Helical Tubes in Crowded Environments

When placed in a crowded environment, a semi-flexible tube is forced to fold so as to make a more compact shape. One compact shape that often arises in nature is the tight helix, especially when the tube thickness is of comparable size to the tube length. In this paper we use an excluded volume effect to model the effects of crowding. This gives us a measure of compactness for configurations of the tube, which we use to look at structures of the semi-flexible tube that minimize the excluded volume. We focus most of our attention on the helix and which helical geometries are most compact. We found that helices of specific pitch to radius ratio 2.512 to be optimally compact. This is the same geometry that minimizes the global curvature of the curve defining the tube. We further investigate the effects of adding a bending energy or multiple tubes to begin to explore the more complete space of possible geometries a tube could form.Comment: 10 page

An Unstructured Parallel Least-Squares Spectral Element Solver for Incompressible Flow Problems

The parallelization of the least-squares spectral element formulation of the Stokes problem has recently been discussed for incompressible flow problems on structured grids. In the present work, the extension to unstructured grids is discussed. It will be shown that, to obtain an efficient and scalable method, two different kinds of distribution of data are required involving a rather complicated parallel conversion between the data. Once the data conversion has been performed, a large symmetric positive definite algebraic system has to be solved iteratively. It is well known that the Conjugate Gradient method is a good choice to solve such systems. To improve the convergence rate of the Conjugate Gradient process, both Jacobi and Additive Schwarz preconditioners are applied. The Additive Schwarz preconditioner is based on domain decomposition and can be implemented such that a preconditioning step corresponds to a parallel matrix-by-vector product. The new results reveal that the Additive Schwarz preconditioner is very suitable for the p-refinement version of the least-squares spectral element method. To obtain good portable programs which may run on distributed-memory multiprocessors, networks of workstations as well as shared-memory machines we use MPI (Message Passing Interface). Numerical simulations have been performed to validate the scalability of the different parts of the proposed method. The experiments entailed simulating several large scale incompressible flows on a Cray T3E and on an SGI Origin 3800 with the number of processors varying from one to more than one hundred. The results indicate that the present method has very good parallel scaling properties making it a powerful method for numerical simulations of incompressible flows

Structural motifs of biomolecules

Biomolecular structures are assemblies of emergent anisotropic building modules such as uniaxial helices or biaxial strands. We provide an approach to understanding a marginally compact phase of matter that is occupied by proteins and DNA. This phase, which is in some respects analogous to the liquid crystal phase for chain molecules, stabilizes a range of shapes that can be obtained by sequence-independent interactions occurring intra- and intermolecularly between polymeric molecules. We present a singularityfree self-interaction for a tube in the continuum limit and show that this results in the tube being positioned in the marginally compact phase. Our work provides a unified framework for understanding the building blocks of biomolecules.Comment: 13 pages, 5 figure

RELEASE: A High-level Paradigm for Reliable Large-scale Server Software

Erlang is a functional language with a much-emulated model for building reliable distributed systems. This paper outlines the RELEASE project, and describes the progress in the first six months. The project aim is to scale the Erlang’s radical concurrency-oriented programming paradigm to build reliable general-purpose software, such as server-based systems, on massively parallel machines. Currently Erlang has inherently scalable computation and reliability models, but in practice scalability is constrained by aspects of the language and virtual machine. We are working at three levels to address these challenges: evolving the Erlang virtual machine so that it can work effectively on large scale multicore systems; evolving the language to Scalable Distributed (SD) Erlang; developing a scalable Erlang infrastructure to integrate multiple, heterogeneous clusters. We are also developing state of the art tools that allow programmers to understand the behaviour of massively parallel SD Erlang programs. We will demonstrate the effectiveness of the RELEASE approach using demonstrators and two large case studies on a Blue Gene

Measurement induced criticality in quasiperiodic modulated random hybrid circuits

We study one-dimensional hybrid quantum circuits perturbed by quenched quasiperiodic (QP) modulations across the measurement-induced phase transition (MIPT). Considering non-Pisot QP structures, characterized by unbounded fluctuations, allows us to tune the wandering exponent $\beta$ to exceed the Luck bound $\nu \ge 1/(1-\beta)$ for the stability of the MIPT where $\nu\cong 4/3$. Via large-scale numerical simulations of random Clifford circuits interleaved with local projective measurements, we find that sufficiently large QP structural fluctuations destabilize the MIPT and induce a flow to a broad family of critical dynamical phase transitions of the infinite QP type that is governed by the wandering exponent, $\beta$. We numerically determine the associated critical properties, including the correlation length exponent consistent with saturating the Luck bound, and a universal activated dynamical scaling with activation exponent $\psi \cong \beta$, finding excellent agreement with the conclusions of real space renormalization group calculations.Comment: 14 pages, 13 figure

Education and articulation: Laclau and Mouffe’s radical democracy in school

This paper outlines a theory of radical democratic education by addressing a key concept in Laclau and Mouffe’s Hegemony and Socialist Strategy: articulation. Through their concept of articulation, Laclau and Mouffe attempt to liberate Gramsci’s theory of hegemony from Marxist economism, and adapt it to a political sphere inhabited by a plurality of struggles and agents none of which is predominant. However, while for Gramsci the political process of hegemony formation has an explicit educational dimension, Laclau and Mouffe ignore this dimension altogether. My discussion starts with elaborating the concept of articulation and analysing it in terms of three dimensions: performance, connection and transformation. I then address the role of education in Gramsci’s politics, in which the figure of the intellectual is central, and argue that radical democratic education requires renouncing that figure. In the final section, I offer a theory of such education, in which both teacher and students articulate their political differences and identities

Democratization in a passive dendritic tree : an analytical investigation

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as “dendritic democracy”. Although well studied experimentally, to date this phenomenon has not been thoroughly explored from a mathematical perspective. In this paper we adopt a passive model of a dendritic tree with distributed excitatory synaptic conductances and analyze a number of key measures of democracy. In particular, via moment methods we derive laws for the transport, from synapse to soma, of strength, characteristic time, and dispersion. These laws lead immediately to synaptic scalings that overcome attenuation with distance. We follow this with a Neumann approximation of Green’s representation that readily produces the synaptic scaling that democratizes the peak somatic voltage response. Results are obtained for both idealized geometries and for the more realistic geometry of a rat CA1 pyramidal cell. For each measure of democratization we produce and contrast the synaptic scaling associated with treating the synapse as either a conductance change or a current injection. We find that our respective scalings agree up to a critical distance from the soma and we reveal how this critical distance decreases with decreasing branch radius