54 research outputs found
Spiral-wave Dynamics Depends Sensitively on nhomogeneities in Mathematical Models of Ventricular Tissue
Every sixth death in industrialised countries occurs because of cardiac
arrhythmias like ventricular tachycardia (VT) and ventricular fibrillation
(VF). There is growing consensus that VT is associated with an unbroken spiral
wave of electrical activation on cardiac tissue but VF with broken waves,
spiral turbulence, spatiotemporal chaos and rapid, irregular activation. Thus
spiral-wave activity in cardiac tissue has been studied extensively.
Nevertheless many aspects of such spiral dynamics remain elusive because of the
intrinsically high-dimensional nature of the cardiac-dynamical system. In
particular, the role of tissue heterogeneities in the stability of cardiac
spiral waves is still being investigated. Experiments with conduction blocks in
cardiac tissue yield a variety of results: some suggest that blocks can
eliminate VF partially or completely, leading to VT or quiescence, but others
show that VF is unaffected by obstacles. We propose theoretically that this
variety of results is a natural manifestation of a fractal boundary that must
separate the basins of the attractors associated, respectively, with VF and VT.
We substantiate this with extensive numerical studies of Panfilov and Luo-Rudy
I models, where we show that the suppression of VF depends sensitively on the
position, size, and nature of the inhomogeneity.Comment: 9 pages, 5 figures
The Exotic Barium Bismuthates
We review the remarkable properties, including superconductivity,
charge-density-wave ordering, and metal-insulator transitions, of lead- and
potassium-doped barium bismuthate. We discuss some of the early theoretical
studies of these systems. Our recent theoretical work, on the negative-U\/,
extended-Hubbard model for these systems, is also described. Both the large-
and intermediate-U\/ regimes of this model are examined, using mean-field and
random-phase approximations, particularly with a view to fitting various
experimental properties of these bismuthates. On the basis of our studies, we
point out possibilities for exotic physics in these systems. We also emphasize
the different consequences of electronic and phonon-mediated mechanisms for the
negative U.\/ We show that, for an electronic mechanism, the \secin
\,\,phases of these bismuthates must be unique, with their transport properties
{\it dominated by charge Cooperon bound states}. This can explain the
observed difference between the optical and transport gaps. We propose other
experimental tests for this novel mechanism of charge transport and comment on
the effects of disorder.Comment: UUencoded LaTex file, 122 pages, figures available on request To
appear in Int. J. Mod. Phys. B as a review articl
Comparison of Anterior Chamber Depth Measurements from the Galilei Dual Scheimpflug Analyzer with IOLMaster
Purpose. To compare anterior chamber depth (ACD), representing the distance between the anterior corneal surface and anterior lens surface measurements between the Galilei Dual Scheimpflug Analyzer and the IOLMaster.
Methods. A retrospective review of 65 individual patient eyes with normal anterior segments, and no prior ocular surgery was performed. Patients underwent ACD measurements with both devices during the same session by a trained examiner. Interdevice agreement was evaluated using paired two-tailed t-tests, Pearson correlation coefficient, and Bland-Altman analysis.
Results. The mean ± standard deviation (SD) ACD for the Galilei and IOLMaster was 3.37 ± 0.36 mm (range from 2.62 to 4.13) and 3.25 ± 0.38 mm (range from 2.34 to 3.92), respectively (Pearson correlation coefficient = 0.96). ACD mean difference was 0.12 mm (P < 0.0001); 95% limits of agreement was from −0.09 to 0.34. The Galilei measured slightly longer ACD values than the IOLMaster. There was no relationship between axial length and interdevice difference.
Conclusion. ACD measurements correlate well between the Galilei and IOLMaster, with Galilei values on average 0.12 mm longer than the IOLMaster
Negative-U extended hubbard model for doped barium bismuthates
We present detailed mean-field and random-phase-approximation studies of the negative-U, extended Hubbard model with a view to understanding the properties of the doped barium bismuthates. In particular, we obtain the phase diagram, the excitation spectrum, and the optical conductivity in the semiconducting phase of the bismuthates. We show by explicit calculations how this model leads to a natural explanation for the two, well-separated transport and optical gaps observed in the semiconducting phases of the bismuthates. We fix the parameters in our model by fitting these experimentally observed gaps; and with these parameter values we compute other properties of these systems. We also show how metallic screening and disorder can decrease the superconducting Tc dramatically. Our theory leads to an exotic charge-transport mechanism, dominated by charge ±2e bosons (cooperons), in the semiconducting phases of these systems
Superfluid, Mott-Insulator, and Mass-Density-Wave Phases in the One-Dimensional Extended Bose-Hubbard Model
We use the finite-size density-matrix-renormalization-group (FSDMRG) method
to obtain the phase diagram of the one-dimensional () extended
Bose-Hubbard model for density in the plane, where and
are, respectively, onsite and nearest-neighbor interactions. The phase diagram
comprises three phases: Superfluid (SF), Mott Insulator (MI) and Mass Density
Wave (MDW). For small values of and , we get a reentrant SF-MI-SF phase
transition. For intermediate values of interactions the SF phase is sandwiched
between MI and MDW phases with continuous SF-MI and SF-MDW transitions. We
show, by a detailed finite-size scaling analysis, that the MI-SF transition is
of Kosterlitz-Thouless (KT) type whereas the MDW-SF transition has both KT and
two-dimensional-Ising characters. For large values of and we get a
direct, first-order, MI-MDW transition. The MI-SF, MDW-SF and MI-MDW phase
boundaries join at a bicritical point at (.Comment: 10 pages, 15 figure
Inertial- and Dissipation-Range Asymptotics in Fluid Turbulence
We propose and verify a wave-vector-space version of generalized extended
self similarity and broaden its applicability to uncover intriguing, universal
scaling in the far dissipation range by computing high-order (\leq 20\/)
structure functions numerically for: (1) the three-dimensional, incompressible
Navier Stokes equation (with and without hyperviscosity); and (2) the GOY shell
model for turbulence. Also, in case (2), with Taylor-microscale Reynolds
numbers 4 \times 10^{4} \leq Re_{\lambda} \leq 3 \times 10^{6}\/, we find
that the inertial-range exponents (\zeta_{p}\/) of the order - p\/
structure functions do not approach their Kolmogorov value p/3\/ as
Re_{\lambda}\/ increases.Comment: RevTeX file, with six postscript figures. epsf.tex macro is used for
figure insertion. Packaged using the 'uufiles' utilit
Hyperviscosity, Galerkin truncation and bottlenecks in turbulence
It is shown that the use of a high power of the Laplacian in the
dissipative term of hydrodynamical equations leads asymptotically to truncated
inviscid \textit{conservative} dynamics with a finite range of spatial Fourier
modes. Those at large wavenumbers thermalize, whereas modes at small
wavenumbers obey ordinary viscous dynamics [C. Cichowlas et al. Phys. Rev.
Lett. 95, 264502 (2005)]. The energy bottleneck observed for finite
may be interpreted as incomplete thermalization. Artifacts arising from models
with are discussed.Comment: 4 pages, 2 figures, Phys. Rev. Lett. in pres
Statistical Properties of Turbulence: An Overview
We present an introductory overview of several challenging problems in the
statistical characterisation of turbulence. We provide examples from fluid
turbulence in three and two dimensions, from the turbulent advection of passive
scalars, turbulence in the one-dimensional Burgers equation, and fluid
turbulence in the presence of polymer additives.Comment: 34 pages, 31 figure
Spiral-Wave Turbulence and Its Control in the Presence of Inhomogeneities in Four Mathematical Models of Cardiac Tissue
Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control schemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation
Scroll-Wave Dynamics in Human Cardiac Tissue: Lessons from a Mathematical Model with Inhomogeneities and Fiber Architecture
Cardiac arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), are among the leading causes of death in the industrialized world. These are associated with the formation of spiral and scroll waves of electrical activation in cardiac tissue; single spiral and scroll waves are believed to be associated with VT whereas their turbulent analogs are associated with VF. Thus, the study of these waves is an important biophysical problem. We present a systematic study of the combined effects of muscle-fiber rotation and inhomogeneities on scroll-wave dynamics in the TNNP (ten Tusscher Noble Noble Panfilov) model for human cardiac tissue. In particular, we use the three-dimensional TNNP model with fiber rotation and consider both conduction and ionic inhomogeneities. We find that, in addition to displaying a sensitive dependence on the positions, sizes, and types of inhomogeneities, scroll-wave dynamics also depends delicately upon the degree of fiber rotation. We find that the tendency of scroll waves to anchor to cylindrical conduction inhomogeneities increases with the radius of the inhomogeneity. Furthermore, the filament of the scroll wave can exhibit drift or meandering, transmural bending, twisting, and break-up. If the scroll-wave filament exhibits weak meandering, then there is a fine balance between the anchoring of this wave at the inhomogeneity and a disruption of wave-pinning by fiber rotation. If this filament displays strong meandering, then again the anchoring is suppressed by fiber rotation; also, the scroll wave can be eliminated from most of the layers only to be regenerated by a seed wave. Ionic inhomogeneities can also lead to an anchoring of the scroll wave; scroll waves can now enter the region inside an ionic inhomogeneity and can display a coexistence of spatiotemporal chaos and quasi-periodic behavior in different parts of the simulation domain. We discuss the experimental implications of our study
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