Integrals of Motion for Critical Dense Polymers and Symplectic Fermions

We consider critical dense polymers ${\cal L}(1,2)$. We obtain for this model the eigenvalues of the local integrals of motion of the underlying Conformal Field Theory by means of Thermodynamic Bethe Ansatz. We give a detailed description of the relation between this model and Symplectic Fermions including the indecomposable structure of the transfer matrix. Integrals of motion are defined directly on the lattice in terms of the Temperley Lieb Algebra and their eigenvalues are obtained and expressed as an infinite sum of the eigenvalues of the continuum integrals of motion. An elegant decomposition of the transfer matrix in terms of a finite number of lattice integrals of motion is obtained thus providing a reason for their introduction.Comment: 53 pages, version accepted for publishing on JSTA

An investigation of the performance of a new Mechanical thrombectomy device using Bond Graph modelling: application to the extraction of blood clots in the middle cerebral artery

A number of thrombectomy devices using a variety of methods have now been developed to facilitate clot removal. We present research involving one such experimental device recently developed in the UK, called a ‘GP’ Thrombus Aspiration Device (GPTAD). This device has the potential to bring about the extraction of a thrombus. Although the device is at a relatively early stage of development, the results look encouraging. In this work, we present an analysis and modeling of the GPTAD by means of the bond graph technique; it seems to be a highly effective method of simulating the device under a variety of conditions. Such modeling is useful in optimizing the GPTAD and predicting the result of clot extraction. The aim of this simulation model is to obtain the minimum pressure necessary to extract the clot and to verify that both the pressure and the time required to complete the clot extraction are realistic for use in clinical situations, and are consistent with any experimentally obtained data. We therefore consider aspects of rheology and mechanics in our modeling

Trace element geochemistry of peridotites from the Izu-Bonin-Mariana Forearc, Leg 125

Trace element analyses (first-series transition elements, Ti, Rb, Sr, Zr, Y, Nb, and REE) were carried out on whole rocks and minerals from 10 peridotite samples from both Conical Seamount in the Mariana forearc and Torishima Forearc Seamount in the Izu-Bonin forearc using a combination of XRF, ID-MS, ICP-MS, and ion microprobe. The concentrations of incompatible trace elements are generally low, reflecting the highly residual nature of the peridotites and their low clinopyroxene content (n ratios in the range of 0.05-0.25; several samples show possible small positive Eu anomalies. LREE enrichment is common to both seamounts, although the peridotites from Conical Seamount have higher (La/Ce)n ratios on extended chondrite-normalized plots, in which both REEs and other trace elements are organized according to their incompatibility with respect to a harzburgitic mantle. Comparison with abyssal peridotite patterns suggests that the LREEs, Rb, Nb, Sr, Sm, and Eu are all enriched in the Leg 125 peridotites, but Ti and the HREEs exhibit no obvious enrichment. The peridotites also give positive anomalies for Zr and Sr relative to their neighboring REEs. Covariation diagrams based on clinopyroxene data show that Ti and the HREEs plot on an extension of an abyssal peridotite trend to more residual compositions. However, the LREEs, Rb, Sr, Sm, and Eu are displaced off this trend toward higher values, suggesting that these elements were introduced during an enrichment event. The axis of dispersion on these plots further suggests that enrichment took place during or after melting and thus was not a characteristic of the lithosphere before subduction. Compared with boninites sampled from the Izu-Bonin-Mariana forearc, the peridotites are significantly more enriched in LREEs. Modeling of the melting process indicates that if they represent the most depleted residues of the melting events that generated forearc boninites they must have experienced subsolidus enrichment in these elements, as well as in Rb, Sr, Zr, Nb, Sm, and Eu. The lack of any correlation with the degree of serpentinization suggests that low-temperature fluids were not the prime cause of enrichment. The enrichment in the high-field-strength elements also suggests that at least some of this enrichment may have involved melts rather than aqueous fluids. Moreover, the presence of the hydrous minerals magnesio-hornblende and tremolite and the common resorption of orthopyroxene indicate that this high-temperature peridotite-fluid interaction may have taken place in a water-rich environment in the forearc following the melting event that produced the boninites. The peridotites from Leg 125 may therefore contain a record of an important flux of elements into the mantle wedge during the initial formation of forearc lithosphere. Ophiolitic peridotites with these characteristics have not yet been reported, perhaps because the precise equivalents to the serpentinite seamounts have not been analyzed

The influence of baryons on the mass distribution of dark matter halos

Using a set of high-resolution N-body/SPH cosmological simulations with identical initial conditions but run with different numerical setups, we investigate the influence of baryonic matter on the mass distribution of dark halos when radiative cooling is NOT included. We compare the concentration parameters of about 400 massive halos with virial mass from $10^{13}$ \Msun to $7.1 \times 10^{14}$ \Msun. We find that the concentration parameters for the total mass and dark matter distributions in non radiative simulations are on average larger by ~3% and 10% than those in a pure dark matter simulation. Our results indicate that the total mass density profile is little affected by a hot gas component in the simulations. After carefully excluding the effects of resolutions and spurious two-body heating between dark matter and gas particles, we conclude that the increase of the dark matter concentration parameters is due to interactions between baryons and dark matter. We demonstrate this with the aid of idealized simulations of two-body mergers. The results of individual halos simulated with different mass resolutions show that the gas profiles of densities, temperature and entropy are subjects of mass resolution of SPH particles. In particular, we find that in the inner parts of halos, as the SPH resolution increases the gas density becomes higher but both the entropy and temperature decrease.Comment: 8 pages, 6 figures, 1 table, ApJ in press (v652n1); updated to match with the being published versio

Wind on the boundary for the Abelian sandpile model

We continue our investigation of the two-dimensional Abelian sandpile model in terms of a logarithmic conformal field theory with central charge c=-2, by introducing two new boundary conditions. These have two unusual features: they carry an intrinsic orientation, and, more strangely, they cannot be imposed uniformly on a whole boundary (like the edge of a cylinder). They lead to seven new boundary condition changing fields, some of them being in highest weight representations (weights -1/8, 0 and 3/8), some others belonging to indecomposable representations with rank 2 Jordan cells (lowest weights 0 and 1). Their fusion algebra appears to be in full agreement with the fusion rules conjectured by Gaberdiel and Kausch.Comment: 26 pages, 4 figure

Nature versus Nurture: The curved spine of the galaxy cluster X-ray luminosity -- temperature relation

The physical processes that define the spine of the galaxy cluster X-ray luminosity -- temperature (L-T) relation are investigated using a large hydrodynamical simulation of the Universe. This simulation models the same volume and phases as the Millennium Simulation and has a linear extent of 500 h^{-1} Mpc. We demonstrate that mergers typically boost a cluster along but also slightly below the L-T relation. Due to this boost we expect that all of the very brightest clusters will be near the peak of a merger. Objects from near the top of the L-T relation tend to have assembled much of their mass earlier than an average halo of similar final mass. Conversely, objects from the bottom of the relation are often experiencing an ongoing or recent merger.Comment: 8 pages, 7 figures, submitted to MNRA

Solvable Critical Dense Polymers

A lattice model of critical dense polymers is solved exactly for finite strips. The model is the first member of the principal series of the recently introduced logarithmic minimal models. The key to the solution is a functional equation in the form of an inversion identity satisfied by the commuting double-row transfer matrices. This is established directly in the planar Temperley-Lieb algebra and holds independently of the space of link states on which the transfer matrices act. Different sectors are obtained by acting on link states with s-1 defects where s=1,2,3,... is an extended Kac label. The bulk and boundary free energies and finite-size corrections are obtained from the Euler-Maclaurin formula. The eigenvalues of the transfer matrix are classified by the physical combinatorics of the patterns of zeros in the complex spectral-parameter plane. This yields a selection rule for the physically relevant solutions to the inversion identity and explicit finitized characters for the associated quasi-rational representations. In particular, in the scaling limit, we confirm the central charge c=-2 and conformal weights Delta_s=((2-s)^2-1)/8 for s=1,2,3,.... We also discuss a diagrammatic implementation of fusion and show with examples how indecomposable representations arise. We examine the structure of these representations and present a conjecture for the general fusion rules within our framework.Comment: 35 pages, v2: comments and references adde

Development of laminar flow control wing surface porous structure

It was concluded that the chordwise air collection method, which actually combines chordwise and spanwise air collection, is the best of the designs conceived up to this time for full chord laminar flow control (LFC). Its shallower ducting improved structural efficiency of the main wing box resulting in a reduction in wing weight, and it provided continuous support of the chordwise panel joints, better matching of suction and clearing airflow requirements, and simplified duct to suction source minifolding. Laminar flow control on both the upper and lower surfaces was previously reduced to LFC suction on the upper surface only, back to 85 percent chord. The study concludes that, in addition to reduced wing area and other practical advantages, this system would be lighter because of the increase in effective structural wing thickness

Geometric Exponents, SLE and Logarithmic Minimal Models

In statistical mechanics, observables are usually related to local degrees of freedom such as the Q < 4 distinct states of the Q-state Potts models or the heights of the restricted solid-on-solid models. In the continuum scaling limit, these models are described by rational conformal field theories, namely the minimal models M(p,p') for suitable p, p'. More generally, as in stochastic Loewner evolution (SLE_kappa), one can consider observables related to nonlocal degrees of freedom such as paths or boundaries of clusters. This leads to fractal dimensions or geometric exponents related to values of conformal dimensions not found among the finite sets of values allowed by the rational minimal models. Working in the context of a loop gas with loop fugacity beta = -2 cos(4 pi/kappa), we use Monte Carlo simulations to measure the fractal dimensions of various geometric objects such as paths and the generalizations of cluster mass, cluster hull, external perimeter and red bonds. Specializing to the case where the SLE parameter kappa = 4p'/p is rational with p < p', we argue that the geometric exponents are related to conformal dimensions found in the infinitely extended Kac tables of the logarithmic minimal models LM(p,p'). These theories describe lattice systems with nonlocal degrees of freedom. We present results for critical dense polymers LM(1,2), critical percolation LM(2,3), the logarithmic Ising model LM(3,4), the logarithmic tricritical Ising model LM(4,5) as well as LM(3,5). Our results are compared with rigourous results from SLE_kappa, with predictions from theoretical physics and with other numerical experiments. Throughout, we emphasize the relationships between SLE_kappa, geometric exponents and the conformal dimensions of the underlying CFTs.Comment: Added reference

Off-Critical Logarithmic Minimal Models

We consider the integrable minimal models ${\cal M}(m,m';t)$, corresponding to the $\varphi_{1,3}$ perturbation off-criticality, in the {\it logarithmic limit\,} $m, m'\to\infty$, $m/m'\to p/p'$ where $p, p'$ are coprime and the limit is taken through coprime values of $m,m'$. We view these off-critical minimal models ${\cal M}(m,m';t)$ as the continuum scaling limit of the Forrester-Baxter Restricted Solid-On-Solid (RSOS) models on the square lattice. Applying Corner Transfer Matrices to the Forrester-Baxter RSOS models in Regime III, we argue that taking first the thermodynamic limit and second the {\it logarithmic limit\,} yields off-critical logarithmic minimal models ${\cal LM}(p,p';t)$ corresponding to the $\varphi_{1,3}$ perturbation of the critical logarithmic minimal models ${\cal LM}(p,p')$. Specifically, in accord with the Kyoto correspondence principle, we show that the logarithmic limit of the one-dimensional configurational sums yields finitized quasi-rational characters of the Kac representations of the critical logarithmic minimal models ${\cal LM}(p,p')$. We also calculate the logarithmic limit of certain off-critical observables ${\cal O}_{r,s}$ related to One Point Functions and show that the associated critical exponents $\beta_{r,s}=(2-\alpha)\,\Delta_{r,s}^{p,p'}$ produce all conformal dimensions $\Delta_{r,s}^{p,p'}<{(p'-p)(9p-p')\over 4pp'}$ in the infinitely extended Kac table. The corresponding Kac labels $(r,s)$ satisfy $(p s-p' r)^2< 8p(p'-p)$. The exponent $2-\alpha ={p'\over 2(p'-p)}$ is obtained from the logarithmic limit of the free energy giving the conformal dimension $\Delta_t={1-\alpha\over 2-\alpha}={2p-p'\over p'}=\Delta_{1,3}^{p,p'}$ for the perturbing field $t$. As befits a non-unitary theory, some observables ${\cal O}_{r,s}$ diverge at criticality.Comment: 18 pages, 5 figures; version 3 contains amplifications and minor typographical correction