Molecular theory of dielectric relaxation in a dense binary dipolar liquid

A molecular theory of dielectric relaxation in a dense binary dipolar liquid is presented. The theory takes into account the effects of intra- and interspecies intermolecular interactions. It is shown that the relaxation is, in general, nonexponential. In certain limits, we recover the biexponential form traditionally used to analyze the experimental data of dielectric relaxation in a binary mixture. However, the relaxation times are widely different from the prediction of the noninteracting rotational diffusion model of Debye for a binary system. Detailed numerical evaluation of the frequency-dependent dielectric function epsilon-(omega) is carried out by using the known analytic solution of the mean spherical approximation (MSA) model for the two-particle direct correlation function for a polar mixture. A microscopic expression for both wave vector (k) and frequency (omega) dependent dielectric function, epsilon-(k,omega), of a binary mixture is also presented. The theoretical predictions on epsilon-(omega) (= epsilon-(k = 0, omega)) have been compared with the available experimental results. In particular, the present theory offers a molecular explanation of the phenomenon of fusing of the two relaxation channels of the neat liquids, observed by Schallamach many years ago.

Remark on factorials that are products of factorials

In a paper published in 1993, Erdos proved that if n! = a! b!, where 1 < a a parts per thousand currency sign b, then the difference between n and b does not exceed 5 log log n for large enough n. In the present paper, we improve this upper bound to ((1 + epsilon)/ log 2) log log n and generalize it to the equation a (1)!a (2)! ... a (k) ! = n!. In a recent paper, F. Luca proved that n - b = 1 for large enough n provided that the ABC-hypothesis holds.

Enhancement of fatigue life of Ni-Ti-Fe shape memory alloys by thermal cycling

The effect of thermal cycling on the load-controlled tension-tension fatigue behavior of a Ni-Ti-Fe shape memory alloy (SMA) at room temperature was studied. Considerable strain accumulation was observed to occur in this alloy under both quasi-static and cyclic loading conditions. Though, in all cases, steady-state is reached within the first 50-100 cycles, the accumulated steady-state strain, epsilon(p.ss), is much smaller in thermally cycled alloy. As a result, the fatigue performance of them was found to be significantly enhanced vis-a-vis the as-solutionized alloy. Furthermore, under load-controlled conditions, the fatigue life of Ni-Ti-Fe alloys was found to be exclusively dependent on epsilon(p.ss). Observations made by profilometry and differential scanning calorimetry (DSC) indicate that the 200-500% enhancement in fatigue life of thermally cycled alloy is due to the homogeneous distribution of the accumulated fatigue strain. (C) 2010 Elsevier B.V. All rights reserved.

Structural features of B-DNA dodecamer crystal structures: Influence of crystal packing versus base sequence

We have analyzed the set of inter and intra base pair parameters for each dinucleotide step in single crystal structures of dodecamers, solved at high and medium resolution and all crystallized in P2(1)2(1)2(1) space group. The objective was to identify whether all the structures which have either the Drew-Dickerson (DD) sequence d[CGCGAATTCGCG] with some base modification or related sequence (non-DD), would display the same sequence dependent structural variability about its palindromic sequence, despite the molecule being bent at one end because of similar crystal lattice packing effect. Most of the local doublet parameters for base pairs steps G2-C3 and G10-C11 positions, symmetrically situated about the lateral twofold, were significantly correlated between themselves. In non-DD sequences, significant correlations between these positional parameters were absent. The different range of local step parameter values at each sequence position contributed to the gross feature of smooth helix axis bending in all structures. The base pair parameters in some of the positions, for medium resolution DD sequence, were quite unlike the high-resolution set and encompassed a higher range of values. Twist and slide are the two main parameters that show wider conformational range for the middle region of non-DD sequence structures in comparison to DD sequence structures. On the contrary, the minor and major groove features bear good resemblance between DD and non-DD sequence crystal structure datasets. The sugar-phosphate backbone torsion angles are similar in all structures, in sharp contrast to base pair parameter variation for high and low resolution DD and non-DD sequence structures, consisting of unusual (epsilon =g(-), xi =t) B-II conformation at the 10(th) position of the dodecamer sequence. Thus examining DD and non-DD sequence structures packed in the same crystal lattice arrangement, we infer that inter and intra base pair parameters are as symmetrically equivalent in its value as the symmetry related step for the palindromic DD sequence about lateral two-fold axis. This feature would lead us to agree with the conclusion that DNA conformation is not substantially affected by end-to-end or lateral inter-molecular interaction due to crystal lattice packing effect. Non-DD sequence structures acquire step parameter values which reflect the altered sequence at each of the dodecamer sequence position in the orthorhombic lattice while showing similar gross features of DD sequence structures

Relaxation system based sub-grid scale modelling for large eddy simulation of Burgers' equation

An implicit sub-grid scale model for large eddy simulation is presented by utilising the concept of a relaxation system for one dimensional Burgers' equation in a novel way. The Burgers' equation is solved for three different unsteady flow situations by varying the ratio of relaxation parameter (epsilon) to time step. The coarse mesh results obtained with a relaxation scheme are compared with the filtered DNS solution of the same problem on a fine mesh using a fourth-order CWENO discretisation in space and third-order TVD Runge-Kutta discretisation in time. The numerical solutions obtained through the relaxation system have the same order of accuracy in space and time and they closely match with the filtered DNS solutions.

DNA Polymerase-β from the pupal ovaries of bombyx mori

The silk glands of Bombyx mori, a highly replicative tissue contains high levels of DNA polymerases α, σ and epsilon (Porson) but not DNA polymerase-β. However, we detected the latter activity in the gonadal tissues, viz. the pupal ovaries and testes of B. mori. The enzyme has been purified to homogeneity from the pupal ovaries by a series of column chromatographic and affinity purification steps. The enzyme satisfied the criteria to be designated as DNA polymerase-β based on its small size, requirement for high concentration of monovalent cations for catalytic activity, sensitivity to ddTTP and insensitivity to aphidicolin. It is a monomeric polypeptide of Mr 40 kDa, and the Km for dNTPs ranges between 8–20 μM. DNA polymerase-β is biochemically and immunologically distinct from DNA polymerase-α from the silk glands of B. mori. The enzyme showed a preference for gapped DNA, and could not elongate ultraviolet irradiated template beyond the pyrimidine dimers. The absence of any associated primase and exonuclease activities from this enzyme, and its conspicuous absence in the highly replicative tissue, imply that it is unlikely to participate in the DNA endoreplication process.

Effect of tolerance on the propagation characteristic of a superconducting thin film microstrip delay line

The propagation constant of a superconducting microstrip transmission delay line is evaluated using the spectral domain immitance approach, modelling the superconductor as a surface current having an equivalent surface impedance found through the complex resistive boundary condition. The sensitivity approach is used to study the beta variations with substrate parameters and film characteristics. Results show that the surface impedance does not have much influence on beta sensitivities with respect to epsilon r, W and h. However, it can be observed that the surface impedance plays a crucial role in determining the optimum design.

Exact analysis of Burgers equation on semiline with flux condition at the origin

The initial boundary value problem for the Burgers equation in the domain x greater-or-equal, slanted 0, t > 0 with flux boundary condition at x = 0 has been solved exactly. The behaviour of the solution as t tends to infinity is studied and the “asymptotic profile at infinity” is obtained. In addition, the uniqueness of the solution of the initial boundary value problem is proved and its inviscid limit as var epsilon → 0 is obtained.

Simultaneous measurement of strain and temperature with a pair of matched fiber Bragg gratings

A novel approach for simultaneous measurement of static/dynamic strain and temperature with a pair of matched fiber Bragg grating(FBG)s is proposed. When a diode laser locked to the mid reflection frequency of reference FBG is used to illuminate the sensor FBG, reflected intensity changes with strain on sensor FBG. Reference FBG responds with temperature on sensor FBG and is immune to strain, hence, wavelength of the diode laser acts as a signature for temperature measurement. Theoretical sensitivity limit for static strain and temperature are 1.2n epsilon / root Hz and 0.0011 degrees C respectively. Proposed sensor shows a great potential in high sensitive strain measurements with a simplified experimental setup.

High sensitive Static fiber Bragg grating strain sensing using lasers locked to relative frequency reference

A novel high sensitive fiber Bragg grating (FBG) strain sensing technique using lasers locked to relative frequency reference is proposed and analyzed theoretically. Static strain on FBG independent of temperature can be measured by locking frequency of diode laser to the mid reflection frequency of matched reference FBG, which responds to temperature similar to that of the sensor FBG, but is immune to strain applied to the same. Difference between light intensities reflected from the sensor and reference FBGs (proportional to the difference between respective pass band gains at the diode laser frequency) is not only proportional to the relative strain between the sensor and reference FBGs but also independent of servo residual frequency errors. Usage of relative frequency reference avoids all complexities involved in the usage of absolute frequency reference, hence, making the system simple and economical. Theoretical limit for dynamic and static strain sensitivities considering all major noise contributions are of the order of 25 (p epsilon) / root Hz and 1.2 n epsilon / root Hz respectively.

The Design and Construction of Synthetic Protein Mimics

A strategy for the modular construction of synthetic protein mimics based on the ability non-protein amino acids to act as stereochemical directors of polypeptide chain folding, is described. The use of alpha-aminoisobutyric acid (Aib) to construct stereochemically rigid helices has been exemplified by crystallographic and spectroscopic studies of several apolar peptides, ranging in length from seven to sixteen residues. The problem of linker design in elaborating alpha,alpha motifs has been considered. Analysis of protein crystal structure data provides a guide to choosing linking sequences. Attempts at constructing linked helical motifs using linking Gly-Pro segments have been described. The use of flexible linkers, like epsilon-aminocaproic acid has been examined and the crystallographic and solution state analysis of a linked helix motif has been presented. The use of bulky sidechain modifications on a helical scaffold, as a means of generating putative binding sites has been exemplified by a crystal structure of a peptide packed in a parallel zipper arrangement.

(Ba3MTiMO9)-Ti-III-O-V (M-III = Fe, Ga, Y, Lu, M-V = Nb, Ta, Sb) perovskite oxides Synthesis, structure and dielectric properties

We describe the synthesis structures and dielectric properties of new perovskite oxides of the formula (Ba3MTiMO9)-Ti-III-O-V for M-III = Fe Ga Y Lu and M-V = Nb Ta Sb While M-V = Nb and Ta oxides adopt disordered/partially ordered 3C perovskite structures where M-III/Ti/M-V metal-oxygen octahedra are corner connected the M-V = Sb oxides show a distinct preference for the 6H structure where Sb-V/Ti-IV metal-oxygen octahedra share a common face forming (Sb Ti)O-9 dimers that are corner-connected to the (MO6)-O-III octahedra The preference of antimony oxides (Sb-V 4d(10)) for the 6H structure which arises from a special Sb-V-O chemical bonding that tends to avoid linear Sb-O-Sb linkages unlike Nb-V/Ta-V d(0) atoms which prefer similar to 180 degrees Nb/Ta-O-Nb/Ta linkages - is consistent with the crystal chemistry of M-V-O oxides in general The dielectric properties reveal a significant difference among Mill members All the oxides with the 3C structure excepting those with Mill = Fe show a normal low loss dielectric behaviour with epsilon = 20-60 in the temperature range 50-400 degrees C the M-III = Fe members with this structure (M-V = Nb Ta) display a relaxor-like ferroelectric behaviour with large E values at frequencies <= 1 MHz (50-500 degrees C) (C) 2010 Elsevier Masson SAS All rights reserved

Boxicity and Poset Dimension

Let G be a simple, undirected, finite graph with vertex set V(G) and edge set E(C). A k-dimensional box is a Cartesian product of closed intervals a(1), b(1)] x a(2), b(2)] x ... x a(k), b(k)]. The boxicity of G, box(G) is the minimum integer k such that G can be represented as the intersection graph of k-dimensional boxes, i.e. each vertex is mapped to a k-dimensional box and two vertices are adjacent in G if and only if their corresponding boxes intersect. Let P = (S, P) be a poset where S is the ground set and P is a reflexive, anti-symmetric and transitive binary relation on S. The dimension of P, dim(P) is the minimum integer l such that P can be expressed as the intersection of t total orders. Let G(P) be the underlying comparability graph of P. It is a well-known fact that posets with the same underlying comparability graph have the same dimension. The first result of this paper links the dimension of a poset to the boxicity of its underlying comparability graph. In particular, we show that for any poset P, box(G(P))/(chi(G(P)) - 1) <= dim(P) <= 2box(G(P)), where chi(G(P)) is the chromatic number of G(P) and chi(G(P)) not equal 1. The second result of the paper relates the boxicity of a graph G with a natural partial order associated with its extended double cover, denoted as G(c). Let P-c be the natural height-2 poset associated with G(c) by making A the set of minimal elements and B the set of maximal elements. We show that box(G)/2 <= dim(P-c) <= 2box(G) + 4. These results have some immediate and significant consequences. The upper bound dim(P) <= 2box(G(P)) allows us to derive hitherto unknown upper bounds for poset dimension. In the other direction, using the already known bounds for partial order dimension we get the following: (I) The boxicity of any graph with maximum degree Delta is O(Delta log(2) Delta) which is an improvement over the best known upper bound of Delta(2) + 2. (2) There exist graphs with boxicity Omega(Delta log Delta). This disproves a conjecture that the boxicity of a graph is O(Delta). (3) There exists no polynomial-time algorithm to approximate the boxicity of a bipartite graph on n vertices with a factor of O(n(0.5-epsilon)) for any epsilon > 0, unless NP=ZPP.

Lattice embedding and equilibrium geometry of metal-halogen chains in the two-band extended Hubbard model

Two-band extended Hubbard model studies show that the shift in optical gap of the metal-halogen (MX) chain upon embedding in a crystalline environment depends upon alternation in the site-diagonal electron-lattice interaction parameter (epsilon(M)) and the strength of electron-electron interactions at the metal site (U(M)). The equilibrium geometry studies on isolated chains show that the MX chains tend to distort for alternating epsilon(M) and small U(M) values.

DNA polymerase alpha-primase complex from the silk glands of the non-mulberry silkworm Philosamia ricini.

The DNA content in the silk glands of the non-mulberry silkworm Philosamia ricini increases continuously during the fourth and fifth instars of larval development indicating high levels of DNA replication in this terminally differentiated tissue. Concomitantly, the DNA polymerase alpha activity also increases in the middle and the posterior silk glands during development, reaching maximal levels in the middle of the fifth larval instar. A comparable level of DNA polymerase delta/epsilon was also observed in this highly replicative tissue. The DNA polymerase alpha-primase complex from the silk glands of P. ricini has been purified to homogeneity by conventional column chromatography as well as by immunoaffinity techniques. The molecular mass of the native enzyme is 560 kDa and the enzyme comprises six non-identical subunits. The identity of the enzyme as DNA polymerase alpha has been established by its sensitivity to inhibitors such as aphidicolin, N-ethylmaleimide, butylphenyl-dGTP, butylanilino-dATP and antibodies to polymerase alpha. The enzyme possesses primase activity capable of initiating DNA synthesis on single-stranded DNA templates. The tight association of polymerase and primase activities at a constant ratio of 6:1 is observed through all the purification steps. The 180 kDa subunit harbours the polymerase activity, while the primase activity is associated with the 45 kDa subunit.