Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster

The scaling properties of self-avoiding walks on a d-dimensional diluted lattice at the percolation threshold are analyzed by a field-theoretical renormalization group approach. To this end we reconsider the model of Y. Meir and A. B. Harris (Phys. Rev. Lett. 63:2819 (1989)) and argue that via renormalization its multifractal properties are directly accessible. While the former first order perturbation did not agree with the results of other methods, we find that the asymptotic behavior of a self-avoiding walk on the percolation cluster is governed by the exponent nu_p=1/2 + epsilon/42 + 110epsilon^2/21^3, epsilon=6-d. This analytic result gives an accurate numeric description of the available MC and exact enumeration data in a wide range of dimensions 2<=d<=6.Comment: 4 pages, 2 figure

Entropy-induced separation of star polymers in porous media

We present a quantitative picture of the separation of star polymers in a solution where part of the volume is influenced by a porous medium. To this end, we study the impact of long-range-correlated quenched disorder on the entropy and scaling properties of $f$-arm star polymers in a good solvent. We assume that the disorder is correlated on the polymer length scale with a power-law decay of the pair correlation function $g(r) \sim r^{-a}$. Applying the field-theoretical renormalization group approach we show in a double expansion in $\epsilon=4-d$ and $\delta=4-a$ that there is a range of correlation strengths $\delta$ for which the disorder changes the scaling behavior of star polymers. In a second approach we calculate for fixed space dimension $d=3$ and different values of the correlation parameter $a$ the corresponding scaling exponents $\gamma_f$ that govern entropic effects. We find that $\gamma_f-1$, the deviation of $\gamma_f$ from its mean field value is amplified by the disorder once we increase $\delta$ beyond a threshold. The consequences for a solution of diluted chain and star polymers of equal molecular weight inside a porous medium are: star polymers exert a higher osmotic pressure than chain polymers and in general higher branched star polymers are expelled more strongly from the correlated porous medium. Surprisingly, polymer chains will prefer a stronger correlated medium to a less or uncorrelated medium of the same density while the opposite is the case for star polymers.Comment: 14 pages, 7 figure

Properties of Bulk Sintered Silver As a Function of Porosity

This report summarizes a study where various properties of bulk-sintered silver were investigated over a range of porosity. This work was conducted within the National Transportation Research Center's Power Device Packaging project that is part of the DOE Vehicle Technologies Advanced Power Electronics and Electric Motors Program. Sintered silver, as an interconnect material in power electronics, inherently has porosity in its produced structure because of the way it is made. Therefore, interest existed in this study to examine if that porosity affected electrical properties, thermal properties, and mechanical properties because any dependencies could affect the intended function (e.g., thermal transfer, mechanical stress relief, etc.) or reliability of that interconnect layer and alter how its performance is modeled. Disks of bulk-sintered silver were fabricated using different starting silver pastes and different sintering conditions to promote different amounts of porosity. Test coupons were harvested out of the disks to measure electrical resistivity and electrical conductivity, thermal conductivity, coefficient of thermal expansion, elastic modulus, Poisson's ratio, and yield stress. The authors fully recognize that the microstructure of processed bulk silver coupons may indeed not be identical to the microstructure produced in thin (20-50 microns) layers of sintered silver. However, measuring these same properties with such a thin actual structure is very difficult, requires very specialized specimen preparation and unique testing instrumentation, is expensive, and has experimental shortfalls of its own, so the authors concluded that the herein measured responses using processed bulk sintered silver coupons would be sufficient to determine acceptable values of those properties. Almost all the investigated properties of bulk sintered silver changed with porosity content within a range of 3-38% porosity. Electrical resistivity, electrical conductivity, thermal conductivity, elastic modulus, Poisson's ratio, and yield stress all depended on the porosity content in bulk-sintered silver. The only investigated property that was independent of porosity in that range was coefficient of thermal expansion

Star copolymers in porous environments: scaling and its manifestations

We consider star polymers, consisting of two different polymer species, in a solvent subject to quenched correlated structural obstacles. We assume that the disorder is correlated with a power-law decay of the pair correlation function g(x)\sim x^{-a}. Applying the field-theoretical renormalization group approach in d dimensions, we analyze different scenarios of scaling behavior working to first order of a double \epsilon=4-d, \delta=4-a expansion. We discuss the influence of the correlated disorder on the resulting scaling laws and possible manifestations such as diffusion controlled reactions in the vicinity of absorbing traps placed on polymers as well as the effective short-distance interaction between star copolymers.Comment: 13 pages, 3 figure

Multifractality of Brownian motion near absorbing polymers

We characterize the multifractal behavior of Brownian motion in the vicinity of an absorbing star polymer. We map the problem to an O(M)-symmetric phi^4-field theory relating higher moments of the Laplacian field of Brownian motion to corresponding composite operators. The resulting spectra of scaling dimensions of these operators display the convexity properties which are necessarily found for multifractal scaling but unusual for power of field operators in field theory. Using a field-theoretic renormalization group approach we obtain the multifractal spectrum for absorbtion at the core of a polymer star as an asymptotic series. We evaluate these series using resummation techniques.Comment: 18 pages, revtex, 6 ps-figure

Low-cost resonant cavity Raman gas probe for multi-gas detection

Raman based gas sensing can be attractive in several industrial applications, due to its multi-gas sensing capabilities and its ability to detect O_2 and N_2. In this article, we have built a Raman gas probe, based on low-cost components, which has shown an estimated detection limit of 0.5 % for 30 second measurements of N_2 and O_2. While this detection limit is higher than that of commercially available equipment, our estimated component cost is approximately one tenth of the price of commercially available equipment. The use of a resonant Fabry-Pérot cavity increases the scattered signal, and hence the sensitivity, by a factor of 50. The cavity is kept in resonance using a piezo-actuated mirror and a photodiode in a feedback loop.The system described in this article was made with minimum-cost components to demonstrate the low-cost principle. However, it is possible to decrease the detection limit using a higher-powered (but still low-cost) laser and improving the collection optics. By applying these improvements, the detection limit and estimated measurement precision will be sufficient for e.g. the monitoring of input gases in combustion processes, such as e.g. (bio-)gas power plants. In these processes, knowledge about gas compositions with 0.1 % (absolute) precision can help regulate and optimize process conditions.The system has the potential to provide a low-cost, industrial Raman sensor that is optimized for specific gas-detection applications

Precision characterisation of two-qubit Hamiltonians via entanglement mapping

We show that the general Heisenberg Hamiltonian with non-uniform couplings can be characterised by mapping the entanglement it generates as a function of time. Identification of the Hamiltonian in this way is possible as the coefficients of each operator control the oscillation frequencies of the entanglement function. The number of measurements required to achieve a given precision in the Hamiltonian parameters is determined and an efficient measurement strategy designed. We derive the relationship between the number of measurements, the resulting precision and the ultimate discrete error probability generated by a systematic mis-characterisation, when implementing two-qubit gates for quantum computing.Comment: 6 Pages, 3 figure

Two-Dimensional Copolymers and Exact Conformal Multifractality

We consider in two dimensions the most general star-shaped copolymer, mixing random (RW) or self-avoiding walks (SAW) with specific interactions thereof. Its exact bulk or boundary conformal scaling dimensions in the plane are all derived from an algebraic structure existing on a random lattice (2D quantum gravity). The multifractal dimensions of the harmonic measure of a 2D RW or SAW are conformal dimensions of certain star copolymers, here calculated exactly as non rational algebraic numbers. The associated multifractal function f(alpha) are found to be identical for a random walk or a SAW in 2D. These are the first examples of exact conformal multifractality in two dimensions.Comment: 4 pages, 2 figures, revtex, to appear in Phys. Rev. Lett., January 199

Polydisperse star polymer solutions

We analyze the effect of polydispersity in the arm number on the effective interactions, structural correlations and the phase behavior of star polymers in a good solvent. The effective interaction potential between two star polymers with different arm numbers is derived using scaling theory. The resulting expression is tested against monomer-resolved molecular dynamics simulations. We find that the theoretical pair potential is in agreement with the simulation data in a much wider polydispersity range than other proposed potentials. We then use this pair potential as an input in a many-body theory to investigate polydispersity effects on the structural correlations and the phase diagram of dense star polymer solutions. In particular we find that a polydispersity of 10%, which is typical in experimental samples, does not significantly alter previous findings for the phase diagram of monodisperse solutions.Comment: 14 pages, 7 figure