Monte Carlo simulation and theory are used to calculate excess thermodynamic properties of binary mixtures of Lennard-Jones chains. Chainlike molecules are formed by Lennard-Jones spherical sites that are tangentially bonded. This molecular model accounts explictly for the most important microscopic features of real chainlike molecules, such as n-alkanes: repulsive and attractive forces between chemical groups and the connectivity of segments to make up the chain. A version of the statistical associating fluid theory, the so-called Soft - SAFT equationofstate, is used to check the theory’s ability to predict this kind of property. Predictions from the theory are directly compared to NPT Monte Carlo simulation results obtained in the present work. The influence of segment size, dispersive energy, and chain length on excess properties is studied using simulation and theory, and results are analyzed and discussed. The equationofstate is then used to predict the general trends of some excess thermodynamic properties of real n-alkane binary mixtures, such as excess volumes and heats. In particular, the temperature and chain-length dependence of these properties is studied. The Soft - SAFT theory is found to be able to correctly describe the most important features of excess thermodynamic properties of n-alkane models.
i = 1, NC (19) where is the fugacity of component i at equilibrium, and and represents the mole fraction and fugacity coefficient of component i in phase j. Fugacity coefficients of any com- ponent in the mixture are obtained by means of an equationofstate. In this work, the GC- EoS model was applied to calculate the fugacity coefficients of all fluid phases. In case of solid-fluid equilibria, we follow the subcooled liquid reference state approach  assum- ing a pure solid phase for the heavy compound ( ). For ILs treated in this work, many of the melting information to precisely evaluate the solid fugacity are not available. Up to our knowledge, no data about the heat capacity is avaible in open literature. With respect to density, experimental data of liquid [Amim][Cl] and solid [C 2 mim][Cl] has been reported
Nowadays, the use of clean solvents is essential for the extraction of natural products with the objective of decreasing the emissions of harmful compounds to humans and the environment. Current regulations have continually diminished the use of Volatile Organic Compounds (VOCs), as some have high toxicity levels, irritation and cancerinogenic effects, while others cause high environmental impacts such as ozone-depletion, global warming and environmental persistence(Kislik, 2011). One alternative that has gained reputation in the past decades is the substitution of hazardous solvents by environment-friendly and non-toxic ones, such as water, carbon dioxide and glycerol. To achieve extraction capacities equivalent with organic solvents, these solvents are coupled with new extraction techniques such as supercritical fluid extraction (SFE), microwave-assisted extraction (MAE), pressurized liquid extraction (PLE) and pressurized hot water extraction (PHWE), which have been thoroughly described in earlier reviews (Azmir et al., 2013; del Valle & de la Fuente, 2006; Plaza & Turner, 2015; Routray & Orsat, 2011; Teo, Tan, Yong, Hew, & Ong, 2010; Wang & Weller, 2006).
Adsorption tests of gas molecules on the measuring-cell walls or the sinker surface were carried out for the latest, now published measurements made with the single-sinker densimeter used in this work [17, 24]. Richter and Kleinrahm reported recently that due to sorption effects the composition of the measured gas could be modified inside the cell and significant errors up to about 0.1 % in density measurements could occur . However, according to the experimental procedure followed with the single-sinker densimeter, in which the cell is evacuated after each isotherm, the differences observed in the trend of the relative deviation in density from the GERG-2008 equationofstate along the period of recording an isotherm are one order of magnitude lower than the uncertainty in density at the working pressure.
We study the dynamics of homogeneous, isotropic universes which are governed by the Eddington- inspired alternative theory of gravity which has a single extra parameter, . Previous results showing singularity-avoiding behavior for > 0 are found to be upheld in the case of domination by a perfect fluid with equationofstate parameter w > 0. The range 1 3 < w < 0 is found to lead to universes which experience unbounded expansion rates while still at a finite density. In the case < 0 the addition of spatial curvature is shown to lead to the possibility of oscillation between two finite densities. Domination by a scalar field with an exponential potential is found to also lead to singularity-avoiding behavior when > 0. Certain values of the parameters governing the potential lead to behavior in which the expansion rate of the universe changes sign several times before transitioning to regular general relativity-like behavior.
We next proceed to investigate the vapor–liquid proper- ties of some branched chains with attractive interactions at the mean-field level of van der Waals. Figure 7 共 a 兲 shows the coexistence diagram of four different molecules, two linear 共 solid lines 兲 , and two branched chains with one articulation point 共 dashed lines 兲 . The molecular architecture of these molecules is shown in Fig. 3. The coexisting curves at low temperatures correspond to isomeric molecules formed by four segments and those at higher temperatures to isomers with five beads. In this figure we have only considered the upper region of the vapor–liquid phase diagram of the sys- tems studied, where the differences between the coexisting properties are larger. As can be observed, the main effect of the presence of one articulation point in the chain on the upper region of the coexistence diagram is to decrease the critical temperature and density with respect to the corre- sponding values for linear isomers. This behavior, predicted by the SAFT-B equationofstate, which is also observed in real systems such as branched alkanes of low molecular weight, 47 can be explained by taking into account the results obtained for the compressibility factor of linear and branched chains. Since the mean-field free-energy contribution at a given packing fraction is the same for any isomer, the differ- ences between the phase behavior of both systems can be attributed to the difference in the equationofstate corre- sponding to the hard sphere reference fluid. In particular, the lower value of the critical temperature of branched chains 共 compared to that of linear molecules 兲 is a direct conse- quence of a higher value for the compressibility factor of branched chains with respect to that of linear molecules at low densities.
of resources such as oil and coal at long-term, in the past decades natural gas-like mixtures, as biogas, have been arise as a possible alternative . In order to continue contributing to its implementation, it is necessary to improve the thermodynamic models used for the calculation and design of the extraction, transportation, storage and distribution systems of biogas-like mixtures. Therefore, the motivation for this research focuses on discussing the scope of the accuracy of the standard equationofstate, EoS GERG-2008, compared with measurements of the speed of sound through a biogas sample and with the thermodynamic properties (heat capacities) derived from these data; as well as provide new accurate experimental results so that, if the scientific community consider appropriate, it can be made new correlations to improve the model.
Roselle (Hibiscus sabdariffa L.) also called roselle fruit or flower of jamaica is a plant used in the traditional medicine due to its wealth of bioactive compounds. These compounds confer beneficial health benefits on it in aqueous infusions prepared with the blossoms of the jamaica flower. In the present study, we determined the antioxidant activity of 64 roselle varieties and quantified the following bioactive compound contents: phenolic; monomeric anthocyanins, and ascorbic acid. The results show that highest antiradical scavenging activity and reductor capacity belonged to varieties with dark-red calyces. Similarly, we found that the bioactive compound concentration increased as the pigmentation of the fresh calyces intensified. Finally, our results demonstrated that the aqueous extracts’ antioxidant activity is correlated with the bioactive compound concentration, this correlation greater with the content of ascorbic acid.
In the symmetric method, most authors choose a polygonal curve as coupling boundary. However, in this case, we do not know how to control the effect of the use of quadratures on the convergence of the method. Moreover, the computation of some coefficients of the system is not easy due to the singularities of the integral operators. In , we presented a new version of the symmetric method based on a parameterization of the artificial boundary, which is a smooth curve, and the use of curved finite elements in the discretization. This procedure allows one to employ the techniques from G.C. Hsiao, P. Kopp and W.L. Wendland  to approximate the boundary terms by simple quadrature formulas and to study the effect of quadratures on convergence. This modified version of the symmetric method has also been used to solve the linear elasticity problem (cf.).
Remark 3. If those non detectable scenarios are removed, then, the previous linear matrix inequalities are a sufficient condition to achieve a given RMS gain and to assure asymptotical stability. As the sampling modeling presented in this work leads to a discrete-time switched linear system, the condition presented here is not necessary for asymptotical stability (as shown in ), but is a necessary condition for polyquadratic stability, and, therefore, is less conservative than establishing quadratic stability with a unique matrix P for the Lyapunov stability assessment. Remark 4. If the RM S norms of disturbances, RM S norm of the derivative of each input, and noise measurement of each sensor are assumed to be known, it is possible to minimize the upper bound on k y ˜ k k RM S minimizing the sum
(an ideal state) because the gas might not behave as a limiting real gas at the pressure of 1 atm. Let’s consider this possibility. The straight line satisfying all these conditions is drawn as a dotted line in Fig. 1; it is formed by lines I and II. Because line I matches exactly the lowest part of the solid line, it describes the behavior of the limiting gas. State 2 must be one point on this dotted line. Line II is an extrapolation of the limiting real gas behavior at pressures higher than those at line I. It therefore describes the behavior of a gas having the properties of a limiting gas at any pressure value, i.e. the behavior of a hypothetical gas (an ideal gas). The standard state is at the intercept of line II with m i –axis, where pressure is by definition equal to 1 atm. Hence, this standard state is a hypothetical state. Then, the integration of the differential equation above gives:
The encoder is designed for highest robustness in industrial applications. It can be operated in the open environment of an EC flat motor and is equipped with additional ESD protection circuitry. Due to the robustness of the MILE technology in terms of magnetic interference, integration of the encoder into the EC 90 flat was possible with minimal change of dimensions.
Note that t is treated here as a constant because the canonical transformations do not affect t. Since the function (19) is a particular case of (7), is a solution of the HJ equation (6), and one can readily verify that (21) is also a solution of Eq. (6), for all values of the parameter α [which is essentially the two- parameter family of solutions (7)].
characterize and compute the corresponding linear state equations. It should be clear that this is a more complex issue since we are attempting to infer the description and properties of internal variables from input-output information. There are obvious limits to what can be inferred since a change ofstate variables does not change the transfer function or unit-impulse response. If there is one stateequation that has the given transfer function, there are an infinite number, all of the same dimension. Perhaps less obvious is the fact that there also are infinite numbers ofstate equations with different dimensions that have the given transfer function.
In this work we show that “full Kostant-Toda” appear in a finite counterpart of the discrete KP hierarchy, and that the results of  remain valid in this context almost verbatim, then a large class of solutions is obtained. Despite the fact that our method is quite different from that used by Kodama and Ye, in the cases of 2 by 2 matrices the solutions turn out to be of the same type. We conjecture that all our solutions are of the type found by Kodama and Ye.
The analysis of nonautonomous differential equations constitutes a complex field in Mathematics on which many researchers, starting from Poincar´e, have actively worked. A large quantity of problems are relevant not only because of their theoreti- cal interest, but also due to their fundamental role in the more accurate mathemati- cal modeling of many different actual phenomena. Generally speaking, the goal is to understand the way in which the intrinsic dynamics of the dynamical system deter- mined by a nonautonomous equation, which is due to the explicit time dependence of the law, affects the behavior of the phenomenon under analysis. Quite often the dynamical scenario described by the analysis reproduces well-known patterns of the autonomous case; but sometimes there appear new scenarios which cannot occur in the autonomous or periodic cases, with a high degree of complexity.
Since no further distinction will be made in the sequel concerning the sign of the parameter a, we will omit the subscript of the linear operator L given by (2.4). 2.2. Estimates. The previous lemma guarantees that L generates a group. In the sequel we will exhibit useful bounds for the related evolution.
Scale invariance (SI) refers to objects or laws that remain invariant if scales of length, energy, etc., are multiplied by a common factor, a process called dilatation. Probability distributions of random processes may display SI. In classical field theory SI most commonly applies to the invariance of a whole theory under dilatations while in quantum field theory SI is usually interpreted in terms of particle physics. In a SI-invariant theory the strength of particle interactions does not depend on the energy of the particles involved. In statistical mechanics SI is a feature of phase transitions. Near a phase transition or critical point fluctuations appear at all length scales, forcing one to look for an explicitly SI theory to describe things. These theories are SI statistical field theories, being formally very similar to scale-invariant quantum field ones .
Alkynes behave in ways broadly similar to alkenes, but being more electroneg- ative, they tend to encourage back donation and bind more strongly. The sub- stituents tend to fold back away from the metal by 30 ◦ –40 ◦ in the complex, and the M − C distances are slightly shorter than in the corresponding alkene com- plexes. The metalacyclopropene model (5.6) seems often to be the most appro- priate description when alkynes act as 2e donors. More interestingly, alkynes can form complexes that appear to be coordinatively unsaturated. For example, 5.7 6 appears to be 14e, and 5.8, 7 is a 16e species if we count the alkyne as a conventional 2e donor. In such cases the alkyne also donates its second C=C π -bonding orbital, which lies at right angles to the first. The alkyne is now a 4e donor 8 and 5.8 can be formulated as an 18e complex. Compound 5.7 might seem to be a 20e complex on this model, but in fact one combination of ligand π orbitals, 5.7a, finds no match among the d orbitals of the metal, and so the true electron count is 18e. An extreme valence bond formulation of the 4e donor form is the bis-carbene (5.9), the bonding of which we look at in Section 11.1. Four electron alkyne complexes are rare for d 6 metals because of a 4e repulsion
Quantitative analysis of transport phenomena was not entirely described up until 1828 with Thomas Graham’s experiments on diffusion in gases and liquids . Later that century in 1855, Adolf Fick codified the experiments of Graham in what we now know as Fick’s Laws. The First Law of Fick’s states that the one dimensional flux of a species i(that is, the particles per unit time that move through a certain area) is deifined as