Evolution of cooperation by reciprocation within structured demes

The iterative two-person Prisoners’ Dilemma game has been generalised to theN-person case. The evolution of cooperation is explored by matching the Tit For Tat (TFT) strategy (Axelrod and Hamilton 1981) against the selfish strategy. Extension of TFT toN-person situations yields a graded set of strategies from the softest TFT, which continues cooperation even if only one of the opponents reciprocates it, to the hardest, which would do so only when all the remaining opponents cooperate. The hardest TFT can go to fixation against the selfish strategy provided it crosses a threshold frequencypc. All the other TFT are invadable by the selfish (D) or the pure defector strategy, while none can invadeD. Yet, provided a thresholdpc is crossed, they can coexist stably withD. AsN, the size of the group increases, the threshold pc also increases, indicating that the evolution of cooperation is more difficult for larger groups. Under certain conditions, only the soft TFT can coexist stably against the selfish strategyD, while the harder ones cannot. An interesting possibility of a complete takeover of the selfish population by successive invasions by harder and harder TFT strategies is also presented.

Convenient construction of tetrahedral finite elements for the quasi-harmonic equation

It is shown that in the finite-element formulation of the general quasi-harmonic equation using tetrahedral elements, for every member of the element family there exists just one numerical universal matrix indpendent of the size, shape and material properties of the element. Thus the element matrix is conveniently constructed by manipulating this single matrix along with a set of reverse sequence codes at the same time accounting for the size, shape and material properties in a simple manner.

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.

Occurrence, divergence and evolution of intrinsic terminators across Eubacteria

In Escherichia coli, the canonical intrinsic terminator of transcription includes a palindrome followed by a U-trail on the transcript. The apparent underrepresentation of such terminators in eubacterial genomes led us to develop a rapid and accurate algorithm, GeSTer, to predict putative intrinsic terminators. Now, we have analyzed 378 genome sequences with an improved version of GeSTer. Our results indicate that the canonical E. coli type terminators are not overwhelmingly abundant in eubacteria. The atypical structures, having stem-loop structures but lacking ‘U’ trail, occur downstream of genes in all the analyzed genomes but different phyla show conserved preference for different types of terminators. This propensity correlates with genomic GC content and presence of the factor, Rho. 60–70% of identified terminators in all the genomes show “optimized” stem-length and ΔG. These results provide evidence that eubacteria extensively rely on the mechanism of intrinsic termination, with a considerable divergence in their structure, positioning and prevalence. The software and detailed results for individual genomes are freely available on request

Microstructural evolution and grain boundary sliding in a superplastic magnesium AZ31 alloy

Tensile experiments on a fine-grained single-phase Mg–Zn–Al alloy (AZ31) at 673 K revealed superplastic behavior with an elongation to failure of 475% at 1 × 10−4 s−1 and non-superplastic behavior with an elongation to failure of 160% at 1 × 10−2 s−1; the corresponding strain rate sensitivities under these conditions were 0.5 and 0.2, respectively. Measurements indicated that the grain boundary sliding (GBS) contribution to strain ξ was 30% under non-superplastic conditions; there was also a significant sharpening in texture during such deformation. Under superplastic conditions, ξ was 50% at both low and high elongations of 20% and 120%; the initial texture became more random under such conditions. In non-superplastic conditions, deformation occurred under steady-state conditions without grain growth before significant flow localization whereas, under superplastic conditions, there was grain growth during the early stages of deformation, leading to strain hardening. The grains retained equiaxed shapes under all experimental conditions. Superplastic deformation is attributed to GBS, while non-superplastic deformation is attributed to intragranular dislocation creep with some contribution from GBS. The retention of equiaxed grain shapes during dislocation creep is consistent with a model based on local recovery related to the disturbance of triple junctions.

Transient pulse evolution of active-mode locking in an intra-cavity frequency-doubled laser

The theory of transient mode locking for an active modulator in an intracavity frequency-doubled laser is presented. The theory is applied to mode-locked and intracavity frequency-doubled Nd:YAG laser and the mode-locked pulse width is plotted as a function of number of round trips inside the cavity. It is found that the pulse compression is faster and the system takes a very short time to approach the steady state in the presence of a second harmonic generating crystal inside the laser cavity. The effect of modulation depth and the second harmonic conversion efficiency on the temporal behavior of the pulse width is discussed.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

Specificity of protein - Nucleic acid interaction and the biochemical evolution

The water soluble carbodiimide mediated condensation of dipeptides of the general form Gly-X was carried out in the presence of mono- and poly-nucleotides. The observed yield of the tetrapeptide was found to be higher for peptide-nucleotide system of higher interaction specificity following mainly the anticodon-amino acid relationship (Basu, H.S. & Podder, S.K., 1981, Ind. J. Biochem. Biophys.,19, 251-253). The yield of the condensation product of L-peptide was more because of its higher interaction specificity. The extent of the racemization during the condensation of Gly-L-Phe, Gly-L-Tyr and Gly-D-Phe was found to be dependent on the specificity of the interaction -the higher the specificity, the lesser the racemization. The product formed was shown to have a catalytic effect on the condensation reaction. These data thus provide a mechanism showing how the specific interaction between amino acids/dipeptides and nucleic acids could lead to the formation of the lsquoprimitiversquo translation machinery.

Existence theorem for a generalized Hammerstein type equation

An existence theorem is obtained for a generalized Hammerstein type equation

Evolution of texture during equal channel angular extrusion of commercially pure aluminum: Experiments and simulations

The evolution of crystallographic texture has been comprehensively studied for commercially pure Al as a function of amount of ECAE deformation for the three major routes of ECAE processing. It has been observed that processing through different routes leads to different type of texture, in both qualitative as well as quantitative sense. The results have been analyzed on the basis of existing concepts on ECAE deformation and simulations have been carried out using the simple shear model of ECAE implemented into the Viscoplastic Self Consistent model of polycrystal plasticity. The simulations revealed that non-octahedral slip is needed to reproduce the experimental texture development.

Solution of a generalized Korteweg—de Vries equation

The solitary-wavelike solution of the generalized Korteweg-de Vries equation with mixed nonlinearity is obtained. Two asymptotic cases of the solution have been discussed and solitary wave solutions have been derived. ©1974 American Institute of Physics.