The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

Secular series and renormalization group for amplitude equations

We have developed a technique that circumvents the process of elimination of secular terms and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems. © 2008 The American Physical Society.

Composition-dependent structural and electronic properties of α-(Si1−xCx)3N4

The highly unusual structural and electronic properties of the α-phase of (Si1-xCx)3N4 are determined by density functional theory (DFT) calculations using the Generalized Gradient Approximation (GGA). The electronic properties of α-(Si 1-xCx)3N4 are found to be very close to those of α-C3N4. The bandgap of α-(Si 1-xCx)3N4 significantly decreases as C atoms are substituted by Si atoms (in most cases, smaller than that of either α-Si3N4 or α-C3N4) and attains a minimum when the ratio of C to Si is close to 2. On the other hand, the bulk modulus of α-(Si1-xCx)3N 4 is found to be closer to that of α-Si3N 4 than of α-C3N4. Plasma-assisted synthesis experiments of CNx and SiCN films are performed to verify the accuracy of the DFT calculations. TEM measurements confirm the calculated lattice constants, and FT-IR/XPS analysis confirms the formation and lengths of C-N and Si-N bonds. The results of DFT calculations are also in a remarkable agreement with the experiments of other authors.

Structural, electronic, and optical properties of wurtzite and rocksalt InN under pressure

Structural stability, electronic, and optical properties of InN under high pressure are studied using the first-principles calculations. The lattice constants and electronic band structure are found consistent with the available experimental and theoretical values. The pressure of the wurtzite-to-rocksalt structural transition is 13.4 GPa, which is in an excellent agreement with the most recent experimental values. The optical characteristics reproduce the experimental data thus justifying the feasibility of our theoretical predictions of the optical properties of InN at high pressures.

Mechanical model and superelastic properties of carbon microcoils with circular cross-section

Here we report on an unconventional Ni-P alloy-catalyzed, high-throughput, highly reproducible chemical vapor deposition of ultralong carbon microcoils using acetylene precursor in the temperature range 700-750 °C. Scanning electron microscopy analysis reveals that the carbon microcoils have a unique double-helix structure and a uniform circular cross-section. It is shown that double-helix carbon microcoils have outstanding superelastic properties. The microcoils can be extended up to 10-20 times of their original coil length, and quickly recover the original state after releasing the force. A mechanical model of the carbon coils with a large spring index is developed to describe their extension and contraction. Given the initial coil parameters, this mechanical model can successfully account for the geometric nonlinearity of the spring constants for carbon micro- and nanocoils, and is found in a good agreement with the experimental data in the whole stretching process.

Excited-state dynamics in diketopyrrolopyrrole-based copolymer for organic photovoltaics investigated by transient optical spectroscopy

We investigate the photoexcited state dynamics in a donor-acceptor copolymer, poly{3,6-dithiophene-2-yl-2,5-di(2-octyldodecyl)-pyrrolo[3,4-c]- pyrrole-1,4-dione-alt-naphthalene} (pDPP-TNT), by picosecond fluorescence and femtosecond transient absorption spectroscopies. Timeresolved fluorescence lifetime measurements of pDPP-TNT thin films reveal that the lifetime of the singlet excited state is 185 ± 5 ps and that singlet-singlet annihilation occurs at excitation photon densities above 6 × 1017 photons/cm3. From the results of singlet-singlet annihilation analysis, we estimate that the single-singlet annihilation rate constant is (6.0 ± 0.2) × 109cm3 s-1 and the singlet diffusion length is -7 nm. From the comparison of femtosecond transient absorption measurements and picosecond fluorescence measurements, it is found that the time profile of the photobleaching signal in the charge-transfer (CT) absorption band coincides with that of the fluorescence intensity and there is no indication of long-lived species, which clearly suggests that charged species, such as polaron pairs and triplet excitons, are not effectively photogenerated in the neat pDPP-TNT polymer.

Hydrolysis of genotoxic methyl-substituted oxiranes : Experimental kinetic and semiempirical studies

The kinetics of acid-catalyzed hydrolysis of seven methylated aliphatic epoxides - R1R2C(O)CR3R4 (A: R1=R2=R3=R4=H; B: R1=R2=R3=H, R4=Me; C: R1=R2=H, R3=R4=Me; D: R1=R3=H, R2=R4=Me(trans); E: R1=R3=H, R2=R4=Me(cis); F: R1=R3=R4=Me, R2=H; G: R1=R2=R3=R4=Me) - has been studied at 36 ± 1.5°C. Compounds with two methyl groups at the same carbon atom of the oxirane ring exhibit highest rate constants (k(eff) in reciprocal molar concentration per second: 11.0 ± 1.3 for C, 10.7 ± 2.1 for F, and 8.7 ± 0.7 for G as opposed to 0.124 ± 0.003 for B, 0.305 ± 0.003 for D, and 0.635 ± 0.036 for E). Ethylene oxide (A) displays the lowest rate of hydrolysis (0.027 M-1 s-1). The results are consistent with literature data available for compounds A, B, and C. To model the reactivities we have employed quantum chemical calculations (MNDO, AM1, PM3, and MINDO/3) of the main reaction species. There is a correlation of the logarithm k(eff) with the total energy of epoxide ring opening. The best correlation coefficients (r) were obtained using the AM1 and MNDO methods (0.966 and 0.957, respectively). However, unlike MNDO, AM1 predicts approximately zero energy barriers for the oxirane ring opening of compounds B, C, E and G, which is not consistent with published kinetic data. Thus, the MNDO method provides a preferential means of modeling the acidic hydrolysis of the series of methylated oxiranes. The general ranking of mutagenicity in vitro, A > B > C, is in line with the concept that this sequence also gradually leaves the expoxide reactivity optimal for genotoxicity toward reactivities leading to higher biological detoxifications.

Competitive interactions of anti-carcinogens with serum albumin: A spectroscopic study of bendamustine and dexamethasone with the aid of chemometrics

Interactions between the anti-carcinogens, bendamustine (BDM) and dexamethasone (DXM), with bovine serum albumin (BSA) were investigated with the use of fluorescence and UV–vis spectroscopies under pseudo-physiological conditions (Tris–HCl buffer, pH 7.4). The static mechanism was responsible for the fluorescence quenching during the interactions; the binding formation constant of the BSA–BDM complex and the binding number were 5.14 × 105 L mol−1 and 1.0, respectively. Spectroscopic studies for the formation of BDM–BSA complex were interpreted with the use of multivariate curve resolution – alternating least squares (MCR–ALS), which supported the complex formation. The BSA samples treated with site markers (warfarin – site I and ibuprofen – site II) were reacted separately with BDM and DXM; while both anti-carcinogens bound to site I, the binding constants suggested that DXM formed a more stable complex. Relative concentration profiles and the fluorescence spectra associated with BDM, DXM and BSA, were recovered simultaneously from the full fluorescence excitation–emission data with the use of the parallel factor analysis (PARAFAC) method. The results confirmed that on addition of DXM to the BDM–BSA complex, the BDM was replaced and the DXM–BSA complex formed; free BDM was released. This finding may have consequences for the transport of these drugs during any anti-cancer treatment.

The harnessing of peptide-monolith constructs for single step plasmid DNA purification

The availability of synthetic peptides has paved the way for their use in tailor-made interactions with biomolecules. In this study, a 16mer LacI-based peptide was used as an affinity ligand to examine the scale up feasibility for plasmid DNA purification. First, the peptide was designed and characterized for the affinity purification of lacO containing plasmid DNA, to be employed as a high affinity ligand for the potential capturing of plasmid DNA in a single unit operation. It was found there were no discernible interactions with a control plasmid that did not encode the lacO nucleotide sequence. The dissociation equilibrium constant of the binding between the 16mer peptide and target pUC19 was 5.0 ± 0.5 × 10-8 M as assessed by surface plasmon resonance. This selectivity and moderated affinity indicate that the 16mer is suitable for the adsorption and chromatographic purification of plasmid DNA. The suitability of this peptide was then evaluated using a chromatography system with the 16mer peptide immobilized to a customized monolith to purify plasmid DNA, obtaining preferential purification of supercoiled pUC19. The results demonstrate the applicability of peptide-monolith supports to scale up the purification process for plasmid DNA using designed ligands via a biomimetic approach.

Binding properties of peptidic affinity ligands for plasmid DNA capture and detection

Peptides constructed from α-helical subunits of the Lac repressor protein (LacI) were designed then tailored to achieve particular binding kinetics and dissociation constants for plasmid DNA purification and detection. Surface plasmon resonance was employed for quantification and characterization of the binding of double stranded Escherichia coli plasmid DNA (pUC19) via the lac operon (lacO) to "biomimics" of the DNA binding domain of LacI. Equilibrium dissociation constants (K D), association (k a), and dissociation rates (k d) for the interaction between a suite of peptide sequences and pUC19 were determined. K D values measured for the binding of pUC19 to the 47mer, 27mer, 16mer, and 14mer peptides were 8.8 ± 1.3 × 10 -10 M, 7.2 ± 0.6 × 10 -10 M, 4.5 ± 0.5 × 10 -8 M, and 6.2 ± 0.9 × 10 -6 M, respectively. These findings show that affinity peptides, composed of subunits from a naturally occurring operon-repressor interaction, can be designed to achieve binding characteristics suitable for affinity chromatography and biosensor devices.

Binding mechanism of affinity ligands for purification of plasmid DNA

Plasmid DNA for therapeutic and vaccination purposes must be highly purified. The high selectivity of affinity chromatography makes it ideal for the isolation of pDNA from complex biological feed stocks. Affinity chromatography makes use of the biological function and/or individual chemical structure of the interacting molecules. However, the success of any affinity purification protocol is dependent on the availability of suitable ligands. In this study, surface plasmon resonance (SPR) based Biacore system has been employed for the detection and quantification of the binding between lac operon (lacO) sequence contained in a pDNA and synthetic peptides based on the DNA-binding domain of the lac repressor protein, lad. The equilibrium dissociation constant (K D) and association and dissociation rate constants (ka, kd) for the interaction between plasmid DNA and designed peptides were determined.

Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation

Wound healing and tumour growth involve collective cell spreading, which is driven by individual motility and proliferation events within a population of cells. Mathematical models are often used to interpret experimental data and to estimate the parameters so that predictions can be made. Existing methods for parameter estimation typically assume that these parameters are constants and often ignore any uncertainty in the estimated values. We use approximate Bayesian computation (ABC) to estimate the cell diffusivity, D, and the cell proliferation rate, λ, from a discrete model of collective cell spreading, and we quantify the uncertainty associated with these estimates using Bayesian inference. We use a detailed experimental data set describing the collective cell spreading of 3T3 fibroblast cells. The ABC analysis is conducted for different combinations of initial cell densities and experimental times in two separate scenarios: (i) where collective cell spreading is driven by cell motility alone, and (ii) where collective cell spreading is driven by combined cell motility and cell proliferation. We find that D can be estimated precisely, with a small coefficient of variation (CV) of 2–6%. Our results indicate that D appears to depend on the experimental time, which is a feature that has been previously overlooked. Assuming that the values of D are the same in both experimental scenarios, we use the information about D from the first experimental scenario to obtain reasonably precise estimates of λ, with a CV between 4 and 12%. Our estimates of D and λ are consistent with previously reported values; however, our method is based on a straightforward measurement of the position of the leading edge whereas previous approaches have involved expensive cell counting techniques. Additional insights gained using a fully Bayesian approach justify the computational cost, especially since it allows us to accommodate information from different experiments in a principled way.

A comprehensive mechanistic kinetic model for dilute acid hydrolysis of switchgrass cellulose to glucose, 5-HMF and levulinic acid

Switchgrass was treated by 1% (w/w) H₂SO₄in batch tube reactors at temperatures ranging from 140–220°C for up to 60 minutes. In this study, release patterns of glucose, 5-hydroxymethylfurfural (5-HMF), and levulinic acid from switchgrass cellulose were investigated through a mechanistic kinetic model. The predictions were consistent with the measured products of interest when new parameters reflecting the effects of reaction limitations, such as cellulose crystallinity, acid soluble lignin–glucose complex (ASL–glucose) and humins that cannot be quantitatively analyzed, were included. The new mechanistic kinetic model incorporating these parameters simulated the experimental data with R² above 0.97. Results showed that glucose yield was most sensitive to variations in the parameter regarding the cellulose crystallinity at low temperatures (140–180°C), while the impact of crystallinity on the glucose yield became imperceptible at elevated temperatures (200–220 °C). Parameters related to the undesired products (e.g. ASL–glucose and humins) were the most sensitive factors compared with rate constants and other additional parameters in impacting the levulinic acid yield at elevated temperatures (200–220°C), while their impacts were negligible at 140–180°C. These new findings provide a more rational explanation for the kinetic changes in dilute acid pretreatment performance and suggest that the influences of cellulose crystallinity and undesired products including ASL–glucose and humins play key roles in determining the generation of glucose, 5-HMF and levulinic acid from biomass-derived cellulose.

Behaviour and strength of hollow flange channel sections under torsion and bending

Hollow flange channel section is a cold-formed high-strength and thin-walled steel section with a unique shape including two rectangular hollow flanges and a slender web. Due to its mono-symmetric characteristics, it will also be subjected to torsion when subjected to transverse loads in practical applications. Past research on steel beams subject to torsion has concentrated on open sections while very few steel design standards give suitable design rules for torsion design. Since the hollow flange channel section is different from conventional open sections, its torsional behaviour remains unknown to researchers. Therefore the elastic behaviour of hollow flange channel sections subject to uniform and non-uniform torsion, and combined torsion and bending was investigated using the solutions of appropriate differential equilibrium equations. The section torsion shear flow, warping normal stress distribution, and section constants including torsion constant and warping constant were obtained. The results were compared with those from finite element analyses that verified the accuracy of analytical solutions. Parametric studies were undertaken for simply supported beams subject to a uniformly distributed torque and a uniformly distributed transverse load applied away from the shear centre. This paper presents the details of this research into the elastic behaviour and strength of hollow flange channel sections subject to torsion and bending and the results.

Validity of BMI as a measure of obesity in Australian white Caucasian and Australian Sri Lankan children

Background: Body mass index (BMI) is used to diagnose obesity. However, its ability to predict the percentage fat mass (%FM) reliably is doubtful. Therefore validity of BMI as a diagnostic tool of obesity is questioned. Aim: This study is focused on determining the ability of BMI-based cut-off values in diagnosing obesity among Australian children of white Caucasian and Sri Lankan origin. Subjects and methods: Height and weight was measured and BMI (W/H2) calculated. Total body water was determined by deuterium dilution technique and fat free mass and hence fat mass derived using age- and gender-specific constants. A %FM of 30% for girls and 20% for boys was considered as the criterion cut-off level for obesity. BMI-based obesity cut-offs described by the International Obesity Task Force (IOTF), CDC/NCHS centile charts and BMI-Z were validated against the criterion method. Results: There were 96 white Caucasian and 42 Sri Lankan children. Of the white Caucasians, 19 (36%) girls and 29 (66%) boys, and of the Sri Lankans 7 (46%) girls and 16 (63%) boys, were obese based on %FM. The FM and BMI were closely associated in both Caucasians (r = 0.81, P<0.001) and Sri Lankans (r = 0.92, P<0.001). Percentage FM and BMI also had a lower but significant association. Obesity cut-off values recommended by IOTF failed to detect a single case of obesity in either group. However, NCHS and BMI-Z cut-offs detected cases of obesity with low sensitivity. Conclusions: BMI is a poor indicator of percentage fat and the commonly used cut-off values were not sensitive enough to detect cases of childhood obesity in this study. In order to improve the diagnosis of obesity, either BMI cut-off values should be revised to increase the sensitivity or the possibility of using other indirect methods of estimating the %FM should be explored.