Bio-inspired computation using synthetic genetic network

Potential of synthetic genetic network, Repressilator, to work as logical computing unit is observed. It is shown that two variables of gene network yield simultaneously, the basic AND or OR gate with their complementary NAND or NOR gate, with the variation of the internal parameter of the system. This allows the gene network to work as a strong candidate for parallel computing. Stability or robustness of gates is also checked in noisy background.     

Classical φ6-field theory in (1+1) dimensions. A model for structural phase transitions

The classical φ⁶-field theory in (1+1) dimensions, is considered as a model for the first order structural phase transitions. The equation of motion is solved exactly; and the presence of domain wall (kink) solutions at and below the transition point, in addition to the usual phonon-like oscillatory solutions, is demonstrated. The domain wall solutions are shown to be stable, and their mass and energies are calculated. Above the transition point there exists exotic unstable kink-like solutions which takes the particle from one hill top to the other of the potential. The partition function of the system is calculated exactly using the functional integral method together with the transfer matrix techniques which necessitates the determination of the eigenvalues of a Schrödinger-like equation. Thus the exact free energy is evaluated which in the low temperature limit has a phonon part and a contribution coming from the domain wall excitations. It was shown that this domain wall free energy differs from that calculated by the use of the domain wall phenomenology proposed by Krumhansl and Schrieffer. The exact solutions of the Schrödinger-like equation are also used to evaluate the displacement-displacement, intensity-intensity correlation functions and the probability distribution function. These results are compared with those obtained from the phenomenology as well as the φ⁴-field theory. A qualitative picture of the central peak observed in structural phase transitions is proposed.     

Fractional Fourier analysis of defocused images

A method is proposed for a consistent analysis of defocused images using the concept of fractional Fourier transforms of Wiener, Condon and Patterson.     

Are spin-dependent forces in charmonium generated through scalar-vector admixture?

I show that if the spin-dependent confining forces are generated through scalar-vector admixture then the ³p_J splittings restrict the vector to scalar ratio to be less than half. Further it is shown that an accurate measurement of the ¹p₁ mass can clearly distinguish this model from vector and scalar exchange models.     

Radial flow of a viscous,incompressible, electrically conducting fluid between two stationary,porous discs in the presence of transverse magnetic field

The problem of incompressible, electrically conducting viscous laminar flow between two non-conducting coaxial discs is studied, in the presence of transverse magnetic field of uniform intensity, when there is constant injection or suction at the discs. The problem is interesting both mathematically and physically. The solution, for small suction or injection, has been obtained for highly viscous fluid. The velocity profiles have also been drawn graphically.     

Charge-current commutator in the framework of analytic regularization

We calculate the charge-current commutator using analytic regularization and show that it is same as that obtained by dimensional regularization on the dimensionality shell.