MeCl is an essential raw material in the manufacture of silicone however all technical grades of MeCl contain concentrations (0.2 - 1.0 % wt) of dimethyl ether (DME) which poison the process. The project industrial partner had previously exhausted numerous separation methods, which all have been deemed not suitable for various reasons. Therefore, adsorption/desorption separation was proposed in this study as a potential solution with less economic and environmental impact. Pure component adsorption/desorption was carried out for DME and MeCl on six different adsorbents namely: zeolite molecular sieves (types 4 Å and 5 Å); silica gels (35-70 mesh, amorphous precipitated, and 35-60 mesh) and granular activated carbon (type 8-12 mesh). Subsequent binary gas mixture adsorption in batch and continuous mode was carried out on both zeolites and all three silica gels following thermal pre-treatment in vacuum. The adsorbents were tested as received and after being subjected to different thermal and vacuum pre-treatment conditions. The various adsorption studies were carried out at low pressure and temperature ranges of 0.5 - 3.5 atm and 20 - 100 °C. All adsorbents were characterised using Brunauer Emmett Teller (BET), thermogravimetric analysis (TGA), scanning electron microscopy (SEM) and energy dispersive x-ray analysis (EDXA) to investigate their physical and chemical properties. The well-known helium (He) expansion method was used to determine the empty manifold and adsorption cell (AC) regions and respective void volumes for the different adsorbents. The amounts adsorbed were determined using Ideal gas laws via the differential pressure method. The heat of adsorption for the various adsorbate-adsorbent (A-S) interactions was calculated using a new calorimetric method based on direct temperature measurements inside the AC. Further adsorption analysis included use of various empirical and kinetic models to determine and understand the behaviour of the respective interactions. The gas purification behaviour was investigated using gas chromatography and mass spectroscopy (GC-MC) analysis. Binary gas mixture samples were syringed from the manifold iii and AC outlet before and after adsorption/desorption analysis through manual sample injections into the GC-MS to detect and quantify the presence of DME and ultimately observe for methyl chloride purification. Convincing gas purification behaviour was confirmed using two different GC columns, thus giving more confidence on the measurement reliability. From the single pure component adsorption of DME and MeCl on the as received zeolite 4A subjected to 1 h vacuum pre-treatment, both gases exhibited pseudo second order adsorption kinetics with DME exhibiting a rate constant nearly double that of MeCl thus suggesting a faster rate of adsorption. From the adsorption isotherm classification both DME and MeCl exhibited Type II and I adsorption isotherm classifications, respectively. The strength of bonding was confirmed by the differential heat of adsorption measurement, which was found to be 23.30 and 10.21 kJ mol-1 for DME and MeCl, respectively. The former is believed to adsorb heterogeneously through hydrogen bonding whilst MeCl adsorbs homogenously via van der Waal’s (VDW) forces. Single pure component adsorption on as received zeolite 5A, silica gels (35-70, amorphous precipitated and 35-60) resulted in similar adsorption/desorption behaviour in similar quantities (mol kg-1). The adsorption isotherms for DME and MeCl on zeolite 5A, silica gels (35-70, amorphous precipitated and 35-60) and activated carbon 8-12 exhibited Type I classifications, respectively. Experiments on zeolite 5A indicated that DME adsorbed stronger, faster and with a slightly stronger strength of interaction than MeCl but in lesser quantities. On the silica gels adsorbents, DME exhibited a slightly greater adsorption capacity whilst adsorbing at a similar rate and strength of interaction compared to MeCl. On the activated carbon adsorbent, MeCl exhibited the greater adsorption capacity at a faster rate but with similar heats of adsorption. The effect of prolonged vacuum (15 h), thermal pre-treatment (150 °C) and extended equilibrium time (15 min) were investigated for the adsorption behaviour of DME and MeCl on both zeolites 4A and 5A, respectively. Compared to adsorption on as received adsorbents subjected to 1 h vacuum the adsorption capacities for DME and MeCl were found to increase by 1.95 % and 20.37 % on zeolite 4A and by 4.52 % and 6.69 % on zeolite 5A, respectively. In addition the empirical and kinetic models and differential heats of adsorption resulted in more definitive fitting curves and trends due to the true equilibrium position of the adsorbate with the adsorbent. Batch binary mixture adsorption on thermally and vacuum pre-treated zeolite 4A demonstrated purification behaviour of all adsorbents used for MeCl streams containing DME impurities, with a concentration as low as 0.66 vol. %. The GC-MS analysis showed no DME detection for the tested concentration mixtures at the AC outlet after 15 or 30 min, whereas MeCl was detectable in measurable amounts. Similar behaviour was also observed when carrying out adsorption in continuous mode. On the other hand, similar studies on the other adsorbents did not show such favourable MeCl purification behaviour. Overall this study investigated a wide range of adsorbents (zeolites, silica gels and activated carbon) and demonstrated for the first time potential to purify MeCl streams containing DME impurities using adsorption/desorption separation under different adsorbent pre-treatment and adsorption operating conditions. The study also revealed for the first time the adsorption isotherms, empirical and kinetic models and heats of adsorption for the respective adsorbentsurface (A-S) interactions. In conclusion, this study has shown strong evidence to propose zeolite 4A for adsorptive purification of MeCl. It is believed that with a technical grade MeCl stream competitive yet simultaneous co-adsorption of DME and MeCl occurs with evidence of molecular sieiving effects whereby the larger DME molecules are unable to penetrate through the adsorbent bed whereas the smaller MeCl molecules diffuse through resulting in a purified MeCl stream at the AC outlet. Ultimately, further studies are recommended for increased adsorption capacities by considering wider operating conditions, e.g. different adsorbent thermal and vacuum pre-treatment and adsorbing at temperatures closer to the boiling point of the gases and different conditions of pressure and temperature.

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Vapor phase carbon adsorption systems are used to remove aromatics, aliphatics, and halogenated hydrocarbons. The adsorption capacity of granular activated carbon is reduced when environmental parameters (temperature, pressure, and humidity) interfere with homogeneous surface diffusion and pore distribution dynamics. The purpose of this study was to investigate the effects of parametric uncertainties in adsorption efficiency. ^ Modified versions of the Langmuir isotherm in conjunction with thermodynamic equations described gaseous adsorption of single component influent onto microporous media. Experimental test results derived from Wang et al. (1999) simulated adsorption kinetics while the Myer and monsoon Langmuir constant accounted for isothermal gas compression and energetic heterogeneity under thermodynamic equilibrium conditions. Responsiveness of adsorption capacity to environmental uncertainties was analyzed by statistical sensitivity and modeled by breakthrough curves. Results indicated that extensive fluctuations in adsorption capacity significantly reduced carbon consumption while isothermal variations had a pronounced effect on saturation capacity. ^

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Materials known as Mn+1AXn phases, where n is 1, 2, or 3, and M represents an early transition metal, A an A-group element, and X is either Carbon and/or Nitrogen [1], are fast becoming technologically important materials due to the interesting combination of unique properties. However, a lot of important information about the high temperature and high pressure behavior of many of these compounds is still missing, which needs to be determined systematically. ^ In this dissertation the synthesis of M2AC (M = Ti, V, Cr, Nb, Zr) and A = (Al, Sn, S) compounds by arc melting, vacuum sintering and piston cylinder synthesis is presented along with the synthesis of Zr 2SC, which has been synthesized for first time in bulk form, by piston cylinder technique. The microstructural analysis by electron microscopy and phase analysis by x-ray diffraction is presented next. Finally, a critical analysis of the behavior of these compounds under the application of extreme pressure (as high as 50 GPa) and temperature (≈ 1000°C) is presented. ^ The high pressure studies, up to 50 GPa, showed that these compounds were structurally intact and their bulk moduli ranged from 140 to 190 GPa. The high temperature studies in the inert atmosphere showed that the M 2SnC compounds were unstable above 650°C and the expansion along the a-axis was higher than that along the c-axis, unlike the other phases. M2SC compounds on the other hand showed negligible difference in the thermal expansion along the two axes. The oxidation study revealed that Ti2AC (Al, S) compounds had highest resistance to oxidation while the M2SnC compounds had the least. Furthermore, from the oxidation study of these compounds, which were short time oxidation experiments, it was found that all of these compounds oxidized to their respective binary oxides. ^

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Most research on stock prices is based on the present value model or the more general consumption-based model. When applied to real economic data, both of them are found unable to account for both the stock price level and its volatility. Three essays here attempt to both build a more realistic model, and to check whether there is still room for bubbles in explaining fluctuations in stock prices. In the second chapter, several innovations are simultaneously incorporated into the traditional present value model in order to produce more accurate model-based fundamental prices. These innovations comprise replacing with broad dividends the more narrow traditional dividends that are more commonly used, a nonlinear artificial neural network (ANN) forecasting procedure for these broad dividends instead of the more common linear forecasting models for narrow traditional dividends, and a stochastic discount rate in place of the constant discount rate. Empirical results show that the model described above predicts fundamental prices better, compared with alternative models using linear forecasting process, narrow dividends, or a constant discount factor. Nonetheless, actual prices are still largely detached from fundamental prices. The bubblelike deviations are found to coincide with business cycles. The third chapter examines possible cointegration of stock prices with fundamentals and non-fundamentals. The output gap is introduced to form the nonfundamental part of stock prices. I use a trivariate Vector Autoregression (TVAR) model and a single equation model to run cointegration tests between these three variables. Neither of the cointegration tests shows strong evidence of explosive behavior in the DJIA and S&P 500 data. Then, I applied a sup augmented Dickey-Fuller test to check for the existence of periodically collapsing bubbles in stock prices. Such bubbles are found in S&P data during the late 1990s. Employing econometric tests from the third chapter, I continue in the fourth chapter to examine whether bubbles exist in stock prices of conventional economic sectors on the New York Stock Exchange. The ‘old economy’ as a whole is not found to have bubbles. But, periodically collapsing bubbles are found in Material and Telecommunication Services sectors, and the Real Estate industry group.

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Group VI metal hexacarbonyls, M(CO)6 (M = Cr, Mo and W), are of extreme importance as catalysts in industry and also of fundamental interest due to the established charge transfer mechanism between the carbon monoxide and the metal. They condense to molecular solids at ambient conditions retaining the octahedral (Oh) symmetry of gas phase and have been extensively investigated by previous workers to understand their fundamental chemical bonding and possible industrial applications. However little is known about their behavior at high pressures which is the focus of this dissertation. Metal hexacarbonyls were subjected to high pressures in Diamond-Anvil cells to understand the pressure effect on chemical bonding using Raman scattering in situ. The high-pressure results on each of the three metal hexacarbonyls are presented and are followed by a critical analysis of the entire family. The Raman study was conducted at pressures up to 45 GPa and X-ray up to 58 GPa. This is followed by a discussion on infra red spectra in conjunction with Raman and X-ray analysis to provide a rationale for polymerization. Finally the probable synthesis of extremely reactive species under high-pressures and as identified via Raman is discussed. The high-pressure Raman scattering, up to 30 GPa, demonstrated the absence of Π-backbonding. The disappearance of parental Raman spectra for (M = Cr, Mo and W) at 29.6, 23.3 and 22.2 GPa respectively was attributed to the total collapse of the Oh symmetry. This collapse under high-pressure lead to metal-mediated polymeric phase characterized by Raman active δ(OCO) feature, originating from intermolecular vibrational coupling in the parent sample. Further increase in pressures up to 45 GPa, did not affect this feature. The pressure quenched Raman spectra, revealed various chemical groups non-characteristic of the parent sample and adsorption of CO in addition to the characteristic δ(OCO) feature. The thus recorded Raman, complemented with the far and mid-infrared pressure quenched spectra, reveal the formation of novel metal-mediated polymers. The X-ray diffraction on W(CO)6 up to 58 GPa revealed the generation of amorphous polymeric pattern which was retained back to ambient conditions.

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The Earth's upper mantle, mainly composed of olivine, is seismically anisotropic. Seismic anisotropy attenuation has been observed at 220km depth. Karato et al. (1992) attributed this attenuation to a transition between two deformation mechanisms, from dislocation creep above 220km to diffusion creep below 220km, induced by a change in water content. Couvy (2005) and Mainprice et al. (2005) predicted a change in Lattice Preferred Orientation induced by pressure, which comes from a change of slip system, from [100] slip to [001] slip, and is responsible for the seismic anisotropy attenuation. Raterron et al. (2007) ran single crystal deformation experiments under anhydrous conditions and observed that the slip system transition occurs around 8GPa, which corresponds to a depth of 260Km. Experiments were done to quantify the effects of water on olivine single crystals deformed using D-DIA press and synchrotron beam. Deformations were carried out in uniaxial compression along [110]c, [011]c, and [101]c, crystallographic directions, at pressure ranging from 4 to 8GPa and temperature between 1373 and 1473K. Talc sleeves about the annulus of the single crystals were used as source of water in the assembly. Stress and specimen strain rates were calculated by in-situ X-ray diffraction and time resolved imaging, respectively. By direct comparison of single crystals strain rates, we observed that [110]c deforms faster than [011]c below 5GPa. However above 6GPa [011]c deforms faster than [110]c. This revealed that [100](010) is the dominant slip system below 5GPa, and above 6GPa [001](010) becomes dominant. According to our results, the slip system transition, which is induced by pressure, occurs at 6GPa. Water influences the pressure where the switch over occurs, by lowering the transition pressure. The pressure effect on the slip systems activity has been quantified and the hydrolytic weakening has also been estimated for both orientations. Data also shows that temperature affects the slip system activity. The regional variation of the depth for the seismic anisotropy attenuation, which would depend on local hydroxyl content and temperature variations and explains the seismic anisotropy attenuation occurring at about 220Km depth in the mantle, where the pressure is about 6GPa. Deformation of MgO single crystal oriented [100], [110] and [111] were also performed. The results predict a change in the slip system activity at 23GPa, again induced by pressure. This explains the seismic anisotropy observed in the lower mantle.

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Transition metals (Ti, Zr, Hf, Mo, W, V, Nb, Ta, Pd, Pt, Cu, Ag, and Au) are essential building units of many materials and have important industrial applications. Therefore, it is important to understand their thermal and physical behavior when they are subjected to extreme conditions of pressure and temperature. This dissertation presents: • An improved experimental technique to use lasers for the measurement of thermal conductivity of materials under conditions of very high pressure (P, up to 50 GPa) and temperature (T up to 2500 K). • An experimental study of the phase relationship and physical properties of selected transition metals, which revealed new and unexpected physical effects of thermal conductivity in Zr, and Hf under high P-T. • New phase diagrams created for Hf, Ti and Zr from experimental data. • P-T dependence of the lattice parameters in α-hafnium. Contrary to prior reports, the α-ω phase transition in hafnium has a negative dT/dP slope. • New data on thermodynamic and physical properties of several transition metals and their respective high P-T phase diagrams. • First complete thermodynamic database for solid phases of 13 common transition metals was created. This database has: All the thermochemical data on these elements in their standard state (mostly available and compiled); All the equations of state (EoS) formulated from pressure-volume-temperature data (measured as a part of this study and from literature); Complete thermodynamic data for selected elements from standard to extreme conditions. The thermodynamic database provided by this study can be used with available thermodynamic software to calculate all thermophysical properties and phase diagrams at high P-T conditions. For readers who do not have access to this software, tabulated values of all thermodynamic and volume data for the 13 metals at high P-T are included in the APPENDIX. In the APPENDIX, a description of several other high-pressure studies of selected oxide systems is also included. Thermophysical properties (Cp, H, S, G) of the high P-T ω-phase of Ti, Zr and Hf were determined during the optimization of the EoS parameters and are presented in this study for the first time. These results should have important implications in understanding hexagonal-close-packed to simple-hexagonal phase transitions in transition metals and other materials.

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There is an increasing demand for DNA analysis because of the sensitivity of the method and the ability to uniquely identify and distinguish individuals with a high degree of certainty. But this demand has led to huge backlogs in evidence lockers since the current DNA extraction protocols require long processing time. The DNA analysis procedure becomes more complicated when analyzing sexual assault casework samples where the evidence contains more than one contributor. Additional processing to separate different cell types in order to simplify the final data interpretation further contributes to the existing cumbersome protocols. The goal of the present project is to develop a rapid and efficient extraction method that permits selective digestion of mixtures. ^ Selective recovery of male DNA was achieved with as little as 15 minutes lysis time upon exposure to high pressure under alkaline conditions. Pressure cycling technology (PCT) is carried out in a barocycler that has a small footprint and is semi-automated. Typically less than 10% male DNA is recovered using the standard extraction protocol for rape kits, almost seven times more male DNA was recovered from swabs using this novel method. Various parameters including instrument setting and buffer composition were optimized to achieve selective recovery of sperm DNA. Some developmental validation studies were also done to determine the efficiency of this method in processing samples exposed to various conditions that can affect the quality of the extraction and the final DNA profile. ^ Easy to use interface, minimal manual interference and the ability to achieve high yields with simple reagents in a relatively short time make this an ideal method for potential application in analyzing sexual assault samples.^

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Most research on stock prices is based on the present value model or the more general consumption-based model. When applied to real economic data, both of them are found unable to account for both the stock price level and its volatility. Three essays here attempt to both build a more realistic model, and to check whether there is still room for bubbles in explaining fluctuations in stock prices. In the second chapter, several innovations are simultaneously incorporated into the traditional present value model in order to produce more accurate model-based fundamental prices. These innovations comprise replacing with broad dividends the more narrow traditional dividends that are more commonly used, a nonlinear artificial neural network (ANN) forecasting procedure for these broad dividends instead of the more common linear forecasting models for narrow traditional dividends, and a stochastic discount rate in place of the constant discount rate. Empirical results show that the model described above predicts fundamental prices better, compared with alternative models using linear forecasting process, narrow dividends, or a constant discount factor. Nonetheless, actual prices are still largely detached from fundamental prices. The bubble-like deviations are found to coincide with business cycles. The third chapter examines possible cointegration of stock prices with fundamentals and non-fundamentals. The output gap is introduced to form the non-fundamental part of stock prices. I use a trivariate Vector Autoregression (TVAR) model and a single equation model to run cointegration tests between these three variables. Neither of the cointegration tests shows strong evidence of explosive behavior in the DJIA and S&P 500 data. Then, I applied a sup augmented Dickey-Fuller test to check for the existence of periodically collapsing bubbles in stock prices. Such bubbles are found in S&P data during the late 1990s. Employing econometric tests from the third chapter, I continue in the fourth chapter to examine whether bubbles exist in stock prices of conventional economic sectors on the New York Stock Exchange. The ‘old economy’ as a whole is not found to have bubbles. But, periodically collapsing bubbles are found in Material and Telecommunication Services sectors, and the Real Estate industry group.

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A pilot scale multi-media filtration system was used to evaluate the effectiveness of filtration in removing petroleum hydrocarbons from a source water contaminated with diesel fuel. Source water was artificially prepared by mixing bentonite clay and tap water to produce a turbidity range of 10-15 NTU. Diesel fuel concentrations of 150 ppm or 750 ppm were used to contaminate the source water. The coagulants used included Cat Floc K-10 and Cat Floc T-2. The experimental phase was conducted under direct filtration conditions at constant head and constant rate filtration at 8.0 gpm. Filtration experiments were run until the filter reached its clogging point as noted by a measured peak pressure loss of 10 psi. The experimental variables include type of coagulant, oil concentration and source water. Filtration results were evaluated based on turbidity removal and petroleum hydrocarbon (PHC) removal efficiency as measured by gas chromatography. Experiments indicated that clogging was controlled by the clay loading on the filter and that inadequate destabilization of the contaminated water by the coagulant limited the PHC removal. ^

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The Rio San Juan Complex is an important occurrence of high pressure/low temperature rocks in the circum-Caribbean region which contains both coherent blueschist units and two varieties of melange in the same area. The melanges contain a diverse assemblage of blocks of various sizes, different degrees of metamorphism, and mineral assemblages. Some high pressure blocks show two stages of metamorphism. The earliest stage is characterized by high pressure-low temperature conditions and the second stage is characterized by high pressure-lower temperature conditions. The geochemistry of thirteen samples from the Rio San Juan Complex has been studied and data have been compared with rocks of adjacent regions. Geochemical evidence indicates that rocks from the Rio San Juan Complex have predominant calc-alkaline affinities with subordinate tholeiitic affinities. This suggests that they have a multiple tectonic provenance.

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The coccolithophore Emiliania huxleyi was cultured under a broad range of carbonate chemistry conditions to distinguish the effects of individual carbonate system parameters on growth, primary production, and calcification. In the first experiment, alkalinity was kept constant and the fugacity of CO2(fCO2) varied from 2 to 600 Pa (1Pa ~ 10 µatm). In the second experiment, pH was kept constant (pHfree = 8) with fCO2 varying from 4 to 370 Pa. Results of the constant-alkalinity approach revealed physiological optima for growth, calcification, and organic carbon production at fCO2 values of ~20Pa, ~40 Pa, and ~80 Pa, respectively. Comparing this with the constant-pH approach showed that growth and organic carbon production increased similarly from low to intermediate CO2 levels but started to diverge towards higher CO2 levels. In the high CO2 range, growth rates and organic carbon production decreased steadily with declining pH at constant alkalinity while remaining consistently higher at constant pH. This suggests that growth and organic carbon production rates are directly related to CO2 at low (sub-saturating) concentrations, whereas towards higher CO2 levels they are adversely affected by the associated decrease in pH. A pH dependence at high fCO2 is also indicated for calcification rates, while the key carbonate system parameter determining calcification at low fCO2 remains unclear. These results imply that key metabolic processes in coccolithophores have their optima at different carbonate chemistry conditions and are influenced by different parameters of the carbonate system at both sides of the optimum.