On the spline collocation method for the single layer equation related to time-fractional diffusion

The boundary element spline collocation method is studied for the time-fractional diffusion equation in a bounded two-dimensional domain. We represent the solution as the single layer potential which leads to a Volterra integral equation of the first kind. We discretize the boundary integral equation with the spline collocation method on uniform meshes both in spatial and time variables. In the stability analysis we utilize the Fourier analysis technique developed for anisotropic pseudodifferential equations. We prove that the collocation solution is quasi-optimal under some stability condition for the mesh parameters. We have to assume that the mesh parameter in time satisfies (h_t=c h^\frac2a)(h_t=c h^{\frac{2}{\alpha}}), where (h) is the spatial mesh parameter.     

Heat Transport in Unsaturated Zone Thermal Energy Storage – Analysis with Two-Phase and Single-Phase Models

We analyze a field experiment where ambient air is injected into the soil during the summer and extracted again during the winter. A multiphase model accounting for the conductive transport as well as the convective transport with the moving liquid and gas phases is used along with a more simplified single-phase model where the convective transport is due to the gas alone. The latter model also accounts for subzero wintertime temperatures. The multiphase model captures well both the seasonal variations and the actual test sequence, the main calibration being in the adjustment of medium permeabilities based on the observed pressure responses. The effect of the injection pump on the temperature and humidity of the injection air needs to be known accurately. Taking into account the humidity of the injection air explicitly instead of using humidity-corrected enthalpy values also has an effect. The effect of various humidity and specific enthalpy assumptions is of the order of 1–1.5°C, while ignoring the wintertime subzero temperatures has an effect of 1–2°C. These differences are of the same order of magnitude as the heterogeneity-introduced differences in field data. Using the simplified single-phase model typically appears to cause a difference of 1–2°C, but can yield an even higher deviation of the order of 3–4°C.     

Testing the neo-classical and the Newtonian theory of production

We search for regularities observed in the production of goods by studying Finnish data. Despite the heterogeneity of sectoral growth rates in Finland, unit root is observed in annual productions in all main sectors and all manufacturing industries. Thus a linear time trend exists in annual flows of production. This is inconsistent with the static neo-classical theory that assumes firms to produce at their equilibrium flow of production. A different framework is thus needed for modeling the behavior of firms. We test a Newtonian type of model for production against the neo-classical one, and our observation is that the former works better with annual data at every manufacturing industry in Finland.     

Hydrolytically active tetranuclear nickel complexes with structural resemblance to the active site of urease

Reaction of the new asymmetric ligand 2-(N-isopropyl-N-((1-methylimidazolyl)methyl)aminomethyl)-6-(N-carboxylmethyl-N-((1-methylimidazolyl)methyl) aminomethyl)-4-methylphenol (ICIMP) with nickel perchlorate and diphenylacetic acid leads to the formation of tetranuclear nickel complexes, whose crystal structures reveal that they consist of dimers of dimers in which each Ni(2) unit has a coordination environment that is similar to the active site of urease. One complex has been shown to coordinate urea and catalyze the hydrolysis of an organophosphate monoester.     

Analysis of eleven iridoid glycosides by micellar electrokinetic capillary chromatography (MECC) and screening of plant samples by partial filling (MECC)-electrospray ionisation mass spectrometry

Of ammonium, lithium and sodium salts of dodecyl sulfate studied as surfactants in the separation of iridoid glycosides by micellar electrokinetic capillary chromatography (MECC), the last one gave the best results. Eleven neutral iridoid glycosides were separated by MECC with sodium dodecyl sulfate as surfactant, and the water–micelle partition coefficients of the compounds were calculated. The separation system was coupled via a coaxial sheath flow electrospray interface to a mass spectrometer, and the partial filling technique was used in the on-line analysis. Seven plant species belonging to five genera (Plantago, Veronica, Melampyrum, Succisa and Valeriana) were screened for the iridoid glycosides by the new method that was developed. The findings confirmed those of an earlier study on five of the iridoid glycosides. Some new iridoid glycosides were found in Plantago lanceolata, Veronica spicata and V. chamaedrys.     

Individual strings of conducting carbon cones and discs in a polymer matrix: Electric field‐induced alignment and their use as a strain sensor

We demonstrate micromechanical strain sensors with integrated readout based on carbon nanocones and discs (CNCs) which are aligned into a string‐like formation using an alternating electric field and studied by AC impedance spectroscopy and electromechanical methods. The CNC particles are first dispersed into a polymer matrix with a particle fraction of 0.1 vol %. This value is well below the percolation threshold (～ 2 vol %), which suppresses particle aggregation and facilitates transparency allowing the use of an UV‐curable polymer. Alignment was carried out with a 1 kHz, 4 kV/cm electric field and is a consequence of dielectrophoretic effect. It develops in minutes and makes the initially insulating, nonaligned material conductive. This is followed by UV curing of the polymer matrix, which renders a solid state device. The stretching of the aligned strings in the cured polymer leads to a reversible piezoresistive effect, and a gauge factor of about 50 is observed. This is in a sharp contrast to CNC films with particle fraction above percolation threshold (13 vol %), which are conductive but not sensitive to stretching. The strings are Ohmic in nature and moreover show higher DC conductivity (22–500 S/m) compared to identically prepared carbon black strings (1–22 S/m). © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Peak dispersion and contributions to plate height in nonaqueous capillary electrophoresis at high electric field strengths: propanol as background electrolyte solvent

Peak dispersion effects in nonaqueous capillary electrophoretic separations of aromatic anionic analytes were investigated in a propanolic background electrolyte solution. Poly(glycidylmethacrylate-co-N-vinylpyrrolidone) coating was applied to the capillary to suppress the electroosmotic flow and to improve the repeatability of the migration times. Electrical field strengths up to 2000 Vcm(-1) were applied in separations and the separation efficiencies were compared with theoretical values calculated on the basis of plate height theory. The contributions to the total plate height were calculated for injection plug length, diffusion, Joule heating, electromigration dispersion, analyte adsorption to the capillary wall, and detector slit aperture length. Analyte diffusion coefficients were measured by Taylor dispersion method, while distribution constants were measured chromatographically. Agreement between the calculated and empirical results was fairly good even though some approximations were required. In most cases the longitudinal diffusion contribution governed the total plate height, while the contribution of Joule heating was insignificant even at exceptionally high field strengths used. The relatively long detection slit aperture was found to influence the separation efficiency strongly, while the other dispersion sources that were investigated were of minor importance, except for adsorption in the case of one analyte. With all analytes, the dispersive effect of longitudinal diffusion was reduced as the field strength was increased, leading to enhanced migration velocities and faster separations.     

Hydrolytic metal-mediated coupling of dialkylcyanamides at a Pt(IV) center giving a new family of diimino ligands

Addition of excess R(2)NCN to an aqueous solution of K(2)[PtCl(4)] led to the precipitation of [PtCl(2)(NCNR(2))(2)] (R(2) = Me(2) 1; Et(2) 2; C(5)H(10) 3; C(4)H(8)O, 4) in a cis/trans isomeric ratio which depends on temperature. Pure isomers cis-1-3 and trans-1-3 were separated by column chromatography on SiO(2), while trans-4 was obtained by recrystallization. Complexes cis-1-3 isomerize to trans-1-3 on heating in the solid phase at 110 degrees C; trans-1 has been characterized by X-ray crystallography. Chlorination of the platinum(II) complexes cis-1-3 and trans-1-4 gives the appropriate platinum(IV) complexes [PtCl(4)(NCNR(2))(2)] (cis-5-7 and trans-5-8). The compound cis-6 was also obtained by treatment of [PtCl(4)(NCMe)(2)] with neat Et(2)NCN. The platinum(IV) complex trans-[PtCl(4)(NCNMe(2))(2)] (trans-5) in a mixture of undried Et(2)O and CH(2)Cl(2) undergoes facile hydrolysis to give trans-[PtCl(4)[(H)=C(NMe(2))OH](2)] (9; X-ray structure has been determined). The hydrolysis went to another direction with the cis-[PtCl(4)(NCNR(2))(2)] (cis-5-7) which were converted to the metallacycles [PtCl(4)[NH=C(NR(2))OC(NR(2))=NH]] (11-13) due to the unprecedented hydrolytic coupling of the two adjacent dialkylcyanamide ligands giving a novel (for both coordination and organic chemistry) diimino linkage. Compounds 11-13 and also 14 (R(2) = C(4)H(8)O) were alternatively obtained by the reaction between cis-[PtCl(4)(MeCN)(2)] and neat undried NCNR(2). The structures of complexes 11, 13, and 14 were determined by X-ray single-crystal diffraction. All the platinum compounds were additionally characterized by elemental analyses, FAB mass-spectrometry, and IR and (1)H and (13)C[(1)H] NMR spectroscopies.     

Platinum(IV)-mediated nitrile-sulfimide coupling: a route to heterodiazadienes

Pt(IV)-mediated addition of the sulfimide Ph2S = NH and the mixed sulfide/sulfimides o- and p-[PhS(=NH)](PhS)-C6H4 by the S=NH group to the metal-bound nitriles in the platinum(IV) complexes [PtCl4(RCN)2] proceeds smoothly at room temperature in CH2Cl2 and results in the formation of the heterodiazadiene compounds [PtCl4[NH=C(R)N=SR'Ph]2] (R' = Ph, R = Me, Et, CH2Ph, Ph; R' = o- and p-(PhS)C6H4; R = Et). While trans-[PtCl4(RCN)2] (R = Et, CH2Ph, Ph) reacting with Ph2S=NH leads exclusively to trans-[PtCl4[NH=C(R)N=SPh2]2], cis/trans-[PtCl4(MeCN)2] leads to cis/trans mixtures of [PtCl4[NH=C(Me)N=SPh2]2] and the latter have been separated by column chromatography. Theoretical calculations at both HF/HF and MP2//HF levels for the cis and trans isomers of [PtCl4[NH=C(Me)N=SMe2]2] indicate a higher stability for the latter. Compounds trans-[PtCl4[E-NH=C(R)N=SPh2]2] (R = Me, Et) and cis-[PtCl4[E-NH=C(Me)N=SPh2][Z-NH=C(Me)N=SPh2]] have been characterized by X-ray crystallography. The complexes [PtCl4[NH=C(R)N=SPh2]2] undergo hydrolysis when treated with HCl in nondried CH2Cl2 to achieve the amidines [PtCl4[NH=C(NH2)R]2] the compound with R = Et has been structurally characterized) and Ph2SO. The heterodiazadiene ligands, formed upon Pt(IV)-mediated RCN/sulfimide coupling, can be liberated from their platinum(IV) complexes [PtCl4[NH=C(R)N=SR'Ph]2] by reaction with Ph2PCH2CH2PPh2 (dppe) giving free NH=C(R)=SR'Ph and the dppe oxides, which constitutes a novel route for such rare types of heterodiazadienes whose number has also been extended. The hybrid sulfide/sulfimide species o- and p-[PhS(=NH)](PhS)C6H4 also react with the Pt(II) nitrile complex [PtCl2(MeCN)2] but the coupling--in contrast to the Pt(IV) species--gives the chelates [PtCl2[M-I=C(Me)N=S(Ph)C6H4SPh]]. The X-ray crystal structure of [PtCl2[M-I=C(Me)N=S(Ph)C6H4SPh-o]] reveals the bond parameters within the metallacycle and shows an unusual close interaction of the sulfide sulfur atom with the platinum.     

Amidines derived from Pt(IV)-mediated nitrile-amino alcohol coupling and their Zn(II)-catalyzed conversion into oxazolines

The reaction between the platinum(IV) complex trans-[PtCl(4)(EtCN)(2)] and the amino alcohols NH(2)CH(2)CH(2)OH, NH(2)CH(2)CH(Me)OH-(R)-(-), NH(2)CH(Ph)CH(2)OH-(R)-(-), NH(2)CH(Et)CH(2)OH-(R)-(-), NH(2)CH(Et)CH(2)OH-(S)-(+), and NH(2)CH(Pr(n)())CH(2)OH proceeds rapidly at room temperature in CH(2)Cl(2) to furnish the amidine complexes [PtCl(4)(HN=C(Et)NH(arcraise;)OH)(2)] (1-6) in good yield (70-80%). The related reaction between the platinum(II) complex trans-[PtCl(2)(EtCN)(2)] and monoethanolamine in a molar ratio of 1:2 in CH(2)Cl(2) results in the addition of 4 equiv of NH(2)CH(2)CH(2)OH per mole of complex to give [Pt(HN=C(Et)NHCH(2)CH(2)OH)(2)(NH(2)CH(2)CH(2)OH)(2)](2+) (7). Formulation of 1-6 is based upon satisfactory C, H, N elemental analyses, electrospray mass spectrometry, IR spectroscopy, and (1)H, (13)C((1)H), (15)N, and (195)Pt NMR spectroscopies, while the structures of trans-[PtCl(4)((Z)-NH=C(Et)NHCH(2)CH(2)OH)(2)] (1), trans-[PtCl(4)((Z)-NH=C(Et)NHCH(2)CH(Me)OH-(R)-(-))(2)] (2), and trans-[PtCl(4)((Z)-NH=C(Et)NHCH(Et)CH(2)OH-(R)-(-))(2)] (4) were determined by X-ray single-crystal diffraction. The Z-amidine configuration of the ligands is preserved in CDCl(3) solutions as confirmed by gradient-enhanced (15)N,(1)H-HMQC spectroscopy and NOE experiments. The amidines, formed upon Pt(IV)-mediated nitrile-amino alcohol coupling, were liberated from their platinum(IV) complexes 1, 3, and 4 by reaction with Ph(2)PCH(2)CH(2)PPh(2) (dppe) giving free NH=C(Et)NHCHRCH(2)OH (R = H 8, Et 9, Ph 10), with the substituents R of different types, and dppe oxides; the P-containing species were identified by (31)P((1)H) NMR spectroscopy. NOESY spectroscopy indicates that the liberated amidines retained the same configuration relative to the C=N double bond, i.e., syn-(H,Et)-NH=C(Et)NHCHRCH(2)OH. The liberated hydroxo-functionalized amidines 8-10 were converted into oxazolines (11-13) in the presence of a catalytic amount of ZnCl(2). A similar catalytic effect has also been reached using anhydrous MSO(4) (M = Cu, Co, Cd), CdCl(2), and AlCl(3).