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.

Dynamics after a sweep through a quantum critical point

The coherent quantum evolution of a one-dimensional many-particle system after slowly sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and nonintegrable regimes. It is known from previous work that universal power laws of the sweep rate appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two different scaling behaviors of the entanglement entropy and a relaxation that is power law in time rather than exponential. The final state of evolution after the quench is not characterized by any effective temperature, and the Loschmidt echo converges algebraically for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.

Hydrophobic Peptide Channels and Encapsulated Water Wires

Peptide nanotubes with filled and empty pores and close-packed structures are formed in closely related pentapeptides. Enantiomorphic sequences, Boc-(D)Pro-Aib-Xxx-Aib-Val-OMe (Xxx = Leu, 1; Val, 2; Ala, 3; Phe, 4) and Boc-Pro-Aib-(D)Xxx-Aib-(D)Val-OMe ((XXX)-X-D = (D)Leu, 5; (D)Val, 6; (D)Ala, 7; (D)Phe, 8), yield molecular structures with a very similar backbone conformation but varied packing patterns in crystals. Peptides 1, 2, 5, and 6 show tubular structures with the molecules self-assembling along the crystallographic six-fold axis (c-axis) and revealing a honeycomb arrangement laterally (ab plane). Two forms of entrapped water wires have been characterized in 2: 2a with d(O center dot center dot center dot O) = 2.6 angstrom and 2b with d(O center dot center dot center dot O) = 3.5 angstrom. The latter is observed in 6 (6a) also. A polymorphic form of 6 (6b), grown from a solution of methanol-water, was observed to crystallize in a monoclinic system as a close-packed structure. Single-file water wire arrangements encapsulated inside hydrophobic channels formed by peptide nanotubes could be established by modeling the published structures in the cases of a cyclic peptide and a dipeptide. In all the entrapped water wires, each water molecule is involved in a hydrogen bond with a previous and succeeding water molecule. The O-H group of the water not involved in any hydrogen bond does not seem to be involved in an energetically significant interaction with the nanotube interior, a general feature of the one-dimensional water wires encapsulated in hydrophobic environements. Water wires in hydrophobic channels are contrasted with the single-file arrangements in amphipathic channels formed by aquaporins.

Modeling and analysis of a tunable piezoelectric structure for transverse shear wave generation

An analytical investigation of the transverse shear wave mode tuning with a resonator mass (packing mass) on a Lead Zirconium Titanate (PZT) crystal bonded together with a host plate and its equivalent electric circuit parameters are presented. The energy transfer into the structure for this type of wave modes are much higher in this new design. The novelty of the approach here is the tuning of a single wave mode in the thickness direction using a resonator mass. First, a one-dimensional constitutive model assuming the strain induced only in the thickness direction is considered. As the input voltage is applied to the PZT crystal in the thickness direction, the transverse normal stress distribution induced into the plate is assumed to have parabolic distribution, which is presumed as a function of the geometries of the PZT crystal, packing mass, substrate and the wave penetration depth of the generated wave. For the PZT crystal, the harmonic wave guide solution is assumed for the mechanical displacement and electric fields, while for the packing mass, the former is solved using the boundary conditions. The electromechanical characteristics in terms of the stress transfer, mechanical impedance, electrical displacement, velocity and electric field are analyzed. The analytical solutions for the aforementioned entities are presented on the basis of varying the thickness of the PZT crystal and the packing mass. The results show that for a 25% increase in the thickness of the PZT crystal, there is ~38% decrease in the first resonant frequency, while for the same change in the thickness of the packing mass, the decrease in the resonant frequency is observed as ~35%. Most importantly the tuning of the generated wave can be accomplished with the packing mass at lower frequencies easily. To the end, an equivalent electric circuit, for tuning the transverse shear wave mode is analyzed.

Theory of laminar flame propagation with non-normal diffusion.

A study has been made of the problem of steady, one-dimensional, laminar flame propagation in premixed gases, with the Lewis number differing from (and equal to) unity. Analytical solutions, using the method of matched asymptotic expansions, have been obtained for large activation energies. Numerical solutions have been obtained for a wide range of the reduced activation temperature parameter (n {geometrically equal to} E/RTb), and the Lewis number δ. The studies reveal that the flame speed eigenvalue is linear in Lewis number for first order and quadratic in Lewis number for second order reactions. For a quick determination of flame speeds, with reasonable accuracy, a simple rule, expressing the flame speed eigenvalue as a function of the Lewis number and the centroid of the reaction rate function, is proposed. Comparisons have been made with some of the earlier works, for both first and second order reactions.

Effect of impulsive change of wall velocity and wall temperature in viscous heat-conducting gas

A study of compression waves produced in a viscous heat-conducting gas by the impulsive start of a one-dimensional piston and by the inpulsive change of piston wall temperature is made using Laplace Transform Technique for Prandt1 number unity. Expressions for velocity, temperature and density have also been obtained using small-time expansion procedure in this case. For arbitrary Prandt1 number solutions have been developed using large-time expansion procedure. A number of graphs exhibiting the distribution of the fluid velocity, temperature and density have been drawn.

Equivalent constitutive model-based design of wave-absorbing material system and controller

A design methodology for wave-absorbing active material system is reported. The design enforces equivalence between an assumed material model having wave-absorbing behavior and a set of target feedback controllers for an array of microelectro-mechanical transducers which are integral part of the active material system. The proposed methodology is applicable to problems involving the control of acoustic waves in passive-active material system with complex constitutive behavior at different length-scales. A stress relaxation type one-dimensional constitutive model involving viscous damping mechanism is considered, which shows asymmetric wave dispersion characteristics about the half-line. The acoustic power flow and asymptotic stability of such material system are studied. A single sensor non-collocated linear feedback control system in a one-dimensional finite waveguide, which is a representative volume element in an active material system, is considered. Equivalence between the exact dynamic equilibrium of these two systems is imposed. It results in the solution space of the design variables, namely the equivalent damping coefficient, the wavelength(s) to be controlled and the location of the sensor. The characteristics of the controller transfer functions and their pole-placement problem are studied. (c) 2005 Elsevier Ltd. All rights reserved.

Long-range synthon Aufbau modules (LSAM) in crystal structures: systematic changes in C6H6-nFn (0 <= n <= 6) fluorobenzenes

We discuss the assembly of a three-dimensional molecular crystal in terms of short-range supramolecular synthons that spontaneously organize themselves according to Aufbau principles into long-range geometries characteristic of the molecules themselves. For this purpose we have examined the systematic changes in the known crystal structures of a family of fluorobenzenes, C6H6-nFn, where 0 <= n <= 6. Crystal assembly is initiated by forming long-range synthon Aufbau modules (LSAM) that carry the imprint of the synthons. For example, when 1 <= n <= 5 the short-range synthons use H center dot center dot center dot F interactions to form the LSAMs. In the n = 0 and n = 6 compounds, the synthons are H center dot center dot center dot C and F center dot center dot center dot C interactions, respectively. The LSAMs are usually one-dimensional. In this study we show that these 1D LSAMs assemble into 2D quasi-hexagonal close-packed layers. The 3D crystal structure is obtained from the various kinds of close-packing known for these 2D layers. The final stages of this 1D -> 2D -> 3D assembly seem to be more influenced by the packing of LSAMs than by any other factor. In these final stages, there may not be so much influence exerted by the stronger short-range synthons. We discuss the evolution of these fluorobenzene crystal structures in terms of putative LSAMs and the purely geometric relationships between the n and (6 - n) compounds that can thus be expected. Such particle-hole pairs show structural similarities. Our discussion is quantified by the interpretation of intermolecular distances in terms of atomic sizes and with qualitative predictions of magnetic model systems.

Long-range synthon Aufbau modules (LSAM) in crystal structures: systematic changes in C6H6-nFn (0 <= n <= 6) fluorobenzenes

We discuss the assembly of a three-dimensional molecular crystal in terms of short-range supramolecular synthons that spontaneously organize themselves according to Aufbau principles into long-range geometries characteristic of the molecules themselves. For this purpose we have examined the systematic changes in the known crystal structures of a family of fluorobenzenes, C6H6-nFn, where 0 <= n <= 6. Crystal assembly is initiated by forming long-range synthon Aufbau modules (LSAM) that carry the imprint of the synthons. For example, when 1 <= n <= 5 the short-range synthons use H center dot center dot center dot F interactions to form the LSAMs. In the n = 0 and n = 6 compounds, the synthons are H center dot center dot center dot C and F center dot center dot center dot C interactions, respectively. The LSAMs are usually one-dimensional. In this study we show that these 1D LSAMs assemble into 2D quasi-hexagonal close-packed layers. The 3D crystal structure is obtained from the various kinds of close-packing known for these 2D layers. The final stages of this 1D -> 2D -> 3D assembly seem to be more influenced by the packing of LSAMs than by any other factor. In these final stages, there may not be so much influence exerted by the stronger short-range synthons. We discuss the evolution of these fluorobenzene crystal structures in terms of putative LSAMs and the purely geometric relationships between the n and (6 - n) compounds that can thus be expected. Such particle-hole pairs show structural similarities. Our discussion is quantified by the interpretation of intermolecular distances in terms of atomic sizes and with qualitative predictions of magnetic model systems.

Structural stability of slender aerospace vehicles: Part I Mathematical modeling

A detailed mechanics based model is developed to analyze the problem of structural instability in slender aerospace vehicles. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic pressure and the propulsive thrust of the vehicle. The model is one-dimensional, and it can be employed to idealized slender vehicles with complex shapes. Condition under which a flexible body with internal stress waves behaves like a perfect rigid body is derived. Two methods are developed for finite element discretization of the system: (1) A time-frequency Fourier spectral finite element method and (2) h-p finite element method. Numerical results using the above methods are presented in Part II of this paper. (C) 2010 Elsevier Ltd. All rights reserved.

Single-File Diffusion of Confined Water Inside SWNTs: An NMR Study

We report a nuclear magnetic resonance (NMR) study of confined water inside similar to 1.4 nm diameter single-walled carbon nanotubes (SWNTs). We show that the confined water does not freeze even up to 223 K. A pulse field gradient (PFG) NMR method is used to determine the mean squared displacement (MSD) of the water molecules inside the nanotubes at temperatures below 273 K, where the bulk water outside the nanotubes freezes and hence does not contribute to the proton NMR signal. We show that the mean squared displacement varies as the square root of time, predicted for single-file diffusion in a one-dimensional channel. We propose a qualitative understanding of our results based on available molecular dynamics simulations.

Hydrogel-assisted synthesis of nanotubes and nanorods of US, ZnS and CuS, showing some evidence for oriented attachment

By carrying out the reaction of appropriate metal compounds with Na2S in the presence of a tripodal cholamide-based hydrogel, nanotubes and nanorods of CdS, ZnS and CuS have been obtained. The nanostructures have been characterized by transmission electron microscopy and spectroscopic techniques. Evidence is presented for the assembly of short nanorods to form one-dimensional chains.

Nonlinear intrinsic instability of solid propellant combustion including gas-phase thermal inertia

The problem of homogeneous solid propellant combustion instability is studied with a one-dimensional flame model, including the effects of gas-phase thermal inertia and nonlinearity. Computational results presented in this paper show nonlinear instabilities inherent in the equations, due to which periodic burning is found even under steady ambient conditions such as pressure. The stability boundary is obtained in terms of Denison-Baum parameters. It is found that inclusion of gas-phase thermal inertia stabilizes the combustion. Also, the effect of a distributed heat release in the gas phase, compared to the flame sheet model, is to destabilize the burning. Direct calculations for finite amplitude pressure disturbances show that two distinct resonant modes exist, the first one near the natural frequency as obtained from intrinsic instability analysis and a second mode occurring at a much higher driving frequency. It is found that er rn in the low frequency region, the response of the propellant is significantly affected by the specific type of gas-phase chemical heat-release model employed. Examination of frequency response function reveals that the role of gas-phase thermal inertia is to stabilize the burning near the first resonant mode. Calculations made for different amplitudes of driving pressure show that the mean burning rate decreases with increasing amplitude. Also, with an increase in the driving amplitude, higher harmonics are generated in the burning rate.

Multiple imaging with an aberration optimized hololens array

The imaging performance of hololenses formed with four different geometries were studied through an analysis of their third-order aberration coefficients. It is found that the geometry proposed by Brandt (1969) gives the least residual aberration with minimum variation of this aberration with the reconstruction angle. When the ideal position of one of the construction beams is changed in order to generate a hololens array, the residual aberration is found to increase sharply, which in turn affects the image resolution among the multiplied images in the output. A hololens array was generated using Brandt's geometry with the help of a one-dimensional sinusoidal grating. The results of multiple imaging with the hololens array are presented. The image resolution is reasonably high and can be further improved by reducing the f-number of the hololenses.

Transport and magnetic properties of conducting polyaniline doped with BX3 (X=F, Cl, and Br)

We report transport and magnetic properties of a different class of highly conducting polyaniline, doped with boron trihalides BX3 (X=F, Cl, and Br). In order to understand the transport mechanism we analyze the temperature dependence of resistivity of a large number of samples, made by pelletizing doped polyaniline powder and by doping films of polyaniline. We find that the charge transport in this class of conducting polyaniline is driven by the charging-energy limited transport of charge carriers, in contrast to the quasi-one-dimensional variable range hopping conduction prevalent in conventional proton-doped polyaniline samples. Magnetic susceptibility provides further insight into the unusually high intrinsic conductivity behavior.