Dynamics of Barrierless and Activated Chemical Reactions in a Dispersive Medium within the Fractional Diffusion Equation Approach

Barrierless chemical reactions have often been modeled as a Brownian motion on a one-dimensional harmonic potential energy surface with a position-dependent reaction sink or window located near the minimum of the surface. This simple (but highly successful) description leads to a nonexponential survival probability only at small to intermediate times but exponential decay in the long-time limit. However, in several reactive events involving proteins and glasses, the reactions are found to exhibit a strongly nonexponential (power law) decay kinetics even in the long time. In order to address such reactions, here, we introduce a model of barrierless chemical reaction where the motion along the reaction coordinate sustains dispersive diffusion. A complete analytical solution of the model can be obtained only in the frequency domain, but an asymptotic solution is obtained in the limit of long time. In this case, the asymptotic long-time decay of the survival probability is a power law of the Mittag−Leffler functional form. When the barrier height is increased, the decay of the survival probability still remains nonexponential, in contrast to the ordinary Brownian motion case where the rate is given by the Smoluchowski limit of the well-known Kramers' expression. Interestingly, the reaction under dispersive diffusion is shown to exhibit strong dependence on the initial state of the system, thus predicting a strong dependence on the excitation wavelength for photoisomerization reactions in a dispersive medium. The theory also predicts a fractional viscosity dependence of the rate, which is often observed in the reactions occurring in complex environments.

The glass transition and crystallization kinetic studies on BaNaB9O15 glasses

Transparent glasses of BaNaB9O15 (BNBO) were fabricated via the conventional melt-quenching technique. The amorphous and the glassy nature of the as-quenched samples were, respectively, confirmed by x-ray powder diffraction and differential scanning calorimetry (DSC). The glass transition and crystallization parameters were evaluated under non-isothermal conditions using DSC. The correlation between the heating rate dependent glass transition and the crystallization temperatures was studied and the Kauzmann temperature was deduced for BNBO glass plates and powdered samples. The values of the Kauzmann temperature for the plates and powdered samples were 776 K and 768 K, respectively. An approximation- free method was used to evaluate the crystallization kinetic parameters for the BNBO glass samples. The effect of the sample thickness on the crystallization kinetics of BNBO glasses was also investigated.

Fractional damping: Stochastic origin and finite approximations

Fractional-order derivatives appear in various engineering applications including models for viscoelastic damping. Damping behavior of materials, if modeled using linear, constant coefficient differential equations, cannot include the long memory that fractional-order derivatives require. However, sufficiently great rnicrostructural disorder can lead, statistically, to macroscopic behavior well approximated by fractional order derivatives. The idea has appeared in the physics literature, but may interest an engineering audience. This idea in turn leads to an infinite-dimensional system without memory; a routine Galerkin projection on that infinite-dimensional system leads to a finite dimensional system of ordinary differential equations (ODEs) (integer order) that matches the fractional-order behavior over user-specifiable, but finite, frequency ranges. For extreme frequencies (small or large), the approximation is poor. This is unavoidable, and users interested in such extremes or in the fundamental aspects of true fractional derivatives must take note of it. However, mismatch in extreme frequencies outside the range of interest for a particular model of a real material may have little engineering impact.

Polymer melt dynamics: Microscopic roots of fractional viscoelasticity

The rheological properties of polymer melts and other complex macromolecular fluids are often successfully modeled by phenomenological constitutive equations containing fractional differential operators. We suggest a molecular basis for such fractional equations in terms of the generalized Langevin equation (GLE) that underlies the renormalized Rouse model developed by Schweizer [J. Chem. Phys. 91, 5802 (1989)]. The GLE describes the dynamics of the segments of a tagged chain under the action of random forces originating in the fast fluctuations of the surrounding polymer matrix. By representing these random forces as fractional Gaussian noise, and transforming the GLE into an equivalent diffusion equation for the density of the tagged chain segments, we obtain an analytical expression for the dynamic shear relaxation modulus G(t), which we then show decays as a power law in time. This power-law relaxation is the root of fractional viscoelastic behavior.

A novel fractional sampling offset estimation in an OFDM system

The Orthogonal Frequency Division Multiplexing (OFDM) is a form of Multi-Carrier Modulation where the data stream is transmitted over a number of carriers which are orthogonal to each other i.e. the carrier spacing is selected such that each carrier is located at the zeroes of all other carriers in the spectral domain. This paper proposes a new novel sampling offset estimation algorithm for an OFDM system in order to receive the OFDM data symbols error-free over the noisy channel at the receiver and to achieve fine timing synchronization between the transmitter and the receiver. The performance of this algorithm has been studied in AWGN, ADSL and SUI channels successfully.

Existence and approximations of solutions to some fractional order functional integral equations

In this paper we shall study a fractional order functional integral equation. In the first part of the paper, we proved the existence and uniqueness of mile and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory oflinear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.

Crystallization and Preliminary X-ray Studies of the Basic Lectin from Winged Bean (Psophocarpus tetragonolobus)

The basic lectin from winged bean (Psophocarpus tetragonolobus) could be crystallized using polyethyleneglycol (PEG) 4000 (I), PEG 8000 (II) and 2-methylpentane-2,4-diol (MPD) (III) as precipitants. Crystal forms I and II grew in the presence of methyl-α-Image -galactopyranoside or N -acetylgalactosamine while III grew in the absence of sugar. The three forms have the same space group (P21212) and similar unit cell dimensions with two dimeric molecules in the asymmetric unit. The unit cell dimensions are a = 156·8 Å, b = 89·0 Å, c = 73·3 Å for I, a = 155·5 Å, b = 92·3 Å, c = 72·5 Å for II and a = 148·3 Å, b = 90·7 Å, c = 73·8 Å for III. The crystals, particularly those grown using PEG 8000, are suitable for high resolution X-ray analysis, which is in progress.

A novel fractional sampling offset estimation in an OFDM system

The Orthogonal Frequency Division Multiplexing (OFDM) is a form of Multi-Carrier Modulation where the data stream is transmitted over a number of carriers which are orthogonal to each other i.e. the carrier spacing is selected such that each carrier is located at the zeroes of all other carriers in the spectral domain. This paper proposes a new novel sampling offset estimation algorithm for an OFDM system in order to receive the OFDM data symbols error-free over the noisy channel at the receiver and to achieve fine timing synchronization between the transmitter and the receiver. The performance of this algorithm has been studied in AWGN, ADSL and SUI channels successfully.

The Role of Interface Modification on Thermal Degradation and Crystallization Behavior of Composites from Commingled Polypropylene Fiber and Banana Fiber

The thermal degradation behavior of banana fiber and polypropylene/banana fiber composites has been studied by thermogravimetric analysis. Banana fiber was found to be decomposing in two stages, first one around 320 degrees C and the second one around 450 degrees C. For chemically treated banana fiber, the decomposition process has been at a higher temperature, indicating thermal stability for the treated fiber. Activation energies for thermal degradation were estimated using Coats and Redfern method. Calorific value of the banana fiber was measured using a constant volume isothermal bomb calorimeter. rystallization studies exhibited an increase in the crystallization temperature and crystallinity of polypropylene upon the addition of banana fiber. POLYM. COMPOS., 31:1113-1123, 2010. (C) 2009 Society of Plastics Engineers.

Analysis of multiple crystal forms of Bacillus subtilis BacB suggests a role for a metal ion as a nucleant for crystallization

Bacillus subtilis BacB is an oxidase that is involved in the production of the antibiotic bacilysin. This protein contains two double-stranded beta-helix (cupin) domains fused in a compact arrangement. BacB crystallizes in three crystal forms under similar crystallization conditions. An interesting observation was that a slight perturbation of the crystallization droplet resulted in the nucleation of a different crystal form. An X-ray absorption scan of BacB suggested the presence of cobalt and iron in the crystal. Here, a comparative analysis of the different crystal forms of BacB is presented in an effort to identify the basis for the different lattices. It is noted that metal ions mediating interactions across the asymmetric unit dominate the different packing arrangements. Furthermore, a normalized B-factor analysis of all the crystal structures suggests that the solvent-exposed metal ions decrease the flexibility of a loop segment, perhaps influencing the choice of crystal form. The residues coordinating the surface metal ion are similar in the triclinic and monoclinic crystal forms. The coordinating ligands for the corresponding metal ion in the tetragonal crystal form are different, leading to a tighter packing arrangement. Although BacB is a monomer in solution, a dimer of BacB serves as a template on which higher order symmetrical arrangements are formed. The different crystal forms of BacB thus provide experimental evidence for metal-ion-mediated lattice formation and crystal packing.

Approximation of solutions to fractional integral equation

In this paper we shall study a fractional integral equation in an arbitrary Banach space X. We used the analytic semigroups theory of linear operators and the fixed point method to establish the existence and uniqueness of solutions of the given problem. We also prove the existence of global solution. The existence and convergence of the Faedo–Galerkin solution to the given problem is also proved in a separable Hilbert space with some additional assumptions on the operator A. Finally we give an example to illustrate the applications of the abstract results.

Cloning, expression, purification, crystallization and preliminary X-ray crystallographic study of the putative SAICAR synthetase (PH0239) from Pyrococcus horikoshii OT3

The study of proteins involved in de novo biosynthesis of purine nucleotides is central in the development of antibiotics and anticancer drugs. In view of this, a protein from the hyperthermophile Pyrococcus horikoshii OT3 was isolated, purified and crystallized using the microbatch method. Its primary structure was found to be similar to that of SAICAR synthetase, which catalyses the seventh step of de novo purine biosynthesis. A diffraction-quality crystal was obtained using Hampton Research Crystal Screen II condition No. 34, consisting of 0.05 M cadmium sulfate hydrate, 0.1 M HEPES buffer pH 7.5 and 1.0 M sodium acetate trihydrate, with 40%(v/v) 1,4-butanediol as an additive. The crystal belonged to space group P3(1), with unit-cell parameters a = b = 95.62, c = 149.13 angstrom. Assuming the presence of a hexamer in the asymmetric unit resulted in a Matthews coefficient (V-M) of 2.3 angstrom(3) Da(-1), corresponding to a solvent content of about 46%. A detailed study of this protein will yield insights into structural stability at high temperatures and should be highly relevant to the development of antibiotics and anticancer drugs targeting the biosynthesis of purine nucleotides.

Deformation and crystallization of Zr-based amorphous alloys in homogeneous flow regime

The purpose of this study is to experimentally investigate the interaction of inelastic deformation and microstructural changes of two Zr-based bulk metallic glasses (BMGs): Zr41.25Ti13.75Cu12.5Ni10Be22.5 (commercially designated as Vitreloy 1 or Vit1) and Zr46.75Ti8.25Cu7.5Ni10Be27.5 (Vitreloy 4, Vit4). High-temperature uniaxial compression tests were performed on the two Zr alloys at various strain rates, followed by structural characterization using differential scanning calorimetry (DSC) and transmission electron microscopy (TEM). Two distinct modes of mechanically induced atomic disordering in the two alloys were observed, with Vit1 featuring clear phase separation and crystallization after deformation as observed with TEM, while Vit4 showing only structural relaxation with no crystallization. The influence of the structural changes on the mechanical behaviors of the two materials was further investigated by jump-in-strain-rate tests, and flow softening was observed in Vit4. A free volume theory was applied to explain the deformation behaviors, and the activation volumes were calculated for both alloys.

Kinetics of two-stage crystallization in Metglas 2826A

Crystallization kinetics of MSI and MSII stages in Metglas 2826A has been investigated by quantitative transmission electron microscopy. The volume fraction of crystallization against time curve has been found to show a plateau in the lower temperature region of annealing. It has been found that the glass transition temperature, T g, has no effect on the sequence reversal of the crystallization reaction. It has been shown that the sequence reversal of transformation stages occurs due to the large difference in the activation energy of crystallization of MSI and MSII. In addition, the change in the morphology of the crystals obtained by annealing the amorphous alloy below and above the glass transition temperature, T g, is reported.