Crack motion in viscoelastic solids: The role of the flash temperature

We present a simple theory of crack propagation in viscoelastic solids. We calculate the energy per unit area, G(v), to propagate a crack, as a function of the crack tip velocity v. Our study includes the non-uniform temperature distribution (flash temperature) in the vicinity of the crack tip, which has a profound influence on G(v). At very low crack tip velocities, the heat produced at the crack tip can diffuse away, resulting in very small temperature increase: in this “low-speed” regime the flash temperature effect is unimportant. However, because of the low heat conductivity of rubber-like materials, already at moderate crack tip velocities a very large temperature increase (of order of 1000 K) can occur close to the crack tip. We show that this will drastically affect the viscoelastic energy dissipation close to the crack tip, resulting in a “hot-crack” propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt, which may result in unstable crack motion, e.g. stick-slip motion or catastrophic failure, as observed in some experiments. In addition, the high crack tip temperature may result in significant thermal decomposition within the heated region, resulting in a liquid-like region in the vicinity of the crack tip. This may explain the change in surface morphology (from rough to smooth surfaces) which is observed as the crack tip velocity is increased above the instability threshold.     

不同惯性系中的力学规律

由力学相对性原理可知，在不同惯性系中，一切力学规律（如牛顿运动定律、动量定理、动量守恒定律、角动量定理等）的形式都相同．但在一个惯性系中机械能（或角动量）守恒，在另一惯性系中观察机械能（或角动量）却不一定守恒．     

Toward a Finite-Dimensional Formulation of Quantum Field Theory

Rules of quantization and equations of motion for a finite-dimensional formulation of quantum field theory are proposed which fulfill the following properties: (a) Both the rules of quantization and the equations of motion are covariant; (b) the equations of evolution are second order in derivatives and first order in derivatives of the spacetime coordinates; and (c) these rules of quantization and equations of motion lead to the usual (canonical) rules of quantization and the (Schrödinger) equation of motion of quantum mechanics in the particular case of mechanical systems. We also comment briefly on further steps to fully develop a satisfactory quantum field theory and the difficuties which may be encountered when doing so.     

Fracture and friction: Stick-slip motion

We discuss the stick-slip motion of an elastic block sliding along a rigid substrate. We argue that for a given external shear stress this system shows a discontinuous nonequilibrium transition from a uniform stick state to uniform sliding at some critical stress which is nothing but the Griffith threshold for crack propagation. An inhomogeneous mode of sliding occurs when the driving velocity is prescribed instead of the external stress. A transition to homogeneous sliding occurs at a critical velocity, which is related to the critical stress. We solve the elastic problem for a steady-state motion of a periodic stick-slip pattern and derive equations of motion for the tip and resticking end of the slip pulses. In the slip regions we use the linear friction law and do not assume any intrinsic instabilities even at small sliding velocities. We find that, as in many other pattern forming system, the steady-state analysis itself does not select uniquely all the internal parameters of the pattern, especially the primary wavelength. Using some plausible analogy to first-order phase transitions we discuss a soft selection mechanism. This allows to estimate internal parameters such as crack velocities, primary wavelength and relative fraction of the slip phase as functions of the driving velocity. The relevance of our results to recent experiments is discussed.     

Heat and fluctuations from order to chaos

The Heat theorem reveals the second law of equilibrium Thermodynamics (i.e. existence of Entropy) as a manifestation of a general property of Hamiltonian Mechanics and of the Ergodic Hypothesis, valid for 1 as well as 10²³ degrees of freedom systems, i.e. for simple as well as very complex systems, and reflecting the Hamiltonian nature of the microscopic motion. In Nonequilibrium Thermodynamics theorems of comparable generality do not seem to be available. Yet it is possible to find general, model independent, properties valid even for simple chaotic systems (i.e. the hyperbolic ones), which acquire special interest for large systems: the Chaotic Hypothesis leads to the Fluctuation Theorem which provides general properties of certain very large fluctuations and reflects the time-reversal symmetry. Implications on Fluids and Quantum systems are briefly hinted. The physical meaning of the Chaotic Hypothesis, of SRB distributions and of the Fluctuation Theorem is discussed in the context of their interpretation and relevance in terms of Coarse Grained Partitions of phase space. This review is written taking some care that each section and appendix is readable either independently of the rest or with only few cross references.     

Propagation of arbitrary initial wave packets in a quantum parametric oscillator: Instability zones for higher order moments

We consider the dynamics of a particle in a parametric oscillator with a view to exploring any quantum feature of the initial wave packet that shows divergent (in time) behaviour for parameter values where the classical motion dynamics of the mean position is bounded. We use Ehrenfest's theorem to explore the dynamics of nth order moment which reduces exactly to a linear non autonomous differential equation of order $n+1$. It is found that while the width and skewness of the packet is unbounded exactly in the zones where the classical motion is unbounded, the kurtosis of an initially non-gaussian wave packet can become infinitely large in certain additional zones. This implies that the shape of the wave packet can change drastically with time in these zones.     

Coherent dynamics of magnetoexcitons in semiconductor nanorings

The coherent dynamics of magnetoexcitons in semiconductor nanorings following pulsed optical excitation is studied. The calculated temporal evolution of the excitonic dipole moment may be understood as a superposition of the relative motion of electrons and holes and a global circular motion associated with the magnetic-field splitting of these states. This dynamics of the electron-hole pairs can be generated either by local optical excitation of an ordered ring or, alternatively, by homogeneous excitation of rings with broken rotational symmetry due to disorder or band tilting. Received 27 September 2000     

Dynamical analysis of bounded and unbounded orbits in a generalized Hénon–Heiles system

The Hénon–Heiles potential was first proposed as a simplified version of the gravitational potential experimented by a star in the presence of a galactic center. Currently, this system is considered a paradigm in dynamical systems because despite its simplicity exhibits a very complex dynamical behavior. In the present paper, we perform a series expansion up to the fifth-order of a potential with axial and reflection symmetries, which after some transformations, leads to a generalized Hénon–Heiles potential. Such new system is analyzed qualitatively in both regimes of bounded and unbounded motion via the Poincaré sections method and plotting the exit basins. On the other hand, the quantitative analysis is performed through the Lyapunov exponents and the basin entropy, respectively. We find that in both regimes the chaoticity of the system decreases as long as the test particle energy gets far from the critical energy. Additionally, we may conclude that despite the inclusion of higher order terms in the series expansion, the new system shows wider zones of regularity (islands) than the ones present in the Hénon–Heiles system.     

The alterations of magnetic resonance relaxation parameters in excised myocardial tissue during NMR spectroscopy: the effects of time, environmental exposure and TTC staining

To investigate the potential impact of air exposure, time delay and vital tissue staining on the MR relaxation parameters in normal and pathological heart tissues, myocardial samples from a canine model of myocardial infarction were subject to (a) air exposure for up to 20 hours or (b) wrapping in Parafilm for up to 20 hours; immersion in (c) full strength pathological stain consisting of triphenyl tetrazolium chloride (TTC), or (d) half strength TTC, or (e) normal saline for 30 minutes. We found that (a) exposure to air produced rapid change in both T1 and T2 such that there is a reduction of T1 by 12.2% and T2 by 14.4% (p less than 0.001) in one hour; (b) airtight wrapping attenuated dramatically these changes, but T1 still was reduced by 2.9% and T2 by 4.8% in one hour (p less than 0.01). These changes followed similar but non-linear changes of tissue water content. T1 did not change significantly after exposure to full strength TTC, but did increase significantly after exposure to half strength TTC, and increased even further after exposure to saline. T2 on the other hand increased significantly with all of these test solutions. We conclude that the in vitro processing of excised myocardial tissues should be done by wrapping in an airtight container with T1 and T2 parameters measured within one hour, if possible. All tissue processing, including stains and saline exposure, should be done after spectrometer measurements.     

The validity of the principle of equivalence in the WKB limit of quantum mechanics

In the context of the causal interpretation of quantum mechanics one can formulate the equation of motion of a quantal particle in the presence of a gravitational field. It is pointed out that, in the WKB limit of high quantum numbers, states exist for which one component of classical equivalence (that all bodies fall at an equal rate independent of their mass) is not recovered, due to quantum effects mediated by the quantum potential.1. The classical limit of the uncertainty relations is obtained when part of the quantum stress tensor of the field may be neglected - it is not necessary or necessarily consistent to let h 0 here either [3].2. In the relativistic case, one can nevertheless still geometrize quantum mechanics in the presence of gravity by introducing metrics that depend on particle characteristics (e.g. Finsler metric). The equation of motion is then a geodesic in this generalized space [8,9].     

Molecular and genomic characterization of pathogenic traits of group A Streptococcus pyogenes

Group A streptococcus (GAS) or Streptococcus pyogenes causes various diseases ranging from self-limiting sore throat to deadly invasive diseases. The genome size of GAS is 1.85–1.9 Mb, and genomic rearrangement has been demonstrated. GAS possesses various surface-associated substances such as hyaluronic capsule, M proteins, and fibronectin/laminin/immunoglobulin-binding proteins. These are related to the virulence and play multifaceted and mutually reflected roles in the pathogenesis of GAS infections. Invasion of GAS into epithelial cells and deeper tissues provokes immune and non-immune defense or inflammatory responses including the recruitment of neutrophils, macrophages, and dendritic cells in hosts. GAS frequently evades host defense mechanisms by using its virulence factors. Extracellular products of GAS may perturb cellular and subcellular functions and degrade tissues enzymatically, which leads to the aggravation of local and/or systemic disorders in the host. In this review, we summarize some important cellular and extracellular substances that may affect pathogenic processes during GAS infections, and the host responses to these.     

On the motion of particles and strings,presymplectic mechanics,and the variational bicomplex

Examples of equations of motion in classical relativistic mechanics are studied: the equations of motion of a charged spinning particle moving in a space-time (with or without torsion) in the presence of an electromagnetic field are derived via Souriau presymplectic reduction. Then, the extension of Souriaus ideas to Lagrangian field theory due to Witten, Crnkovi, Zuckerman is reviewed using the variational bicomplex, the basic properties of the Lund–Regge equations describing the motion of a string interacting with a scalar field and moving in Minkowski spacetime are recalled, and a symplectic structure for their space of solutions is found.This revised version was published online in April 2005. The publishing date was inserted.     

Matrix Algebras in Non-Hermitian Quantum Mechanics

In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schrödinger's picture of quantum dynamics. Here it is shown in both cases how to map the algebra of commutators, defining the time evolution in terms of a non-Hermitian Hamiltonian, onto a non-Hamiltonian algebra with a Hermitian Hamiltonian. The logic behind such a derivation is reversible, so that any Hermitian Hamiltonian can be used in the formulation of non-Hermitian dynamics through a suitable algebra of generalized (non-Hamiltonian) commutators.
These results provide a general structure (a template) for non-Hermitian equations of motion to be used in the computer simulation of open quantum systems dynamics.     

On the pre‐metric foundations of wave mechanics I: massless waves

The mechanics of wave motion in a medium are founded in conservation laws for the physical quantities that the waves carry, combined with the constitutive laws of the medium, and define Lorentzian structures only in degenerate cases of the dispersion laws that follow from the field equations. It is suggested that the transition from wave motion to point motion is best factored into an intermediate step of extended matter motion, which then makes the dimension‐codimension duality of waves and trajectories a natural consequence of the bicharacteristic (geodesic) foliation associated with the dispersion law. This process is illustrated in the conventional case of quadratic dispersion laws, as well as quartic ones, which include the Heisenberg–Euler dispersion law. It is suggested that the contributions to geodesic motion from the non‐quadratic nature of a dispersion law might represent another source of quantum fluctuations about classical extremals, in addition to the diffraction effects that are left out by the geometrical optics approximation.     

Estimating time to contact during pursuit eye movements: Comparison between geometric model prediction and human performance

While an object is approaching a particular location, we can make an estimate of the time when the object will arrive at that location. A geometric model predicts that the estimate of time-to-contact (TTC) is greatly improved by using the rate of change of visual direction of the object when the object is moving with a slow velocity toward a point of nearest approach at a distance far from the observer. It has been shown that pursuit eye movements provide the rate of change of visual direction of an approaching object. We conducted psychophysical experiments, and compared TTC estimates during pursuit eye movements to those during fixation. We found that the differences in TTC estimates between fixation and pursuit show a qualitatively similar pattern to the geometric model prediction. However, the results also show that the magnitudes of the TTC estimation errors are greater than the theoretical values from the geometric model, indicating that the human visual system has a perceptual bias in estimating TTC. These results suggest that the human visual system estimates TTC during pursuit eye movements in a different way from the geometric model, although the effect of these eye movements on TTC estimates in human performance is qualitatively consistent with the model prediction.     

Time and Classical and Quantum Mechanics: Indeterminacy Versus Discontinuity

It is postulated there is not a precise static instant in time underlying a dynamical physical process at which the relative position of a body in relative motion or a specific physical magnitude would theoretically be precisely determined. It is concluded it is exactly because of this that time (relative interval as indicated by a clock) and the continuity of a physical process is possible, with there being a necessary trade off of all precisely determined physical values at a time, for their continuity through time. This explanation is also shown to be the correct solution to the motion and infinity paradoxes, excluding the Stadium, originally conceived by the ancient Greek mathematician Zeno of Elea. Quantum Cosmology, Imaginary Time and Chronons are also then discussed, with the latter two appearing to be superseded on a theoretical basis.     

A Unified Framework for Relativity and Curvilinear-Time Newtonian Mechanics

Classical mechanics is presented so as to render the new formulation valid for an arbitrary temporal variable, as opposed to Newton’s Absolute Time only. Newton’s theory then becomes formally identical (in a precise sense) to relativity, albeit in a three-dimensional manifold. (The ultimate difference between the two dynamics is traced to the existence of the relativistic ‘mass-shell’ condition.) A classical Lagrangian is provided for our formulation of the equations of motion and it is related to one of the known forms of the corresponding relativistic Lagrangian, which is the analogue of the Polyakov Lagrangian of string theory. Dedicated to Emeritus Professor D. Speiser (Université Catholique de Louvain, Belgium) who provided the inspiration for this article.     

Mean-square displacement of a stochastic oscillator: Linear vs quadratic noise

Using the Langevin equations, we calculated the stationary second-order moment (mean-square displacement) of a stochastic harmonic oscillator subject to an additive random force (Brownian motion in a parabolic potential) and to different types of multiplicative noise (random frequency or random damping or random mass). The latter case describes Brownian motion with adhesion, where the particles of the surrounding medium may adhere to the oscillator for some random time after the collision. Since the mass of the Brownian particle is positive, one has to use quadratic (positive) noise. For all types of multiplicative noise considered, replacing linear noise by quadratic noise leads to an increase in stability.