Spontaneous generation of optical activity in urea inclusion compounds vis-a-vis current theories

A novel test of recent theories of the origin of optical activity has been designed based on the inclusion of certain alkyl 2-methylhexanoates into urea channels.

Solution of a System of Generalized Abel Integral Equations Using Fractional Calculus

A method is presented for obtaining useful closed form solution of a system of generalized Abel integral equations by using the ideas of fractional integral operators and their applications. This system appears in solving certain mixed boundary value problems arising in the classical theory of elasticity.

Homogeneous precipitation from solution by urea hydrolysis: a novel chemical route to the a-hydroxides of nickel and cobalt

Homogeneous precipitation from solution by hydrolysis of urea at elevated temperatures (T=120 degrees C) yields novel ammonia-intercalated alpha-type hydroxide phases of the formula M(OH)(x)(NH3)(0.4)(H2O)(y)(NO3)(2-x) where x=2, y=0.68 for M=Ni and x=1.85, y=0 for M=Co. These triple-layered hexagonal phases (a=3.08+/-0.01 Angstrom, c=21.7+/-0.05 Angstrom) are more crystalline than similar phases obtained by chemical precipitation or electrosynthesis. This method can be adapted as a convenient chemical route to the bulk synthesis of alpha-hydroxides.

Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33 degrees of freedom vibrating systems with fractional dampers. Limited studies have also been conducted by combining finite element modeling with experimental data on accelerances measured in laboratory conditions on a system consisting of two steel beams rigidly joined together by a rubber hose. The method based on sensitivity of frequency response functions is shown to be more efficient than the eigensensitivity based method in identifying system parameters, especially for large scale systems.

Fractional power dependence of rate on activation energy for reactions with very low internal barriers

The dynamics of reactions with low internal barriers are studied both analytically and numerically for two different models. Exact expressions for the average rate,kI, are obtained by solving the associated first passage time problems. Both the average rate constant, kI, and the numerically calculated long-time rate constant, kL, show a fractional power law dependence on the barrier height for very low barriers. The crossover of the reaction dynamics from low to high barrier is investigated.

Water stress induced alterations in ornithine aminotransferase of ragi (Eleusine coracana): Protection by proline against heat inactivation and denaturation by urea and guanidinium chloride

Water stress resulted in a specific response leading to a large and significant increase (80-fold) in free proline content of ragi (Eleusine coracana) leaves and seedlings. L-Proline protected ornithine aminotransferase, an enzyme in the pathway for proline biosynthesis, isolated from normal and stressed ragi leaves against heat inactivation and denaturation by urea and guanidinium chloride. The protection of the stressed enzyme by L-proline was much more complete than that of the enzyme isolated from normal leaves. While L-ornithine, one of the substrates, protected the stressed enzyme against inactivation, it enhanced the rate of inactivation of the normal enzyme. α-Ketoglutarate protected both the normal and stressed enzyme against inactivation and denaturation. These results support the suggestion that ornithine aminotransferase has undergone a structural alteration during water stress. In view of the causal relationship between elevated temperature and water stress of plants under natural conditions, the protection afforded by proline against inactivation and denaturation of the enzyme from stressed leaves assumes significance. These results provide an explanation for a possible functional importance of proline accumulation during water stress.

A comprehensive study of interference and clearance fit pins in large plates

Pin joints in structures are designed for interference, push or clearance fits. That is, the diameter of the pin is made greater than, equal to or less than the hole diameter. Consider an interference fit pin in a plate subjected to a continuously increasing in-plane load.

Beyond fractional derivatives: local approximation of other convolution integrals

Dynamic systems involving convolution integrals with decaying kernels, of which fractionally damped systems form a special case, are non-local in time and hence infinite dimensional. Straightforward numerical solution of such systems up to time t needs O(t(2)) computations owing to the repeated evaluation of integrals over intervals that grow like t. Finite-dimensional and local approximations are thus desirable. We present here an approximation method which first rewrites the evolution equation as a coupled in finite-dimensional system with no convolution, and then uses Galerkin approximation with finite elements to obtain linear, finite-dimensional, constant coefficient approximations for the convolution. This paper is a broad generalization, based on a new insight, of our prior work with fractional order derivatives (Singh & Chatterjee 2006 Nonlinear Dyn. 45, 183-206). In particular, the decaying kernels we can address are now generalized to the Laplace transforms of known functions; of these, the power law kernel of fractional order differentiation is a special case. The approximation can be refined easily. The local nature of the approximation allows numerical solution up to time t with O(t) computations. Examples with several different kernels show excellent performance. A key feature of our approach is that the dynamic system in which the convolution integral appears is itself approximated using another system, as distinct from numerically approximating just the solution for the given initial values; this allows non-standard uses of the approximation, e. g. in stability analyses.

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.