Rate processes with dynamical disorder: a direct variational approach

Using path integral approach, we develop variational approximations to the calculation of survival probability for rate processes with dynamical disorder. We derive both upper and lower bounds to the survival probability using Jensen's inequality. The inequalities involve the use of a trial action for which the path integrals can be evaluated exactly. Any parameter in the trial action can be varied to optimize the bounds. We have also derived a lower bound to the rate of the process. As a simple illustration, we apply the method to the problem of a particle undergoing Brownian motion in a harmonic potential well, in the presence of a delta function sink, for which one can calculate the exact survival probability numerically. The calculation confirms the two inequalities. The method should be very useful in similar but more complex problems where even numerical solution is not possible.     

Spectrally resolved phase-shifting interferometry for accurate group-velocity dispersion measurements

We report an accurate method to measure the group-velocity dispersion (GVD) of transparent materials by use of spectrally resolved phase-shifting interferometry. The GVD of silica glass slide measured using an eight-step phase-shifting algorithm agrees well with that calculated using the Sellmeier dispersion equation over the entire visible wavelength region, with a rms error of < or =0.0036 microm(-2), better than that of other measurement methods reported so far.     

Correspondence between Yang-Mills Condensate Dark Energy with Various Kinds of Scalar Field Models of Dark Energy

In this work, we study a new kind of dark energy (DE), which is named as "Yang-Mills condensate" (YMC). We study the stability and w_de-w'_de analysis of YMC DE model. Then we correspond it with quintessence, k-essence, tachyon, phantom, dilaton, DBI-essence and hessence scalar field models of DE in FRW spacetime to reconstruct potentials as well as the dynamics for these scalar fields for describing the acceleration of the universe. We also analyze the models in graphically to interpret the nature of the scalar fields and corresponding potentials.     

Dinucleosides with non-natural backbones: a new class of ribonuclease A and angiogenin inhibitors

Ribonuclease?A (RNase A) serves as a convenient model enzyme in the identification and development of inhibitors of proteins that are members of the ribonuclease superfamily. This is principally because the biological activity of these proteins, such as angiogenin, is linked to their catalytic ribonucleolytic activity. In an attempt to inhibit the biological activity of angiogenin, which involves new blood vessel formation, we employed different dinucleosides with varied non-natural backbones. These compounds were synthesized by coupling aminonucleosides with dicarboxylic acids and amino- and carboxynucleosides with an amino acid. These molecules show competitive inhibition with inhibition constant (K(i)) values of (59±3) and (155±5) μM for RNase A. The compounds were also found to inhibit angiogenin in a competitive fashion with corresponding K(i) values in the micromolar range. The presence of an additional polar group attached to the backbone of dinucleosides was found to be responsible for the tight binding with both proteins. The specificity of different ribonucleolytic subsites were found to be altered because of the incorporation of a non-natural backbone in between the two nucleosidic moieties. In spite of the replacement of the phosphate group by non-natural linkers, these molecules were found to selectively interact with the ribonucleolytic site residues of angiogenin, whereas the cell binding site and nuclear translocation site residues remain unperturbed. Docked conformations of the synthesized compounds with RNase A and angiogenin suggest a binding preference for the thymine-adenine pair over the thymine-thymine pair.     

Dinucleosides with Non‐Natural Backbones: A New Class of Ribonuclease A and Angiogenin Inhibitors

Ribonuclease A (RNase A) serves as a convenient model enzyme in the identification and development of inhibitors of proteins that are members of the ribonuclease superfamily. This is principally because the biological activity of these proteins, such as angiogenin, is linked to their catalytic ribonucleolytic activity. In an attempt to inhibit the biological activity of angiogenin, which involves new blood vessel formation, we employed different dinucleosides with varied non‐natural backbones. These compounds were synthesized by coupling aminonucleosides with dicarboxylic acids and amino‐ and carboxynucleosides with an amino acid. These molecules show competitive inhibition with inhibition constant (K_i) values of (59±3) and (155±5) μM for RNase A. The compounds were also found to inhibit angiogenin in a competitive fashion with corresponding K_i values in the micromolar range. The presence of an additional polar group attached to the backbone of dinucleosides was found to be responsible for the tight binding with both proteins. The specificity of different ribonucleolytic subsites were found to be altered because of the incorporation of a non‐natural backbone in between the two nucleosidic moieties. In spite of the replacement of the phosphate group by non‐natural linkers, these molecules were found to selectively interact with the ribonucleolytic site residues of angiogenin, whereas the cell binding site and nuclear translocation site residues remain unperturbed. Docked conformations of the synthesized compounds with RNase A and angiogenin suggest a binding preference for the thymine–adenine pair over the thymine–thymine pair.     

Thermodynamics of Modified Chaplygin Gas and Tachyonic Field

Here we generalize the results of the work of Myung () in modified Chaplygin gas model and tachyonic field model. Here we have studied the thermodynamical behavior and the equation of state in terms of volume and temperature for both models. We have used the solution and the corresponding equation of state of our previous work (Chattopadhyay et al., Astrophys. Space Sci. 314:41, 2008). for tachyonic field model. We have also studied the thermodynamical stability using thermal equation of state for the tachyonic field model and have shown that there is no critical points during thermodynamical expansion. The determination of T _∗ due to expansion for the tachyonic field have been discussed by assuming some initial conditions. Here, the thermal quantities have been investigated using some reduced parameters.     

Interaction between three moving Griffith cracks at the interface of two dissimilar elastic media

The paper deals with the interaction between three Griffith cracks propagating under antiplane shear stress at the interface of two dissimilar infinite elastic half-spaces. The Fourier transform technique is used to reduce the elastodynamic problem to the solution of a set of integral equations which has been solved by using the finite Hilbert transform technique and Cooke’s result. The analytical expressions for the stress intensity factors at the crack tips are obtained. Numerical values of the interaction effect have been computed for and results show that interaction effects are either shielding or amplification depending on the location of each crack with respect to other and crack tip spacing.