On the Renormalization of the Kardar-Parisi-Zhang equation

The Kardar-Parisi-Zhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally subtracted perturbation expansion about d = 2. For the KPZ roughening transition in dimensions d > 2, this renormalization group yields the dynamic exponent z* = 2 and the roughness exponent chi* = 0, which are exact to all orders in epsilon = (2 - d)/2. The expansion becomes singular in d = 4, which is hence identified with the upper critical dimension of the KPZ equation. The implications of this perturbation theory for the strong-coupling phase are discussed. In particular, it is shown that the correlation functions and the coupling constant defined in minimal subtraction develop an essential singularity at the strong-coupling fixed point.Comment: 21 pp. (latex, now texable everywhere, no other changes), with 2 fig

Relationship between Crystalline Order and Exciton Diffusion Length in Molecular Organic Semiconductors

No Abstract.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69160/1/1233_ftp.pd

Family resemblances: A common fold for some dimeric ion-coupled secondary transporters

Membrane transporter proteins catalyze the passage of a broad range of solutes across cell membranes, allowing the uptake and efflux of crucial compounds. Because of the difficulty of expressing, purifying, and crystallizing integral membrane proteins, relatively few transporter structures have been elucidated to date. Although every membrane transporter has unique characteristics, structural and mechanistic similarities between evolutionarily diverse transporters have been identified. Here, we compare two recently reported structures of membrane proteins that act as antimicrobial efflux pumps, namely MtrF from Neisseria gonorrhoeae and YdaH from Alcanivorax borkumensis, both with each other and with the previously published structure of a sodium-dependent dicarboxylate transporter from Vibrio cholerae, VcINDY. MtrF and YdaH belong to the p-aminobenzoyl-glutamate transporter (AbgT) family and have been reported as having architectures distinct from those of all other families of transporters. However, our comparative analysis reveals a similar structural arrangement in all three proteins, with highly conserved secondary structure elements. Despite their differences in biological function, the overall "design principle" of MtrF and YdaH appears to be almost identical to that of VcINDY, with a dimeric quaternary structure, helical hairpins, and clear boundaries between the transport and scaffold domains. This observation demonstrates once more that the same secondary transporter architecture can be exploited for multiple distinct transport modes, including cotransport and antiport. Based on our comparisons, we detected conserved motifs in the substrate-binding region and predict specific residues likely to be involved in cation or substrate binding. These findings should prove useful for the future characterization of the transport mechanisms of these families of secondary active transporters

Glassy Solutions of the Kardar-Pasrisi-Zhang Equation

It is shown that the mode-coupling equations for the strong-coupling limit of the KPZ equation have a solution for d>4 such that the dynamic exponent z is 2 (with possible logarithmic corrections) and that there is a delta function term in the height correlation function = (A/k^{d+4-z}) \delta(w/k^z) where the amplitude A vanishes as d -> 4. The delta function term implies that some features of the growing surface h(x,t) will persist to all times, as in a glassy state.Comment: 11 pages, Revtex, 1 figure available upon request (same as figure 1 in ref [10]) Important corrections have been made which yield a much simpler picture of what is happening. We still find "glassy" solutions for d>4 where z is 2 (with possible logarithmic corrections). However, we now find no glassy solutions below d=4. A (linear) stability analysis (for d>4) has been included. Also one Author has been adde

A two-species model of a two-dimensional sandpile surface: a case of asymptotic roughening

We present and analyze a model of an evolving sandpile surface in (2 + 1) dimensions where the dynamics of mobile grains ({\rho}(x, t)) and immobile clusters (h(x, t)) are coupled. Our coupling models the situation where the sandpile is flat on average, so that there is no bias due to gravity. We find anomalous scaling: the expected logarithmic smoothing at short length and time scales gives way to roughening in the asymptotic limit, where novel and non-trivial exponents are found.Comment: 7 Pages, 6 Figures; Granular Matter, 2012 (Online

Comparison of Different Parallel Implementations of the 2+1-Dimensional KPZ Model and the 3-Dimensional KMC Model

We show that efficient simulations of the Kardar-Parisi-Zhang interface growth in 2 + 1 dimensions and of the 3-dimensional Kinetic Monte Carlo of thermally activated diffusion can be realized both on GPUs and modern CPUs. In this article we present results of different implementations on GPUs using CUDA and OpenCL and also on CPUs using OpenCL and MPI. We investigate the runtime and scaling behavior on different architectures to find optimal solutions for solving current simulation problems in the field of statistical physics and materials science.Comment: 14 pages, 8 figures, to be published in a forthcoming EPJST special issue on "Computer simulations on GPU

Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation

A systematic analysis of the Burgers--Kardar--Parisi--Zhang equation in $d+1$ dimensions by dynamic renormalization group theory is described. The fixed points and exponents are calculated to two--loop order. We use the dimensional regularization scheme, carefully keeping the full $d$ dependence originating from the angular parts of the loop integrals. For dimensions less than $d_c=2$ we find a strong--coupling fixed point, which diverges at $d=2$, indicating that there is non--perturbative strong--coupling behavior for all $d \geq 2$. At $d=1$ our method yields the identical fixed point as in the one--loop approximation, and the two--loop contributions to the scaling functions are non--singular. For $d>2$ dimensions, there is no finite strong--coupling fixed point. In the framework of a $2+\epsilon$ expansion, we find the dynamic exponent corresponding to the unstable fixed point, which describes the non--equilibrium roughening transition, to be $z = 2 + {\cal O} (\epsilon^3)$, in agreement with a recent scaling argument by Doty and Kosterlitz. Similarly, our result for the correlation length exponent at the transition is $1/\nu = \epsilon + {\cal O} (\epsilon^3)$. For the smooth phase, some aspects of the crossover from Gaussian to critical behavior are discussed.Comment: 24 pages, written in LaTeX, 8 figures appended as postscript, EF/UCT--94/3, to be published in Phys. Rev. E

Quality standards for the management of alcohol-related liver disease: consensus recommendations from the British Association for the Study of the Liver and British Society of Gastroenterology ARLD special interest group

Objective Alcohol-related liver disease (ALD) is the most common cause of liver-related ill health and liver-related deaths in the UK, and deaths from ALD have doubled in the last decade. The management of ALD requires treatment of both liver disease and alcohol use; this necessitates effective and constructive multidisciplinary working. To support this, we have developed quality standard recommendations for the management of ALD, based on evidence and consensus expert opinion, with the aim of improving patient care.Design A multidisciplinary group of experts from the British Association for the Study of the Liver and British Society of Gastroenterology ALD Special Interest Group developed the quality standards, with input from the British Liver Trust and patient representatives.Results The standards cover three broad themes: the recognition and diagnosis of people with ALD in primary care and the liver outpatient clinic; the management of acutely decompensated ALD including acute alcohol-related hepatitis and the posthospital care of people with advanced liver disease due to ALD. Draft quality standards were initially developed by smaller working groups and then an anonymous modified Delphi voting process was conducted by the entire group to assess the level of agreement with each statement. Statements were included when agreement was 85% or greater. Twenty-four quality standards were produced from this process which support best practice. From the final list of statements, a smaller number of auditable key performance indicators were selected to allow services to benchmark their practice and an audit tool provided.Conclusion It is hoped that services will review their practice against these recommendations and key performance indicators and institute service development where needed to improve the care of patients with ALD