Defibrillation via the elimination of spiral turbulence in a model for ventricular fibrillation

Ventricular fibrillation, the major reason behind sudden cardiac death, is turbulent cardiac electrical activity in which rapid, irregular disturbances in the spatiotemporal electrical activation of the heart make it incapable of any concerted pumping action. Methods of controlling ventricular fibrillation include electrical defibrillation as well as injected medication. Electrical defibrillation, though widely used, involves subjecting the whole heart to massive, and often counterproductive, electrical shocks. We propose a defibrillation method that uses a very low-amplitude shock (of order mV) applied for a brief duration (of order 100 ms) and over a coarse mesh of lines on our model ventricle.     

The role of cardiac tissue structure in defibrillation

The purpose of this paper is to investigate the relationship between cardiac tissue structure, applied electric field, and the transmembrane potential induced in the process of defibrillation. It outlines a general understanding of the structural mechanisms that contribute to the outcome of a defibrillation shock. Electric shocks defibrillate by changing the transmembrane potential throughout the myocardium. In this process first and foremost the shock current must access the bulk of myocardial mass. The exogenous current traverses the myocardium along convoluted intracellular and extracellular pathways channeled by the tissue structure. Since individual fibers follow curved pathways in the heart, and the fiber direction rotates across the ventricular wall, the applied current perpetually engages in redistribution between the intra- and extracellular domains. This redistribution results in changes in transmembrane potential (membrane polarization): regions of membrane hyper- and depolarization of extent larger than a single cell are induced in the myocardium by the defibrillation shock. Tissue inhomogeneities also contribute to local membrane polarization in the myocardium which is superimposed over the large-scale polarization associated with the fibrous organization of the myocardium. The paper presents simulation results that illustrate various mechanisms by which cardiac tissue structure assists the changes in transmembrane potential throughout the myocardium. (c) 1998 American Institute of Physics.     

Integration of shock absorption and energy harvesting using a hydraulic rectifier

Hydraulic shock absorbers have been widely used to dissipate kinetic energy of the shocks into surrounding environment. By employing oscillatory motion to drive power generator, the shock energy can be converted into electricity for harvesting. However, the frequent bidirectional oscillation of the generator can cause a large impact force. This further leads to deteriorated energy harvesting performance, moving parts fatigue, and even system failure. As such, this study introduces four check values to form a hydraulic rectifier to integrate the shock absorption and energy harvesting functionalities. The bidirectional oscillation of the shock and the vibration is converted into unidirectional rotation to drive the generator. Following the proposed concept, a prototype energy-harvesting shock absorber has been designed and fabricated. An electromechanical model has also been developed to examine the response behavior of the prototype device. The prototype performance has been characterized based on the experimental results from three test setups. Both mechanical and electrical parameters of the electromechanical model have been identified based on our cyclic loading experiments. The results have shown that the developed energy-harvesting shock absorber is capable of harvesting the energy and absorbing the shock simultaneously. In our experiments, a maximum of 248.8 W instantaneous power (a maximum of 114.1 W on average) has been captured and a maximum of 38.81% energy harvesting efficiency has been achieved via harmonic excitation with an amplitude of 8 mm and a frequency of 2 Hz, when the load resistance is tuned to 7.5 Ω.     

Behavior of viscous solutions in Lagrangian formulation

In this paper, the behavior of shock-capturing methods in Lagrangian coordinate is investigated. The relation between viscous shock and inviscid one is analyzed quantitatively, and the procedure of a viscous shock formation and propagation with a jump type initial data is described. In general, a viscous shock profile and a discontinuous one include different energy and momentum, and these discrepancies result in the generation of waves in all families when a single wave Riemann problem (shock or rarefaction) is solved. Employing this method, some anomalous behavior, such as, viscous shock interaction, shock passing through ununiform grids, postshock oscillations and lower density phenomenon is explained well. Using some classical schemes to solve the inviscid flow in Lagrangian coordinate may be not adequate enough to correctly describe flow motion in the discretized space. Partial discrepancies between von Neumann artificial viscosity method and Godunov method are exhibited. Some reviews are given to those methods which can ameliorate even eliminate entropy errors. A hybrid scheme based on the understanding to the behavior of viscous solution is proposed to suppress the overheating error.     

Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor–Green vortex, Shu–Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.     

Temperature overshoots for a 4-velocity unidimensional discrete Boltzmann model

We propose a 4-velocity unidimensional discrete Boltzmann model with two different speeds 2, 1 and two different masses 1, 2. With the three conservation laws of mass, momentum, and energy satisfied, we can introduce a nontrivial temperature. First, we determine the similarity shock waves satisfying physical properties: positivity, shock stability, inequalities of the subsonic and supersonic flows, increase or decrease of both mass and temperature across the shock. It results that either the speed of the shock front is higher than the speed 1 of the slow particles and the shocks are compressive or less than 1 and the shocks are rarefactive. We observe overshoots of the temperature, across the shock, with bumps higher and higher as the shock front speed increases. Second, we study the (1+1)-dimensional shock waves. They represent the superposition and collision of two compressive shocks traveling in opposite directions and we observe temperature overshoots for not too large times.     

Velocity and timing of multiple spherically converging shock waves in liquid deuterium

The fuel entropy and required drive energy for an inertial confinement fusion implosion are set by a sequence of shocks that must be precisely timed to achieve ignition. This Letter reports measurements of multiple spherical shock waves in liquid deuterium that facilitate timing inertial confinement fusion shocks to the required precision. These experiments produced the highest shock velocity observed in liquid deuterium (U(s) = 135 km/s at ～2500 GPa) and also the first observation of convergence effects on the shock velocity. Simulations model the shock-timing results well when a nonlocal transport model is used in the coronal plasma.     

Particle acceleration at astrophysical shocks: A theory of cosmic ray origin

The theory of first order Fermi acceleration at collisionless astrophysical shock fronts is reviewed. Observations suggest that shock waves in different astrophysical environments accelerate cosmic rays efficiently. In the first order process, high energy particles diffuse through Alfvén waves that scatter them and couple them to the background plasma. These particles gain energy, on the average, every time they cross the schock front and bounce off approaching scattering centers. Calculations demonstrate that the distribution function transmitted by a plane shock is roughly a power law in momentum with slope similar to that inferred in galactic cosmic ray sources. The generation of the scattering Alfvén waves by the streaming cosmic rays is described and it is argued that the wave amplitude is probably non-linear within sufficiently strong astrophysical shocks. Hydromagnetic scattering can operate on the thermal particles as well, possibly establishing the shock structure. This suggests a model of strong collisionless shocks in which high energy particles are inevitably produced very efficiently. Observable consequences of this model, together with its limitations and some alternatives, are described. Cosmic ray origin and astrophysical shocks can no longer be considered separately.     

Performance of a cantilever piezoelectric energy harvester impacting a bump stop

Piezoelectric cantilever beam energy harvesters are commonly used to convert ambient vibration into electrical energy. In practical applications, energy harvesters are subjected to large shocks which can shorten the service life by causing mechanical failure. In this work, a bump stop is introduced into the design of a piezoelectric cantilever beam energy harvester to limit the maximum displacement of the cantilever and prevent excessively high bending stresses developing as a result of shocks. In addition to limiting the maximum displacement of the beam, it is inevitable that the deflected shape of the beam and the electrical output are modified. A theoretical model for a piezoelectric cantilever beam harvester impacting against a stop is derived, which aims to develop an understanding of the vibration characteristics of the cantilever and quantify how the electrical output of the harvester is affected by the stop. An experiment is set up to measure the dynamics and the electrical output of a bimorph energy harvester and to validate the theoretical model. Numerical simulation results are presented for energy harvesters with different initial gaps and different stop locations, and it is found that the reduction in maximum bending stress is at the expense of the electrical power of the harvester.     

Generation of Ultrahigh-Velocity Collisionless Electrostatic Shocks Using an Ultra-Intense Laser Pulse Interacting with Foil-Gas Target

Ultra high-velocity collisionless shocks are generated using an ultra-intense laser interacting with foil-gas target,which consists of copper foil and helium gas.The energy of helium ions accelerated by shock and the proton probing image of the shock electrostatic field show that the shock velocity is 0.02c,where c is the light speed.The numerical and theory studies indicate that the collisionless shock velocity exceeding 0.1 c can be generated by a laser pulse with picosecond duration and an intensity of 10~(20) W/cm~2.This system may be relevant to the study of mildly relativistic velocity collisionless shocks in astrophysics.     

Multiplicity of detonation regimes in systems with a multi-peaked thermicity

The study investigates detonations with multiple quasi-steady velocities that have been observed in the past in systems with multi-peaked thermicity, using Fickett's detonation analogue. A steady-state analysis of the travelling wave predicts multiple states, however, all but the one with the highest velocity develop a singularity after the sonic point. Simulations show singularities are associated with a shock wave which overtakes all sonic points, establishing a detonation travelling at the highest of the predicted velocities. Under a certain parameter range, the steady-state detonation can have multiple sonic points and solutions. Embedded shocks can exist behind sonic points, where they link the weak and strong solutions. Sonic points whose characteristics do not diverge are found to be unstable, and to be the source of the embedded shocks. Numerical simulations show that these shocks are only quasi-stable. This is believed to be due in part to a feature of the model which permits shocks anywhere behind a sonic point.     

SiO_2/CH/Au复合黑腔诊断孔电火花加工技术

通过电火花加工技术,采用含碳较高的煤油作为电介质,利用导电性能及加工性能较好的紫铜作电极材料,实现了SiO2/CH/Au复合黑腔侧表面方形诊断孔的精密加工。采用OLYMPUS STM6测量显微镜对诊断孔尺寸,结果表明:孔的尺寸加工精度可控制在±10μm内,同一电极加工的诊断孔尺寸一致性可控制在±5μm内。采用扫描电镜能谱分析SiO2/CH/Au加工导电层的成分,结果表明:电火花加工过程中,由于电介质分解生成游离态的碳以及电极材料铜熔融后沉积在CH和SiO2层表面,形成辅助导电层。通过加工辅助导电层,产生的瞬时高温使SiO2和CH层熔融气化,从而实现对绝缘层的加工。     

Random Walk of Second Class Particles in Product Shock Measures

We consider shock measures in a class of conserving stochastic particle systems on ℤ. These shock measures have a product structure with a step-like density profile and include a second class particle at the shock position. We show for the asymmetric simple exclusion process, for the exponential bricklayers’ process, and for a generalized zero range process, that under certain conditions these shocks, and therefore the second class particles, perform a simple random walk. Some previous results, including random walks of product shock measures and stationary shock measures seen from a second class particle, are direct consequences of our more general theorem. Multiple shocks can also be handled easily in this framework. Similar shock structure is also found in a nonconserving model, the branching coalescing random walk, where the role of the second class particle is played by the rightmost (or leftmost) particle.     

Focusing of noncircular self-similar shock waves

We study the focusing of noncircular shock waves in a perfect gas. We construct an explicit self-similar solution by combining three convergent plane waves with regular shock reflections between them. We then show, with a numerical Riemann solver, that there are initial conditions with smooth shocks whose intermediate asymptotic stage is described by the exact solution. Unlike the focusing of circular shocks, our self-similar shocks have bounded energy density.     

Arrhythmogenesis in the heart: Multiscale modeling of the effects of defibrillation shocks and the role of electrophysiological heterogeneity

The mechanisms of initiation of ventricular arrhythmias as well as those behind the complex spatiotemporal wave dynamics and its filament organization during ventricular fibrillation (VF) are the topic of intense research and debate. Mechanistic inquiry into the various mechanisms that lead to arrhythmia initiation and VF maintenance is hampered by the inability of current experimental techniques to resolve, with sufficient accuracy, electrical behavior confined to the depth of the ventricles. The objective of this article is to demonstrate that realistic 3D simulations of electrical activity in the heart are capable of bringing a new level of understanding of the mechanisms that underlie arrhythmia initiation and subsequent organization. The article does this by presenting the results of two multiscale simulation studies of ventricular electrical behavior. The first study aims to uncover the mechanisms responsible for rendering the ventricles vulnerable to electric shocks during a specific interval of time, the vulnerable window. The second study focuses on elucidating the role of electrophysiological heterogeneity, and specifically, differences in action potential duration in various ventricular structures, in VF organization. Both studies share common multiscale modeling approaches and analysis, including characterization of scroll-wave filament dynamics.     

Disappearance of holographic and interference fringes accompanies optical diagnostics of a supersonic bow shock flow

Preliminary results of optical diagnostics of bow shocks in a supersonic wind tunnel by applying dual-hologram shear interferometry technique are discussed. A strong refraction effect of the probing beam penetrating a region in the vicinity of a bow shock over a blunt nose cone model has been discovered. On a signal hologram the effect leads to the disappearance of holographic fringes in a narrow region attached to the shock wave front. A reconstructed interferogram in this region manifests the absence of an interference pattern.Computer simulations were performed for a part of the probing beam penetrating the area of high-density steep gradients of compressed air attached to the central part of the shock front of a bow shock. The compressed area was modeled as a hyperbolic cap. The bow shock was assumed axisymmetric. The simulations made it possible to evaluate angles of deflections and found conformity with reconstructed interferograms (shadowgraphs).It is concluded that in the above-indicated region of bow shocks probing light is deviated refractively into some angles, which could be large enough for light rays to be blocked out and never arrive at the detector (photo film). In the case when interferometric fringes disappear, the effect of strong refraction makes it impossible to measure air density gradients in some critical region.     

Jump relations for shocks in an anisotropic magnetized plasma

The jump relations for shocks moving into a collision-free anisotropic magnetized plasma are investigated under the assumption of isotropy of the plasma behind the shock front. The plasma ahead of the shock is assumed to be stable against the fire-hose instability and the mirror instability. In order to facilitate comparison with the work of Bazer and Ericson on isotropic shocks our nomenclature has been adapted to theirs. It turns out that as in the case of isotropic shocks the density ratio can be at most four corresponding to γ=5/3, that the change in magnetic field is bounded and that except for the case of Alfvén shocks the transverse parts of the magnetic field are collinear. It is further shown that the influence of the anisotropy is greatest for nearly equal thermal and magnetic energy densities. In the case of negative anisotropy no compressive shocks are possible with a major decrease in magnetic field if the thermal energy density much exceeds the magnetic energy density. A new kind of shock is shown to result from the analysis, the major effect of which is to destroy the anisotropy with only small changes in density, magnetic field and velocity vector. Its propagation speed is unbounded. Furthermore it has turned out that compressive, magnetic field increasing shocks have lower bounds in the density jump and magnetic field change for negative and positive anisotropy, respectively. In the collision-free case no unique entropy condition depending only on the total pressure components and densities can be given before the solution of the problem of shock structure. Therefore even expansive shocks may be admissible. The applicability of the isotropy assumption and ad-hoc-assumptions of other authors are briefly discussed.     

Standing Rankine-Hugoniot Shocks in Black Hole Accretion Discs

We study the problem of standing shocks in viscous disc-like accretion flows around black holes. For the first time we parametrize such a flow with two physical constants, namely the specific angular momentum accreted by the black hole j and the energy quantity K. By providing the global dependence of shock formation in the j- K parameter space, we show that a significant parameter region can ensure solutions with Rankine-Hugoniot shocks; and that the possibilities of shock formation are the largest for inviscid flows, decreasing with increasing viscosity, and ceasing to exist for a strong enough viscosity. Our results support the view that the standing shock is an essential ingredient in black hole accretion discs and is a general phenomenon in astrophysics, and that there should be a continuous change from the properties of inviscid flows to those of viscous ones.     

Stability of Viscous Shocks in Isentropic Gas Dynamics

In this paper, we examine the stability problem for viscous shock solutions of the isentropic compressible Navier–Stokes equations, or p-system with real viscosity. We first revisit the work of Matsumura and Nishihara, extending the known parameter regime for which small-amplitude viscous shocks are provably spectrally stable by an optimized version of their original argument. Next, using a novel spectral energy estimate, we show that there are no purely real unstable eigenvalues for any shock strength. By related estimates, we show that unstable eigenvalues are confined to a bounded region independent of shock strength. Then through an extensive numerical Evans function study, we show that there are no unstable spectra in the entire right-half plane, thus demonstrating numerically that large-amplitude shocks are spectrally stable up to Mach number M ≈ 3000 for 1 ≤ γ ≤ 3. This strongly suggests that shocks are stable independent of amplitude and the adiabatic constant γ. We complete our study by showing that finite-difference simulations of perturbed large-amplitude shocks converge to a translate of the original shock wave, as expected. This work was supported in part by the National Science Foundation award numbers DMS-0607721 and DMS-0300487.     

Dispersive nature of high mach number collisionless plasma shocks: Poynting flux of oblique whistler waves

Whistler wave trains are observed in the foot region of high Mach number quasiperpendicular shocks. The waves are oblique with respect to the ambient magnetic field as well as the shock normal. The Poynting flux of the waves is directed upstream in the shock normal frame starting from the ramp of the shock. This suggests that the waves are an integral part of the shock structure with the dispersive shock as the source of the waves. These observations lead to the conclusion that the shock ramp structure of supercritical high Mach number shocks is formed as a balance of dispersion and nonlinearity.