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.

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.

Unfolding of Plasmodium falciparum Triosephosphate Isomerase in Urea and Guanidinium Chloride: Evidence for a Novel Disulfide Exchange Reaction in a Covalently Cross-Linked Mutant†

The conformational stability of Plasmodium falciparum triosephosphate isomerase (TIMWT) enzyme has been investigated in urea and guanidinium chloride (GdmCl) solutions using circular dichroism, fluorescence, and size-exclusion chromatography. The dimeric enzyme is remarkably stable in urea solutions. It retains considerable secondary, tertiary, and quaternary structure even in 8 M urea. In contrast, the unfolding transition is complete by 2.4 M GdmCl. Although the secondary as well as the tertiary interactions melt before the perturbation of the quaternary structure, these studies imply that the dissociation of the dimer into monomers ultimately leads to the collapse of the structure, suggesting that the interfacial interactions play a major role in determining multimeric protein stability. The C-m(urea)/C-m(GdmCl) ratio (where C-m is the concentration of the denaturant required at the transition midpoint) is unusually high for triosephosphate isomerase as compared to other monomeric and dimeric proteins. A disulfide crosslinked mutant protein (Y74C) engineered to form two disulfide cross-links across the interface (13-74') and (13'-74) is dramatically destablized in urea. The unfolding transition is complete by 6 M urea and involves a novel mechanism of dimer dissociation through intramolecular thiol-disulfide exchange.

N-H center dot center dot center dot O and C-H center dot center dotcenter dot O interaction mimicry in the 1:1 molecular complexes of 5,5-diethylbarbituric acid with urea and acetamide

The analogy between N-H center dot center dot center dot O and C-H center dot center dot center dot O intermolecular interactions is studied with variable temperature (180-100 K) single crystal X-ray diffraction analysis.5,5-Diethylbarbituric acid (barbital) forms isostructural molecular complexes (co-crystals) with urea (1) and acetamide (2) that respectively contain these analogous interactions.The behaviour of these two interactions as a function of temperature is very similar. This indicates that the C-H center dot center dot center dot O bond in barbital acetamide plays a similar chemical and structural role as does the N-H center dot center dot center dot O bond in barbital urea. The close relationship between these interactions and their comparable nature is further adduced from the formation of a ternary solid solution (3) of barbital, urea and acetamide. The fact that the C-H center dot center dot center dot O interaction in barbital acetamide is weaker than the N-H center dot center dot center dot O interaction in barbital urea is shown by the fact that acetamide is under expressed and urea is over expressed with respect to the quantities of these substances present in solution prior to crystallization of these ternary crystals.

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.

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.

Synthesis and Antileukemic Activity of 1-((S)-2-Amino-4,5,6,7-tetrahydrobenzo[d]thiazol-6-yl)-3-(substituted phenyl)urea Derivatives

Heterocyclic urea derivatives play an important role as anticancer agents because of their good inhibitory activity against receptor tyrosine kinases (RTKs), raf kinases, protein tyrosine kinases (PTKs), and NADH oxidase, which play critical roles in many aspects of tumorigenesis. Benzothiazole moiety constitutes an important scaffold of drugs, possessing several pharmacological functions, mainly the anticancer activity. Based on these interesting properties of benzothiazoles and urea moiety to obtain new biologically active agents, we synthesized a series of novel 1-((S)-2-amino-4,5,6.7-tetrahydrobenzo[d]thiazol-6-yl)-3-(substituted phenyl)urea derivatives and evaluated for their efficacy as antileukemic agents against two human leukemic cell lines (K562 and Reh). These compounds showed good and moderate cytotoxic effect to cancer cell lines tested. Compounds with electron-withdrawing chloro and fluoro substituents on phenyl ring showed good activity and compounds with electron-donating methoxy group showed moderate activity. Compound with electron-withdrawing dichloro substitution on phenyl ring of aryl urea showed good activity. Further, lactate dehydrogenase (LDH) assay, flow cytometric analysis of annexin V-FITC/propidium iodide (PI) double staining and DNA fragmentation studies showed that compound with dichloro substitution on phenyl ring of aryl urea can induce apoptosis.

Electrochemical reduction of oxygen on gold and boron-doped diamond electrodes in ambient temperature, molten acetamide-urea-ammonium nitrate eutectic melt

The electrochemical reduction of oxygen has been studied on gold, boron-doped diamond (BDD) and glassy carbon (GC) electrodes in a ternary eutectic mixture of acetamide (CH3CONH2), urea (NH2CONH2) and ammonium nitrate (NH4NO3). Cyclic voltammetry (CV), differential pulse voltammetry (DPV), chronoamperometry and rotating disk electrode (RDE) voltammetry techniques have been employed to follow oxygen reduction reaction (ORR). The mechanism for the electrochemical reduction of oxygen on polycrystalline gold involves 2-step. 2-electron pathways of O-2 to H2O2 and further reduction of H2O2 to H2O. The first 2-electron reduction of O-2 to H2O2 passes through superoxide intermediate by 1-electron reduction of oxygen. Kinetic results suggest that the initial 1-electron reduction of oxygen to HO2 is the rate-determining step of ORR on gold surfaces. The chronoamperometric and ROE studies show a potential dependent change in the number of electrons on gold electrode. The oxygen reduction reaction on boron-doped diamond (BOO) seems to proceed via a direct 4-electron process. The reduction of oxygen on the glassy carbon (GC) electrode is a single step, irreversible, diffusion limited 2-electron reduction process to peroxide. (C) 2010 Elsevier Ltd. All rights reserved.

Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton

According to Wen's theory, a universal behavior of the fractional quantum Hall edge is expected at sufficiently low energies, where the dispersion of the elementary edge excitation is linear. A microscopic calculation shows that the actual dispersion is indeed linear at low energies, but deviates from linearity beyond certain energy, and also exhibits an "edge roton minimum." We determine the edge exponent from a microscopic approach, and find that the nonlinearity of the dispersion makes a surprisingly small correction to the edge exponent even at energies higher than the roton energy. We explain this insensitivity as arising from the fact that the energy at maximum spectral weight continues to show an almost linear behavior up to fairly high energies. We also study, in an effective-field theory, how interactions modify the exponent for a reconstructed edge with multiple edge modes. Relevance to experiment is discussed.

Fractional-factorial design of a porous-carbon fuel-cell electrode

The use of fractional-factorial methods in the optimization of porous-carbon electrode structure is discussed with respect to weight-loss of carbon during gas treatment, weight and mixing time of binder, compaction temperature, time and pressure, and pressure of feed gas. The experimental optimization of an air electrode in alkaline solution is described.

Analysis of clearance fit pin joints

The analysis of clearance fit joints falls within the realm of mixed boundary problems with moving boundaries. In this paper, this problem is solved by a simple continuum method of analysis applying an inverse technique; the region of contact is specified and the corresponding causative load is evaluated. Illustrations are given for a rigid clearance fit pin in a large elastic plate with smooth zero-shear interface between pin and plate, under biaxial plate stress at infinity and due to load transfer through pin.