Nonlinear Breaking of Wave Fronts in a Vibrationally Relaxing Gas

1982 ◽  
Vol 49 (1) ◽  
pp. 10-12
Author(s):  
R. Shyam ◽  
V. D. Sharma ◽  
V. V. Menon
Keyword(s):  
Wave Front ◽  
Vibrational Relaxation ◽  
Method Of Characteristics ◽  
Spherically Symmetric ◽  
Wave Fronts ◽  
Compressive Wave ◽  
Initial Discontinuity ◽  
Explicit Criteria ◽  
Front Curvature ◽  
Relaxing Gas

Using the method of characteristics, some explicit criteria for the nonlinear breaking of wave fronts in a plane, cylindrically or spherically symmetric flows of a vibrationally relaxing gas are obtained. It is shown that except a spherically converging compressive wave, all compressive waves break only when the initial discontinuity at the wave-head exceeds a critical value, and the effects of vibrational relaxation and that of the wave front curvature are to increase the time of their breaking. It is found that the stabilizing influences of vibrational relaxation and that of the wave front curvature are not strong enough to overcome the breaking tendency of a spherically converging compressive wave; in fact, in contrast to a cylindrically converging wave, it always breaks down before the formation of a focus, no matter how small be the initial discontinuity at the wave-head.

scholarly journals Wave Fronts in a Causality-Violating Gödel-Type Metric

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Thomas P. Kling ◽  
Faizuddin Ahmed ◽  
Megan Lalumiere
Keyword(s):  
Wave Front ◽  
Space Time ◽  
Wave Fronts ◽  
Light Rays ◽  
Synchronized Clocks

The light rays and wave fronts in a linear class of the Gödel-type metric are examined to reveal the causality-violating features of the space-time. Noncausal features demonstrated by the development of unusual wave front singularities are shown to be related to the nonmonotonic advance of time along the light rays, as measured by a system of observers at rest with respect to one another with synchronized clocks.

scholarly journals Analysis of a self-centring detonation wave generator

2021 ◽  
pp. 34-47
Author(s):  
Waldemar Trzciński ◽  
Józef Paszula ◽  
Leszek Szymańczyk
Keyword(s):  
Theoretical Analysis ◽  
Detonation Wave ◽  
Wave Front ◽  
Point Location ◽  
Wave Fronts ◽  
Initiation Point ◽  
X Ray ◽  
Detonation Wave Front ◽  
Main Charge ◽  
Wave Generator

The aim of the study was to determine the parameters of a detonator generating a self-centring detonation wave, based on experimental and theoretical analysis. The methods for manufacturing selfcentring detonation wave generators available in literature were reviewed and a detonator comprised of two explosives was proposed. The detonator geometry was analysed for its ability to centre the detonation wave. A physical detonator model was created and the detonation wave front downstream of the detonator, analysed and the detonator’s capability to compensate an off-centre detonation initiation, evaluated. The wave fronts were recorded using pulsed x-ray radiography. The study showed that the proposed detonator provides a symmetrical initiation of the main charge for the initiation point (location) offset, lower than the assumed maximum offset.

scholarly journals Characterization of Wave Fronts of Ultradistributions Using Directional Short-Time Fourier Transform

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 240
Author(s):  
Sanja Atanasova ◽  
Snježana Maksimović ◽  
Stevan Pilipović
Keyword(s):  
Fourier Transform ◽  
Wave Front ◽  
Short Time Fourier Transform ◽  
Wave Fronts ◽  
Directional Wave ◽  
Tempered Ultradistributions ◽  
Short Time

In this paper we give a characterization of Sobolev k-directional wave front of order p∈[1,∞) of tempered ultradistributions via the directional short-time Fourier transform.

On the breakdown of characteristics solutions in flows with vibrational relaxation

1967 ◽  
Vol 27 (1) ◽  
pp. 49-57 ◽  
Author(s):  
B. S. H. Rarity
Keyword(s):  
Relaxation Time ◽  
Mach Number ◽  
Supersonic Flow ◽  
Steady Flow ◽  
Speed Of Sound ◽  
Vibrational Relaxation ◽  
Precise Measure ◽  
Derivatives Of ◽  
Relaxing Gas ◽  
Flow Case

The breakdown of the characteristics solution in the neighbourhood of the leading frozen characteristic is investigated for the flow induced by a piston advancing with finite acceleration into a relaxing gas and for the steady supersonic flow of a relaxing gas into a smooth compressive corner. It is found that the point of breakdown moves outwards along the leading characteristic as the relaxation time decreases and that there is no breakdown of the solution on the leading characteristic if the gas has a sufficiently small, but non-zero, relaxation time. A precise measure of this relaxation time is derived. The paper deals only with points of breakdown determined by initial derivatives of the piston path or wall shape. In the steady-flow case, the Mach number based on the frozen speed of sound must be greater than unity.

scholarly journals Null Wave Front and Ryu–Takayanagi Surface

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1297
Author(s):  
Jun Tsujimura ◽  
Yasusada Nambu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Cosmological Constant ◽  
Minimal Surface ◽  
Wave Front ◽  
Entanglement Entropy ◽  
Necessary Condition ◽  
Quantum Field ◽  
Wave Fronts ◽  
Sufficient And Necessary Condition

The Ryu–Takayanagi formula provides the entanglement entropy of quantum field theory as an area of the minimal surface (Ryu–Takayanagi surface) in a corresponding gravity theory. There are some attempts to understand the formula as a flow rather than as a surface. In this paper, we consider null rays emitted from the AdS boundary and construct a flow representing the causal holographic information. We present a sufficient and necessary condition that the causal information surface coincides with Ryu–Takayanagi surface. In particular, we show that, in spherical symmetric static spacetimes with a negative cosmological constant, wave fronts of null geodesics from a point on the AdS boundary become extremal surfaces and therefore they can be regarded as the Ryu–Takayanagi surfaces. In addition, from the viewpoint of flow, we propose a wave optical formula to calculate the causal holographic information.

scholarly journals Wave-front curvature as a cause of slow conduction and block in isolated cardiac muscle.

1994 ◽  
Vol 75 (6) ◽  
pp. 1014-1028 ◽  
Author(s):  
C Cabo ◽  
A M Pertsov ◽  
W T Baxter ◽  
J M Davidenko ◽  
R A Gray ◽  
...  
Keyword(s):  
Cardiac Muscle ◽  
Wave Front ◽  
Slow Conduction ◽  
Front Curvature

scholarly journals Second Summary-Introduction: Steady One-Dimensional Fluid-Magnetic Collisionless Shock Theory

1960 ◽  
Vol 12 ◽  
pp. 459-467
Author(s):  
A. A. Blank ◽  
H. Grad
Keyword(s):  
Wave Front ◽  
Mean Free Path ◽  
Finite Amplitude ◽  
Wave Profile ◽  
The State ◽  
Compressive Wave ◽  
Dissipative Effects ◽  
Dissipative Mechanism ◽  
Weak Shocks ◽  
Shock Profile

Shock-waves represent one of the most important mechanisms for creating and heating a plasma. In classical non-dissipative gas dynamics, the formation of a shock is indicated by the progressive steepening of a finite-amplitude compressive wave front to the point where it becomes multivalued and consequently without physical meaning. This difficulty is avoided by the inclusion of dissipative effects, usually in the form of heat flow and viscosity. The dissipative mechanisms become more effective as the wave front steepens, and the result is a steady wave profile for which the non-linear and dissipative effects are counterbalanced. The scale length for the dissipative transition zone or wave profile is the mean-free-path; the actual thickness may range from one to several mean-free-paths, or even more for very weak shocks. Given the strength of the shock, the state on one side of the shock may be computed from the state on the other side directly from the laws of conservation of mass, momentum and energy (Hugoniot relations). Accordingly, the nature of the particular dissipative mechanism affects only the shape of the shock profile but not the end states.

Meandering and unstable reentrant wave fronts induced by acetylcholine in isolated canine right atrium

1997 ◽  
Vol 273 (1) ◽  
pp. H356-H370 ◽  
Author(s):  
T. Ikeda ◽  
T. J. Wu ◽  
T. Uchida ◽  
D. Hough ◽  
M. C. Fishbein ◽  
...  
Keyword(s):  
Wave Front ◽  
Current Strength ◽  
Right Atrial ◽  
New Wave ◽  
Wave Fronts ◽  
Bipolar Electrodes ◽  
Upper Limit Of Vulnerability ◽  
Before And After ◽  
Simultaneous Decrease ◽  
Front Dynamics

The mechanism(s) by which acetylcholine (ACh) increases atrial vulnerability to reentry and maintains its activity for longer durations remains poorly defined. In the present study we used high-resolution activation maps to test the hypothesis that ACh promotes meandering of atrial reentrant wave fronts, resulting in breakup and the generation of new wave fronts that sustain the activity. Reentry was induced in 11 isolated canine right atrial tissues (3.8 x 3.2 cm) by a premature point stimulus (S2) before and after superfusion with ACh (15 x 10(-6) M). Endocardial isochronal activation maps were constructed with the use of 509 bipolar electrodes (1.6-mm spatial resolution), and the dynamics of the activation wave fronts were visualized with animation. A vulnerable period was found during which an S2 current strength > 4.4 +/- 2.5 mA [lower limit of vulnerability (LLV)] and < 26 +/- 13 mA [upper limit of vulnerability (ULV)] induced a single stationary reentrant wave front that lasted 3 +/- 2.5 s with a period of 159 +/- 17 ms (16 episodes). AC shortened the refractory period from 100 +/- 12 to 59 +/- 9 ms (P < 0.001) and increased vulnerability to reentry induction by simultaneous decrease in the LLV (0.7 +/- 0.2 mA, P < 0.001) and an increase in the ULV (82 +/- 24 mA, P < 0.01). ACh accelerated the rate (period of 110 +/- 16 ms, P < 0.001) and converted the stationary reentrant wave front to a nonstationary (meandering) reentrant wave front showing polymorphic electrograms, i.e., “fibrillation-like” activity (22 episodes). Rapid meandering of the reentry tip led to wave front breakup (18 episodes) and the generation of new wave fronts (19 episodes). These wave front dynamics also led to sustained (76 +/- 224 s, P < 0.001) fibrillation-like electrograms. We conclude that ACh increases the ULV and promotes meandering of a single reentrant wave front, leading to breakup and the generation of new wave fronts. Single meandering and complex wave front dynamics cause fibrillation-like activity and sustain the activity for longer duration.

On diffracted wave fronts

1979 ◽  
Vol 84 (1-2) ◽  
pp. 35-54
Author(s):  
Peter Wolfe
Keyword(s):  
Wave Equation ◽  
Wave Front ◽  
Incident Wave ◽  
Spherical Wave ◽  
Small Time ◽  
Time Interval ◽  
Wave Fronts ◽  
Incident Plane ◽  
Small Time Interval ◽  
Propagation Of Singularities

SynopsisIn this paper we study the wave equation, in particular the propagation of discontinuities. Two problems are considered: diffraction of a normally incident plane pulse by a plane screen and diffraction of a spherical wave by the same screen. It is shown that when an incident wave front strikes the edge of the screen a diffracted wave front is produced. The discontinuities are precisely computed in a neighbourhood of the edge for a small time interval after the arrival of the incident wave front and a theorem of Hörmander on the propagation of singularities is used to obtain a globalresult.

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