Investigation of twin-wall structure at the nanometre scale using atomic force microscopy

The structure of twin walls and their interaction with defects has important implications for the behaviour of a variety of materials including ferroelectric, ferroelastic, co-elastic and superconducting crystals. Here, we present a method for investigating the structure of twin walls with nanometre-scale resolution. In this method, the surface topography measured using atomic force microscopy is compared with candidate displacement fields, and this allows for the determination of the twin-wall thickness and other structural features. Moreover, analysis of both complete area images and individual line-scan profiles provides essential information about local mechanisms of twin-wall broadening, which cannot be obtained by existing experimental methods. The method is demonstrated in the ferroelectric material PbTiO(3), and it is shown that the accumulation of point defects is responsible for significant broadening of the twin walls. Such defects are of interest because they contribute to the twin-wall kinetics and hysteresis.     

Inapproximability Results for Set Splitting and Satisfiability Problems with No Mixed Clauses

We prove hardness results for approximating set splitting problems and also instances of satisfiability problems which have no mixed clauses, i.e., every clause has either all its literals unnegated or all of them negated. Results of Håstad imply tight hardness results for set splitting when all sets have size exactly $k \ge 4$ elements and also for non-mixed satisfiability problems with exactly $k$ literals in each clause for $k \ge 4$. We consider the case $k=3$. For the MAX E3-SET SPLITTING, problem in which all sets have size exactly 3, we prove an NP-hardness result for approximating within any factor better than ${\frac{19}{20}}$. This result holds even for satisfiable instances of MAX E3-SET SPLITTING, and is based on a PCP construction due to Håstad. For non-mixed MAX 3SAT, we give a PCP construction which is a slight variant of the one given by Håstad for MAX 3SAT, and use it to prove the NP-hardness of approximating within a factor better than ${\frac{11}{12}}$.     

Anticonvulsant activity of enzyme inhibitors in rats

Three liver microsomal enzyme inhibitors, proadifen, 2,4-dichloro-6-phenylphenoxyethyldiethylamine, and 2,4-dichloro-6-phenylphenoxyethylamine, and a hepatotoxic agent, carbon tetrachloride, were tested for anticonvulsant activity in adult male albino rats using the maximal electroshock seizure technique. All four substances exhibited significant anticonvulsant activity 1 hr after intraperitoneal administration. This protection was absent when tested 24 hr later.     

Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy

In this paper, we present error-correcting codes that achieve the information-theoretically best possible tradeoff between the rate and error-correction radius. Specifically, for every 0 < R < 1 and epsiv < 0, we present an explicit construction of error-correcting codes of rate that can be list decoded in polynomial time up to a fraction (1- R - epsiv) of worst-case errors. At least theoretically, this meets one of the central challenges in algorithmic coding theory. Our codes are simple to describe: they are folded Reed-Solomon codes, which are in fact exactly Reed-Solomon (RS) codes, but viewed as a code over a larger alphabet by careful bundling of codeword symbols. Given the ubiquity of RS codes, this is an appealing feature of our result, and in fact our methods directly yield better decoding algorithms for RS codes when errors occur in phased bursts. The alphabet size of these folded RS codes is polynomial in the block length. We are able to reduce this to a constant (depending on epsiv) using existing ideas concerning ldquolist recoveryrdquo and expander-based codes. Concatenating the folded RS codes with suitable inner codes, we get binary codes that can be efficiently decoded up to twice the radius achieved by the standard GMD decoding.     

Application of digital image correlation method to biogel

This study adopts the digital image correlation (DIC) method to measure the mechanical properties under tension in agarose gels. A second polynomial stress–strain equation based on a pore model is proposed in this work. It shows excellent agreement with experimental data and was verified by finite element simulation. Evaluation of the planer strain field by DIC allows measurement of strain localization and Poisson's ratio. At high stresses, Poisson's ratio is found to exceed the standard assumption of 0.5 which is shown to be a result of pore water leakage. Local failure strains are found to be approximately twice those determined by crosshead displacements. Viscous properties of agarose gels are investigated by performing the tensile tests at various loading rates. Increases in loading rate do not cause much difference in the shape of stress–strain curves, but result in increases in ultimate stress and strain. POLYM. ENG. SCI., 50:1585–1593, 2010. © 2010 Society of Plastics Engineers     

Algorithms for Modular Counting of Roots of Multivariate Polynomials

Given a multivariate polynomial P(X ₁,…,X _n ) over a finite field , let N(P) denote the number of roots over . The modular root counting problem is given a modulus r, to determine N _r (P)=N(P)mod r. We study the complexity of computing N _r (P), when the polynomial is given as a sum of monomials. We give an efficient algorithm to compute N _r (P) when the modulus r is a power of the characteristic of the field. We show that for all other moduli, the problem of computing N _r (P) is -hard. We present some hardness results which imply that our algorithm is essentially optimal for prime fields. We show an equivalence between maximum-likelihood decoding for Reed-Solomon codes and a root-finding problem for symmetric polynomials. P. Gopalan’s and R.J Lipton’s research was supported by NSF grant CCR-3606B64. V. Guruswami’s research was supported in part by NSF grant CCF-0343672 and a Sloan Research Fellowship.     

Tunneling radial cracks in layered structures from contact loading

Glass/epoxy laminates glued onto a compliant substrate are indented with a hard ball. The damage is characterized by a set of transverse cracks which pop out from the subsurface of the glass layers due to flexure and propagate stably in the radial direction with load in a bell-shape front under a diminishing stress field. Compliant interlayers, even extremely thin ones, are effective in inhibiting crossover fracture. This leads to crack tunneling and crack multiplication in the hard layers, which enhances energy dissipation and reduces the spread of damage relative to the basic bilayer configuration. The experiments show that the fracture in a given layer is well approximated by a power-law relation of the form c^3/2K_C/P = δ, where P, c, and K_C are the indentation load, crack length and fracture toughness, in that order, and δ an implicit function of the layer position and material and geometric variables, derived with the aid of available tunnel crack solutions.The model specimen studied provides a useful insight into the fracture behavior of natural, biological and synthetic layered structures from concentrated loading. The analysis shows that the crack arrest capability of a thin interlayer increases in proportion to the modulus misfit ratio between the layer and interlayer, and that the spread of radial cracks in a laminate of given thickness reduces in proportion to n^1/3, where n is the number layers in the laminate.     

Effect of Quasi-Static Loading Rate on Damage Formation in Silicon Carbide Reinforced Calcium Aluminosilicate Unidirectional Composites

For experiments at higher and lower loading rates, significant differences in the mechanical responses of unidirectional silicon carbide reinforced calcium aluminosilicate composites were observed. Axial and transverse stress–strain measurements, acoustic emission measurements, and post-test microstructural observations all indicated that there are changes in the sequence and extent of the formation of damage. The differences are attributed to rate-dependent matrix cracking due to environmental effects and rate dependencies associated with the fiber–matrix interface.     

Combinatorial bounds for list decoding

Informally, an error-correcting code has "nice" list-decodability properties if every Hamming ball of "large" radius has a "small" number of codewords in it. We report linear codes with nontrivial list-decodability: i.e., codes of large rate that are nicely list-decodable, and codes of large distance that are not nicely list-decodable. Specifically, on the positive side, we show that there exist codes of rate R and block length n that have at most c codewords in every Hamming ball of radius H^-1(1-R-1/c)·n. This answers the main open question from the work of Elias (1957). This result also has consequences for the construction of concatenated codes of good rate that are list decodable from a large fraction of errors, improving previous results of Guruswami and Sudan (see IEEE Trans. Inform. Theory, vol.45, p.1757-67, Sept. 1999, and Proc. 32nd ACM Symp. Theory of Computing (STOC), Portland, OR, p. 181-190, May 2000) in this vein. Specifically, for every ε > 0, we present a polynomial time constructible asymptotically good family of binary codes of rate Ω(ε⁴) that can be list-decoded in polynomial time from up to a fraction (1/2-ε) of errors, using lists of size O(ε^-2). On the negative side, we show that for every δ and c, there exists τ < δ, c₁ > 0, and an infinite family of linear codes {C_i}_i such that if n_i denotes the block length of C_i, then C _i has minimum distance at least δ · n_i and contains more than c₁ · n_i^c codewords in some Hamming ball of radius τ · n_i. While this result is still far from known bounds on the list-decodability of linear codes, it is the first to bound the "radius for list-decodability by a polynomial-sized list" away from the minimum distance of the code