Total Specific Heat Research Articles

Thermal and structural characteristics of date-pits as digested by Trichoderma reesei

The objective of this study was to develop functional date-pits by mold digestion for the potential use in food products. Whole date-pits (WDP) and defatted date-pits (DDP) were digested by mold Trichoderma reesei at 20 °C. T. reesei consumed date-pits as nutrients for their growth, and DDP showed higher growth of molds as compared to the WDP. The mold digested WDP and DDP samples showed an increased water solubility and hygroscopicity as compared to the samples prepared by autoclaved. This indicated that the mold digestion transformed date-pits to hydrophilic characteristics. Thermal analysis indicated a structural change at −3.2 °C for the untreated WDP and it was followed by a glass transition shift (i.e. onset: 138 °C and a specific heat change: 295 J/kg oC), and an endothermic peak at 196 °C with enthalpy of 68 J/g for the solids melting-decomposition. Similar characteristics were also observed for treated samples with the two glass transitions. The total specific heat changes for WDP, autoclaved-WDP, and digested-WDP were observed as 295, 367, and 328 J/kg oC, respectively. The total specific heat changes for DDP, autoclaved-DDP, and digested-DDP were observed as 778, 1329, and 1877 J/kg oC, respectively. This indicated that mold digestion transformed more amorphous fraction in the DDP. The energy absorption intensities of the Fourier Transform Infrared (FTIR) spectra for the selected functional groups decreased by the mold digestion.

Measurement of Physicochemical Properties and CO2, N2, Ar, O2, and H2O Unary Adsorption Isotherms of Purolite A110 and Lewatit VP OC 1065 for Application in Direct Air Capture.

Direct air capture (DAC) using solid adsorbents has gained significant attention as a carbon dioxide removal (CDR) technology to help limit global temperature rise to below 2 °C. One large area of focus is the development of new adsorbent materials for DAC. However, the necessary data needed to employ these materials in process models for adsorbent screening are rarely available. Here, we showcase Purolite A110, a commercially available amine-functionalized polymeric resin, as a new candidate adsorbent for DAC and compare its properties to a current benchmark, Lewatit VP OC 1065. For both materials, we report their chemical features and composition, skeletal, particle, and bed density, total pore volume, particle porosity, BET area, thermal stability, and specific heat capacity. We determine their equilibrium sorption properties by measuring the volumetric CO2 isotherms at 288, 298, 308, 333, 343, 353, and 393 K, N2 and H2O isotherms at 288, 298, and 308 K, and Ar and O2 isotherms at 298 K. For CO2, N2, and H2O, we also present the corresponding isotherm model fitting parameters and heats of adsorption. These data can help facilitate process modeling and optimization studies to properly assess these adsorbents at scale.

Effect of nano-crystallization and atomic substitution on electronic and heat properties of Bi2Te3

The specific heat of nano-crystalline (NC) Bi2Te3 (20 nm) in the temperature range of 150 K to 300 K is theoretically studied and compared with the specific heat of the bulk Bi2Te3 materials. Carrier concentration and Hall coefficient are also evaluated using free electron model and compared with experimental results. Lattice (phonon) specific heat has been observed with an overlap repulsive potential with the help of Debye model. For Nano Crystalline materials having high interface volume ratio, the Debye temperature and phonon frequencies are reasonably less at the interfaces than at the core of nano-crystal. Such softening of phonon frequencies at interfaces results in enhancement of Specific Heat in nano-structures. Total specific heat would include interface, core and electronic specific heat. The temperature derivative of the internal energy yields the electronic contribution to specific heat. The present analysis based on the softening of phonon frequencies mechanism is sufficient to describe the enhancement in specific heat by nano-crystallization.

Thermodynamic properties and effective mass of a weakly-interacting Bose gas using the static fluctuation approximation

The Static Fluctuation Approximation is used to investigate the thermodynamic properties and the single-particle effective mass of a weakly-interacting Bose gas. These properties include: the transition temperature, condensate fraction, energy spectrum, total energy, and specific heat capacity. The effects of the potential strength, number density, and temperature on these properties are studied. The transition temperature decreases as the potential strength increases, or the number density decreases. Also, the condensate fraction decreases drastically with increasing potential strength or decreasing density number. The total energy and specific heat indicate that the system is in the classical (quantum) regime at temperatures greater (less) than the transition temperature. The specific heat has a peak at the transition temperature. Regarding the effective mass: in higher excited states, it is close to the ‘bare’ mass, regardless of the potential strength and number density; but, in low-lying states, it is tangibly affected by these variables.

Characteristics of crystalline and amorphous fractions of date-pits as treated by alcohol-water pressure cooking

Date-pits are waste from date fruit processing industry and their valorisation as a lignocellulose biomaterial could generate economic gain. In this work, defatted date-pits (DDP) from whole date-pits (WDP), was soaked in alcohol-water followed by pressure-cooking. Two fractions of date-pits were developed, one as residue fraction (REP) and another one was supernatant fraction (SUP). REP showed higher level of hemicellulose and lower level of lignin (P < 0.05) compared to SUP. Similar water absorption, increased hygroscopicity, and decreased solubility were observed for REP compared to SUP. SEM showed that REP with bigger size particles as compared to the SUP fraction. SUP fraction showed two glass transitions, while REP showed single glass transition. Total specific heat changes of REP, and SUP fractions were 149 and 1032 J/kg oC, respectively, which indicated that SUP is mainly amorphous in composition. This was also supported by XRD data having Ruland-crystallinity of 52.0% (i.e. REP) and 9.6% (i.e. SUP), respectively. FTIR analysis indicated different molecular structure of SUP as compared to REP fraction as evidenced from the highest energy absorption for all selected functional groups. Overall, the results showed that this extraction method was effective to produce two distinctive fractions of date-pits with varied crystallinity.

Dimensionless Scaling and Prediction of Vortex Tube Temperature Separation

Ranque–Hilsch vortex tubes split an incoming fluid stream into two outgoing streams: one with a higher total temperature than the incoming fluid and the other with a lower total temperature. This 90-year-old device accomplishes its temperature separation with no moving parts and no external power sources, and despite a diversity of extant theories regarding the underlying mechanism, it is clear that a rapidly swirling flow inside the tube is key to its operation. While many parametric studies have characterized the degree of temperature separation as a function of a host of variables (e.g., inlet pressure, inlet temperature, working gas, tube geometry), no previous effort has identified the governing nondimensional parameters that would simplify further characterization. In the present work, we nondimensionalize the energy equation as it applies to Ranque–Hilsch vortex tubes and identify the governing nondimensional parameters and nondimensional dependent variables. The governing nondimensional parameters are shown to be the Reynolds number, the Péclet number, and a lesser-known nondimensionalization of the Joule–Thomson coefficient, . To discern the dependence of temperature separation on these nondimensional parameters, experimental data were analyzed. We show that a unique dimensionless form of the product of the total temperature, density, and specific heat collapses across a wide range of the aforementioned governing nondimensional parameters, although some dependence remains evident, particularly in the case of , for which an extremely wide range of values were obtained through comparison of carbon dioxide with air. A method is demonstrated to predict temperature separation for new cooling scenarios, reducing the experimental burden for new applications.

Specific Heat of the Kagome Antiferromagnet Herbertsmithite in High Magnetic Fields

Measuring the specific heat of herbertsmithite single crystals in high magnetic fields (up to $34$ T) allows us to isolate the low-temperature kagome contribution while shifting away extrinsic Schottky-like contributions. The kagome contribution follows an original power law $C_{p}(T\rightarrow0)\propto T^{\alpha}$ with $\alpha\sim1.5$ and is found field-independent between $28$ and $34$ T for temperatures $1\leq T\leq4$ K. These are serious constrains when it comes to replication using low-temperature extrapolations of high-temperature series expansions. We manage to reproduce the experimental observations if about $10$ % of the kagome sites do not contribute. Between $0$ and $34$ T, the computed specific heat has a minute field dependence then supporting an algebraic temperature dependence in zero field, typical of a critical spin liquid ground state. The need for an effective dilution of the kagome planes is discussed and is likely linked to the presence of copper ions on the interplane zinc sites. At very low temperatures and moderate fields, we also report some small field-induced anomalies in the total specific heat and start to elaborate a phase diagram.

Ab initio thermodynamics of one-component plasma for astrophysics of white dwarfs and neutron stars

ABSTRACT Using path-integral Monte Carlo (PIMC) simulations, we have calculated energy of a crystal composed of atomic nuclei and uniform incompressible electron background in the temperature and density range, covering fully ionized layers of compact stellar objects, white dwarfs, and neutron stars, including the high-density regime, where ion quantization is important. We have approximated the results by convenient analytic formulae, which allowed us to integrate and differentiate the energy with respect to temperature and density to obtain various thermodynamic functions such as Helmholtz free energy, specific heat, pressure, entropy etc. In particular, we have demonstrated, that the total crystal specific heat can exceed the well-known harmonic lattice contribution by a factor of 1.5 due to anharmonic effects. By combining our results with the PIMC thermodynamics of a quantum Coulomb liquid, updated in the present work, we were able to determine density dependences of such melting parameters as the Coulomb coupling strength at melting, latent heat, and a specific heat jump. Our results are necessary for realistic modelling of thermal evolution of compact degenerate stars.

Feasibility of construction and installation site of differential pressure sensors for gas energy efficient plant for coarse and fine purification

The paper substantiates the construction and location of differential pressure sensors for a coarse and fine gas energy-saving plant. Energy saving is achieved by installing filtering cylindrical elements of fine and coarse purification one inside the other, optimizing their shape and substantiating the location of the differential pressure sensors. The results of the studies show that the total specific heat consumption for heating and ventilation of purification plants from all energy-saving measures for the proposed option is 1.85 times lower than the existing analogue of the non-optimized shape and measuring the pressure drop at the inlet and outlet branch pipes. The article also proved that the static gas pressure in the lower part of filter elements of the coarse and fine purification will always be higher than in their upper part. This results in a proportionally higher amount of inlet gas and therefore more solids settling in the bottom of the filter element. Measurement of the pressure drop in the lower part of the filter element, the most clogged with solid particles, makes it possible to receive a signal at the dispatching console earlier and provides a time reserve for technical personnel to timely remove accumulated blockages from coarse purification elements and prompt replacement of fine purification elements.

A comparative study between GGA, WC-GGA, TB-mBJ and GGA + U approximations on magnetocaloric effect, electronic, optic and magnetic properties of BaMnS2 compound: DFT calculations and Monte Carlo simulations

The magnetocaloric effect, electronic, optical and magnetic properties of BaMnS2 are studied using the Wu-Cohen-Generalized Gradients Approximation (WC-GGA), GGA, Tran and Blaha modified Becke-Johnson potential (TB-mBJ) and GGA + U(U is the Hubbard potential) approximations and Monte Carlo simulations. BaMnS2 has an antiferromagnetic behavior and a semiconductor character with a narrow band gap follows the trend WC-GGA < GGA < mBJ < GGA + U. The GGA + U transformed and increased the nature of the band gap, causing an apparent change in physical properties. The difference energy calculated between the magnetic configurations confirms that the ground state antiferromagnetic (AFM) is more stable than the paramagnetic (PM) states. The total magnetization, susceptibility, specific heat and magnetic entropy and relative cooling power of this compound are studied. The maximum value of the magnetic entropy was obtained near the paramagnetic AFM- PM transition for (WC-GGA, GGA) and GGA + U equal to 38.31 J.kg−1.K−1 and 16.72 J.kg−1.K−1 respectively.

Further development of the change-point model – Differentiating thermal power characteristics for a residential district in a cold climate

The building and service sector accounts for nearly 40% of total energy use in Sweden. The existing, historic building stock accounts for large part of this energy use and comprises an important part of the national pursuit to increase energy efficiency. One main problem for decreasing energy use in the existing building stock is the lack of data describing thermal performance characteristics. This paper presents a novel development of the change-point model for predicting the thermal performance of buildings using selected time periods based on time-dependent variations in climate and user behavior. The predicted thermal power characteristics include total specific heat losses (Qtotal), energy use for hot water circulation (HWC) and hot tap water (HTW), and balance temperature. A residential district with 73 historic buildings in Linköping, Sweden, has been used as the study object.The developed model is shown to be effective and robust for describing building thermal performance. The average R2 was 0.70 for predictions of specific heat losses. The sensitivity analyses conclude that the selected time steps and months correspond to the highest R2 value. The average variation width for prediction of the balance temperature is 0.9 °C for buildings in the interquartile range based on a three-year comparison of hourly heating power supply data. Moreover, from a property owner perspective, the model is shown to be useful for identifying deviating thermal power characteristics and can easily be used to get an overview of a district.

Magnetic and magnetothermal properties of Gd75Cu25 prepared by melt-spinning

Magnetic and magnetothermal properties of melt-spun Gd75Cu25 alloy were studied. A second-order magnetic phase transition is observed at the Curie temperature of 144 K. The peak value of the magnetic entropy change −ΔSmpk = 7.0 J kg−1 K−1 is observed near the Curie point under the magnetic field change 0–5 T, while the refrigerant capacity is found to be 594 J kg−1. The specific heat exhibits a wide transition near the Curie temperature, and the non-magnetic contributions to the total specific heat are described using the Debye temperature ΘD = 155 K and the electronic specific heat coefficient γ = 65 mJ mol−1 K−2.

Mechanism and quantitative study of specific heat change during glass transition of amorphous polystyrene and Pd&lt;sub&gt;40&lt;/sub&gt;Ni&lt;sub&gt;10&lt;/sub&gt;Cu&lt;sub&gt;30&lt;/sub&gt;P&lt;sub&gt;20&lt;/sub&gt;

&lt;sec&gt;The nature of glass transition is one of the most interesting problems in modern condensed matter physics. There is a theory that shows that when the particle's diffusion motion probability &lt;i&gt;P&lt;/i&gt; is less than &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ {{\rm{e}}^{ - 2{{\rm{e}}^3}}}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200331_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200331_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, the proportion of particles whose diffusion motion is frozen is not less than 1 + 2e&lt;sup&gt;3&lt;/sup&gt;/ln&lt;i&gt;P&lt;/i&gt;. Based on the modulus temperature formula of this theory and the experimental modulus-temperature curve of polystyrene in the literature, the free volume expansion coefficient of polystyrene is determined to be in a range of 0.00045－0.00052. &lt;/sec&gt;&lt;sec&gt;In this paper, we first quantitatively study the specific heat temperature relationship in the glass transition of polystyrene. Based on this theory, the specific heat-temperature formula in the glass transition region is derived. The material in the glass transition region is a mixture of rubber and glass, and this two-component (rubber and glass) system’s total specific heat is the product of the specific heat of the rubber and the percentage of rubber in the two-component system plus the product of the specific heat of the glass and the percentage of glass in the two-component system. Let &lt;i&gt;b&lt;/i&gt; be the number of atoms in the main chain of the segment, then the proportion of rubber will be the &lt;i&gt;b&lt;/i&gt;-th power of free volume fraction. This specific heat-temperature formula with polystyrene is tested. By substituting the obtained free volume expansion coefficient of the polystyrene into the specific heat-temperature formula, the resulting formula can accurately and quantitatively describe the specific heat-temperature relationship in the glass transition of polystyrene without fitting any parameters. &lt;/sec&gt;&lt;sec&gt;In this paper, we also study the change of motion in the glass transition of polystyrene. According to the analysis, the glass transition process of polystyrene is a process in which the diffusion movement of the main chain atoms is activated or frozen, which is consistent with the conclusions of relevant research on amorphous alloys. When the main chain atom is used as the molar unit of measurement, the specific heat change in the glass transition of polystyrene is 1.61&lt;i&gt;R&lt;/i&gt; (&lt;i&gt;R&lt;/i&gt; is the gas constant), which is consistent with the law, i.e. “the specific heat change in the glass transition of the amorphous alloy is about 1.5&lt;i&gt;R&lt;/i&gt;”. These consistent conclusions predict that the glass transitions of amorphous alloys and glass transitions of polystyrene have the same essence. Based on this idea, the specific heat temperature formulas of the amorphous alloy Pd&lt;sub&gt;40&lt;/sub&gt;Ni&lt;sub&gt;10&lt;/sub&gt;Cu&lt;sub&gt;30&lt;/sub&gt;P&lt;sub&gt;20&lt;/sub&gt; and polystyrene are verified and prove to be consistent.&lt;/sec&gt;

Magnetic Properties of NiFe2O4 Compound: Ab Initio Calculation and Monte Carlo Simulation

The structural, electronic, and magnetic properties of the NiFe2O4 compound are studied using several theoretical methods such as first-principle calculations based on density functional theory (DFT), Monte Carlo simulations, and mean-field theory. The exchange-correlation potential was resolved by generalized gradient approximation (GGA) that underestimates the band gap energy value; therefore, this later needed to be corrected using the GGA + U approximation. The gap energy value (1.10 eV) obtained by the theoretical method is in good agreement with experimental value (0.99 eV). Using ab initio calculations, the exchange-coupling interactions are J1 = 40.665 meV, J2 = 45.382 meV, and J3 = −3.260 meV. Moreover, the semiconductor NiFe2O4 compound exhibits a second-order ferromagnetic-paramagnetic phase transition around TC = 844 K; this value is in good agreement with experimental results. The total magnetization, susceptibility, and specific heat of this compound are investigated.

Thermal properties of commercial hydrobionts’ tissues in the freezing process

The paper describes changes in thermal properties in the process of freezing of marine raw materials. The study objects were the skin of giant octopus (Octopus dofleini L.), pallium of Pacific squid (Todarodes pacificus L.), milt of Pacific herring (Clupea pallasii L .), a nd muscle t issue of Japanese c ucumaria (Cucumaria japonica L.). The mathematical relations of the studied thermal parameters allowing the calculation of specific heat capacity, thermal conductivity coefficient and tissue density of the studied objects in the process of freezing were obtained. It was found that the change in the total specific heat capacity during the freezing of all the objects under study was of the same type: first, this figure increases due to the intensive ice formation in the tissues of hydrobionts, and then decreases due to a significant decrease in the content of the liquid aqueous phase. The values of the total specific heat capacity before the freezing of seafood were determined (kJ/kg·K): 4.26 for squid, 3.58 for milt of Pacific herring, 3.66 for octopus skin, and 3.95 for the shell of cucumaria. It was revealed that an increase in the amount of frozen out water decreased the density of samples of frozen raw materials. This was due to the high (77.4–88.9%) content of water, turning into ice, which has a lower density index. The values of hydrobionts’ tissue density before freezing were obtained ( 0 ρ , kg/m3): 1226.74 for squid, 1209.6 for milt of Pacific herring, 1128.55 for octopus skin, and 031.26 for shell of cucumaria. It was established that the thermal conductivity of the hydrobiont tissue samples in the process of freezing increased with the growth of the proportion of frozen out water contained, approaching the thermal conductivity of ice. The calculated values of thermal conductivity coefficient of seafood tissue prior to freezing equal (W/m·K): 0.52 for squid, 0.47 for milt of Pacific herring, 0.63 for octopus skin, and 0.53 for cucumaria. The obtained thermal characteristics values of the objects studied are recommended for use in technical and technological calculations of aquatic biological resources cooling treatment processes.

Theoretical analysis of cross-plane lattice thermal conduction in graphite**Project supported by the National Natural Science Foundation of China (Grant No. 51376094) and Jiangsu Overseas Visiting Scholar Program for University Prominent Young & Middle-aged Teachers and Presidents.

A theoretical analysis of the cross-plane lattice thermal conduction in graphite is performed by using first-principles calculations and in the single-mode relaxation time approximation. The out-of-plane phonon acoustic mode ZA and optical mode have almost 80% and 20% of contributions to cross-plane heat transfer, respectively. However, these two branches have a small part of total specific heat above 300 K. Phonons in the central 16% of Brillouin zone contribute 80% of cross-plane transport. If the group velocity angle with respect to the graphite layer normal is less than 30°, then the contribution is 50% at 300 K. The ZA phonons with long cross-plane mean free path are focused in the cross-plane direction, and the largest mean free path is on the order of several micrometers at room temperature. The average value of cross-plane mean free path at 300 K is 112 nm for ZA phonons with group velocity angle with respect to the layer normal being less than 15°. The average value is dropped to 15 nm when phonons of all branches in the whole Brillouin zone are taken into account, which happens because most phonons have small or even no contributions.

A molecular-field study on the magnetocaloric effect in Er2Fe17

A method, based on the molecular field theory of ferrimagnetism, and standard relations for the electronic and lattice heat capacities and entropies, is used to calculate the magnetocaloric effect (MCE) in Er2Fe17. This compound has a Curie temperature in the vicinity of room temperature and could be, therefore, of practical interest. The magnetization, magnetic, lattice, electronic and total entropies and specific heats, for different magnetic fields, have been calculated as function of temperature up to and beyond Tc. The magnetocaloric effect i.e. the isothermal magnetic entropy change ΔSM and the adiabatic temperature change, ΔTad for different magnetic fields, have been studied in the temperature range 0-400K. As an example of our results, the maximum isothermal magnetic entropy change ΔSM in Er2Fe17 is in the range 5-6J/kgK, for a magnetic field change of 80kOe. The adiabatic temperature change, ΔTad has a maximum value in the range 1.5-2.1K for ΔH=80kOe. For the purpose of comparison, a giant magnetocaloric bench-mark material, with first-order phase transition e.g. Gd5Si2Ge2 has a maximum ΔSm and ΔTad (for a field change of 50 kOe) in the range 20–36 J/kg. K and 11–17 K respectively. Our results are in fair agreement with available results of other studies on this compound, in which more involved Hamiltonian was used e.g. taking crystal electric field into account.

Anomalous spin frustration enforced by a magnetoelastic coupling in the mixed-spin Ising model on decorated planar lattices

The mixed spin-1/2 and spin-S Ising model on a decorated planar lattice accounting for lattice vibrations of decorating atoms is treated by making use of the canonical coordinate transformation, the decoration-iteration transformation, and the harmonic approximation. It is shown that the magnetoelastic coupling gives rise to an effective single-ion anisotropy and three-site four-spin interaction, which are responsible for the anomalous spin frustration of the decorating spins in virtue of a competition with the equilibrium nearest-neighbor exchange interaction between the nodal and decorating spins. The ground-state and finite-temperature phase diagrams are constructed for the particular case of the mixed spin-1/2 and spin-1 Ising model on a decorated square lattice for which thermal dependencies of the spontaneous magnetization and specific heat are also examined in detail. It is evidenced that a sufficiently strong magnetoelastic coupling leads to a peculiar coexistence of the antiferromagnetic long-range order of the nodal spins with the disorder of the decorating spins within the frustrated antiferromagnetic phase, which may also exhibit double reentrant phase transitions. The investigated model displays a variety of temperature dependencies of the total specific heat, which may involve in its magnetic part one or two logarithmic divergences apart from one or two additional round maxima superimposed on a standard thermal dependence of the lattice part of the specific heat.

The low temperature specific heat of single crystal Er-Al2 compound

The low temperature heat capacity of the ErAl2 single crystal compound have been measured in the temperature 2– 40 K using a modified adiabatic continues heating technique. The magnetic contributions to the total specific heat were extracted using similar but nonmagnetic “lattice blank”, which gives a good description of the non-magnetic contributions to the heat capacities. The magnetic specific heat exhibits large anomaly at the highly cooperative magnetic phase transition, which lies at about 12 K. A broad Schottky anomaly was shown centered at about 30 K. The magnetic contributions to the heat capacity of the ErAl2 compound, Cm(T) have been calculated using mean field approximation. The Hamiltonian has been taken to be the sum of crystal field and isotropic exchange terms. A computer program based on the molecular field approximation has been written to calculate the crystal field levels and the magnetic contributions to the heat capacity as a function of temperature in the ErAl2 compound. The critical exponent analysis showed that α′ ≈ α and A′/A ≈ 1.9. The low temperature magnetic specific heats behave as T3/2 in support of the spin wave excitations predictions.

A microscopic study of neon and argon gases within the static fluctuation approximation (SFA)

The thermodynamic properties of neon and argon gases are studied within the static fluctuation approximation (SFA). These properties include the total internal energy, pressure, entropy, compressibility and specific heat. The results are compared with those recently obtained within the Galitskii–Migdal–Feynman (GMF) formalism. The overall agreement is very good. An exception, however, is the specific-heat results for neon. While SFA gives results rather similar to those of the ideal gas, the corresponding GMF results are quite different. It is argued that the discrepancy seems to have arisen from quantum effects in conformity with very recent Monte Carlo computations. Whenever possible, our SFA results are compared to experimental data.