Random Isotropic Structures and Possible Glass Transitions in Diblock Copolymer Melts

We study the microstructural glass transitions in diblock-copolymer melts using a thermodynamic replica approach. Our approach performs an expansion in terms of the natural smallness parameter -- the inverse of the scaled degree of polymerization, which allows us to systematically study the approach to mean-field behavior as the degree of polymerization increases. We find that in the limit of infinite long polymer chains, both the onset of glassiness and the vitrification transition (Kauzmann temperature) collapse to the mean-field spinodal, suggesting that the spinodal can be regarded as the mean-field signature for glass transitions in this class of systems. We also study the order-disorder transitions (ODT) within the same theoretical framework; in particular, we include the leading-order fluctuation corrections due to the cubic interaction in the coarse-grained Hamiltonian, which has been ignored in previous works on the ODT in block copolymers. We find that the cubic term stabilizes both the ordered (body-centered-cubic) phase and the glassy state relative to the disordered phase. While in melts of symmetric copolymers the glass transition always occurs after the order-disorder transition (below the ODT temperature), for asymmetric copolymers, it is possible that the glass transition precedes the ordering transition.Comment: An error corrected in the referenc

Further results on independent Metropolis-Hastings-Klein sampling

Sampling from a lattice Gaussian distribution is emerging as an important problem in coding and cryptography. This paper gives a further analysis of the independent Metropolis-Hastings-Klein (MHK) algorithm we presented at ISIT 2015. We derive the exact spectral gap of the induced Markov chain, which dictates the convergence rate of the independent MHK algorithm. Then, we apply the independent MHK algorithm to lattice decoding and obtained the decoding complexity for solving the CVP as Õ(e∥Bx-c∥2 / mini ∥b̂i∥2). Finally, the tradeoff between decoding radius and complexity is also established

Filtering for uncertain 2-D discrete systems with state delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.This paper is concerned with the problem of robust H∞ filtering for two-dimensional (2-D) discrete systems with time-delays in states. The 2-D systems under consideration are described in terms of the well-known Fornasini–Marchesini local state-space (FMLSS) models with time-delays. Our attention is focused on the design of a full-order filter such that the filtering error system is guaranteed to be asymptotically stable with a prescribed H∞ disturbance attenuation performance. Sufficient conditions for the existence of desired filters are established by using a linear matrix inequality (LMI) approach, and the corresponding filter design problem is then cast into a convex optimization problem that can be efficiently solved by resorting to some standard numerical software. Furthermore, the obtained results are extended to more general cases where the system matrices contain either polytopic or norm-bounded parameter uncertainties. A simulation example is provided to illustrate the effectiveness of the proposed design method.This work was partially supported by the National Natural Science Foundation of China (60504008), Program for New Century Excellent Talents in University of China and the Postdoctoral Science Foundation of China (20060390231)

Quantum storage and information transfer with superconducting qubits

We design theoretically a new device to realize the general quantum storage based on dcSQUID charge qubits. The distinct advantages of our scheme are analyzed in comparison with existing storage scenarios. More arrestingly, the controllable XY-model spin interaction has been realized for the first time in superconducting qubits, which may have more potential applications besides those in quantum information processing. The experimental feasibility is also elaborated.Comment: 4 pages, 2 figure

Electron-hydrogen scattering in Faddeev-Merkuriev integral equation approach

Electron-hydrogen scattering is studied in the Faddeev-Merkuriev integral equation approach. The equations are solved by using the Coulomb-Sturmian separable expansion technique. We present $S$- and $P$-wave scattering and reactions cross sections up to the $H(n=4)$ threshold.Comment: 2 eps figure