Efficiency of the Incomplete Enumeration Algorithm for Monte-Carlo Simulation of Linear and Branched Polymers

We study the efficiency of the incomplete enumeration algorithm for linear and branched polymers. There is a qualitative difference in the efficiency in these two cases. The average time to generate an independent sample of configuration of polymer with n monomers varies as n ² for linear polymers for large n, but as exp(cn ^α) for branched (undirected and directed) polymers, where 0<α<1. On the binary tree, our numerical studies for n of order 10⁴ gives α = 0.333±0.005. We argue that α =1/3 exactly in this case. An erratum to this article can be found at .     

Emergent cooperation amongst competing agents in minority games

We study a variation of the minority game. There are N agents. Each has to choose between one of two alternatives every day, and there is a reward to each member of the smaller group. The agents cannot communicate with each other, but try to guess the choice others will make, based only on the past history of the number of people choosing the two alternatives. We describe a simple probabilistic strategy using which the agents, acting independently, and trying to maximize their individual expected payoff, still achieve a very efficient overall utilization of resources, and the average deviation of the number of happy agents per day from the maximum possible can be made O(N^?), for any ?>0. We also show that a single agent does not expect to gain by not following the strategy.     

Quenched Averages for Self-Avoiding Walks and Polygons on Deterministic Fractals

We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W _n (S), and rooted self-avoiding polygons P _n (S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for P _n (S), and W _n(S) for an arbitrary point S on the lattice. These are used to compute the averages ,, and over different positions of S. We find that the connectivity constant μ, and the radius of gyration exponent are the same for the annealed and quenched averages. However, , and , where the exponents and , take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives and , to be compared with the known annealed values and .     

Effect of disorder on relaxation in the one-dimensional Glauber model

We study the long-time relaxation of magnetization in a disordered linear chain of Ising spins from an initially aligned state. The coupling constants are ferromagnetic and nearest-neighbor only, taking valuesJ ₀ andJ ₁ with probabilitiesp and 1–p, respectively. The time evolution of the system is governed by the Glauber master equation. It is shown that for large timest, the magnetizationM(t) varies as [exp(–₀ t](t), where ₀ is a function of the stronger bond strengthJ ₀ only, and (t) decreases slower than an exponential. For very long times, we find that ln (t) varies as –t ^1/3. For low enough temperatures, there is an intermediate time regime when ln (t) varies as –t ^1/2. The results can be extended to more general probability distributions of ferromagnetic coupling constants, assuming thatM(t) can only increase if any bond in the chain is strengthened. If the coupling constants have a continuous distribution in which the probability density varies as a power law near some maximum valueJ ₀, we find that ln (t) varies as –t ^1/3(lnt)^2/3 for large times.     

On the topological characterization of two-dimensional phase transitions

It is shown that for the two-dimensional planar-rotator model the variance of the number of vortices inside a large loop is proportional to the perimeter of the loop at all temperatures. A similar result holds for the variance of the charge inside a loop in the lattice Coulomb gas model. Hence a topological distinction between the high and low temperature phases of these models (area law versus perimeter law) is not possible.     

Uhf to Ka band upconverter

A balanced upconverter circuit has been developed in planar transmission line configuration using NEC GaAs beam lead Schottky barrier diodes. RF power output of +1.6 dBm SSB is obtained at Ka-band when up converter is driven by +17 dBm IF and +20 dBm LO signal.     

Studies on defect formation in femtosecond laser-irradiated PMMA and PDMS

We report here our results on the spectroscopic and elemental analysis of femtosecond (fs) laser-modified regions in polymers of polymethylmethacrylate (PMMA) and polydimethylsiloxane (PDMS) in the context of defect formation and emission in the visible region. Different physical and chemical models are used to explain the changes in modified regions. We found that the emission intensity, recorded from the fs-modified regions of polymers, decreased over time to a constant value. We also demonstrate that these materials are suitable for the preparation of the microstructures en route for light guiding applications. The fs laser-irradiated regions exhibited paramagnetic behavior as was confirmed from electron spin resonance studies through the formation of peroxide-type free radicals. Raman mapping was performed in the modified regions which consisted of defects and found that the modulations in intensity are predominant in the central portion of the structure compared to edges. Elemental analysis has been performed in the modified regions using field emission scanning electron microscope instrument and energy-dispersive X-ray absorption spectroscopy to estimate the percentage contents of individual elements which resulted in defect formation such as paramagnetic and optical centers.     

Spin squeezing and quantum correlations

We discuss the notion of spin squeezing considering two mutually exclusive classes of spin-s states, namely, oriented and non-oriented states. Our analysis shows that the oriented states are not squeezed while non-oriented states exhibit squeezing. We also present a new scheme for construction of spin-s states using 2s spinors oriented along different axes. Taking the case of s=1, we show that the ‘non-oriented’ nature and hence squeezing arise from the intrinsic quantum correlations that exist among the spinors in the coupled state.     

Theory of transport of long polymer molecules through carbon nanotube channels

A theory of transport of long chain polymer molecules through carbon nanotube (CNT) channels is developed using the Fokker-Planck equation and direct molecular dynamics simulations. The mean transport or translocation time tau is found to depend on the chemical potential energy, the entropy, and the diffusion coefficient. A power law dependence tau approximately N2 is found, where N is the number of monomers in a molecule. For 10(5)-unit long polyethylene molecules, tau is estimated to be approximately 1 micros. The diffusion coefficient of long polymer molecules inside CNTs, like that of short ones, is found to be a few orders of magnitude larger than in ordinary silicate based zeolite systems.