Gamow vectors explain the shock profile

Dispersive shock waves dominate wave-breaking phenomena in Hamiltonian systems. In the absence of loss, these highly irregular and disordered waves are potentially reversible. However, no experimental evidence has been given about the possibility of inverting the dynamics of a dispersive shock wave and turn it into a regular wave-front. Nevertheless, the opposite scenario, i.e., a smooth wave generating turbulent dynamics is well studied and observed in experiments. Here we introduce a new theoretical formulation for the dynamics in a highly nonlocal and defocusing medium described by the nonlinear Schroedinger equation. Our theory unveils a mechanism that enhances the degree of irreversibility. This mechanism explains why a dispersive shock cannot be reversed in evolution even for an arbitrarirly small amount of loss. Our theory is based on the concept of nonlinear Gamow vectors, i.e., power dependent generalizations of the counter-intuitive and hereto elusive exponentially decaying states in Hamiltonian systems. We theoretically show that nonlinear Gamow vectors play a fundamental role in nonlinear Schroedinger models: they may be used as a generalized basis for describing the dynamics of the shock waves, and affect the degree of irreversibility of wave-breaking phenomena. Gamow vectors allow to analytically calculate the amount of breaking of time-reversal with a quantitative agreement with numerical solutions. We also show that a nonlocal nonlinear optical medium may act as a simulator for the experimental investigation of quantum irreversible models, as the reversed harmonic oscillator.

Dynamics of regular polygonal shock waves (SWs), generated at thin wire explosion, with a closed surface front and numbers of sides n = 3, 4, 5, 6, 8, 10, 12, and 16 in the plane of polygons is experimentally studied. Depending on the initial Mach number MPSW0 of such waves and the number n, two convergence modes are implemented: convergence with and without changes in the number of sides n. It is shown that the shape of the reflected wave front differs from the shape of the converging SW front for polygonal SWs with n ≥ 8, i.e., it becomes smooth. The number MPSW0 is determined depending on initial characteristics of an SW generator and gas. A significant amplification of such SWs with n ≥ 12 is observed near to the center of polygons; their maximum amplification is estimated.

Revealing the expansion and interaction dynamics of multiple shock waves (SWs) induced by a femtosecond laser is important for controlling laser processing. However, the dynamics of SWs is a complex and ultrafast process, making it difficult to determine the specific laws that govern their evolution. In this study, we observed the various evolutionary and interaction processes of SWs generated by a femtosecond laser on fused quartz using pump–probe shadowgraphy. First, we discovered a time-invariant hemispherical plasma chamber (HPC) composed mainly of air plasma before the expansion of material SW, differing from other studies wherein the plasma chamber is usually not observed. Second, the coupling process between the plasma pressure waves (PPWs) and the material SW was studied. After the expansion of material SW, the front plasma of the HPC was ionized again, generating two PPWs in opposite directions and affecting the further expansion of material SW. Eventually, the material SW broke through the HPC and PPWs and evolved into a single SW that expanded continuously. Additionally, it was demonstrated that double pulses with different time delays could effectively control the SW coupling process and plasma evolution, thereby improving the laser-processing efficiency.

Quantum mechanical irrebersibility

When describing a quantum mechanical system, it is convenient to consider state vectors that do not belong to the Hilbert space. In the first part of this paper, we survey the various formalisms have been introduced for giving a rigorous mathematical justification to this procedure: rigged Hilbert spaces (RHS), scales or lattices of Hilbert spaces (LHS), nested Hilbert spaces, partial inner product spaces. Then we present three types of applications in quantum mechanics, all of them involving spaces of analytic functions. First we present a LHS built around the Bargmann space, thus giving a natural frame for the Fock-Bargmann (or phase space) representation. Then we review the RHS approach to scattering theory (resonances, Gamow vectors, etc.). Finally, we reformulate the Weinberg-van Winter integral equation approach to scattering in the LHS language, and this allows us to prove that it is in fact a particular case of the familiar complex scaling method.

The formulation of quantum mechanics in rigged Hilbert spaces is used to study the vector states for resonance states or Gamow vectors. An important part of the work is devoted to the construction of Gamow vectors for resonances that appear as multiple poles on the analytic continuation of theS-matrix,S(E). The kinematical behavior of these vectors is also studied. This construction allow for generalized spectral decompositions of the Hamiltonian and the evolutionary semigroups, valid on certain locally convex spaces. Also a first attempt is made to define the resonance states as densities in an extension of the Liouville space, here called rigged Liouville space.

The behavior of sinusoidally-rippled shock fronts is a fundamental research topic in the dynamics of shock waves [1]. The Whitham’s ray-shock theory, which is sometimes called the geometrical-shock-dynamics (GSD) theory, is known as a simple method for analyzing the behavior of a non-planar shock front. In this theory, narrow ray tubes corresponding to the light rays in the geometrical optics are placed perpendicularly to the every portions of a non-planar shock front, and the evolution of the shock front is calculated by tracking the shock front in each ray tube sequentially. When the behavior of an inert sinusoidally-rippled shock front is analyzed by the GSD theory and the Chester-Chisnell-Whitham’s (CCW’s) A-M relationship [2], where A is the cross-sectional area of a ray tube and M is the propagation Mach number of the shock wave in the ray tube, the amplitude of the shock-front ripple oscillates as the shock wave propagates [3]. Actually, the behavior of an inert sinusoidally-rippled shock front is influenced by the fluid motion in the shock-compressed region, and the amplitude of the shock-front ripple shows damped oscillation as the shock wave propagates [1,3,4,5].

Results are presented of a numerical solution of the Korteweg-de Vries-Burgers equation that describes the propagation and establishment process for a stationary structure to a shock wave in a gas-liquid medium. Data are obtained on the time for the establishment of a stationary structure of a shock wave, propagation velocity, and amplitude oscillations in the front of the shock wave. Experiments are discussed on the basis of the results obtained for the study of shock waves in a liquid containing gas bubbles.

In this four-year project (including one-year extension), the project director and his research team built a shock-wave-plasma apparatus to study shock wave dynamics in glow discharge plasmas in nitrogen and argon at medium pressure (1–20 Torr), carried out various plasma and shock diagnostics and measurements that lead to increased understanding of the shock wave acceleration phenomena in plasmas. The measurements clearly show that in the steady-state dc glow discharge plasma, at fixed gas pressure the shock wave velocity increases, its amplitude decreases, and the shock wave disperses non-linearly as a function of the plasma current. In the pulsed discharge plasma, at fixed gas pressure the shock wave dispersion width and velocity increase as a function of the delay between the switch-on of the plasma and shock-launch. In the afterglow plasma, at fixed gas pressure the shock wave dispersion width and velocity decrease as a function of the delay between the plasma switch-off and shock-launch. These changes are found to be opposite and reversing towards the room temperature value which is the initial condition for plasma ignition case. The observed shock wave properties in both igniting and afterglow plasmas correlate well with the inferred temperature changes in the two plasmas.

Physics of meteor generated shock waves in the Earth’s atmosphere – A review

Experimental studies on shock wave and particle dynamics in a needle-free drug delivery device

The diffraction over a corner normal to the direction of travel of a shock wave has been well documented. This has also been extended to the diffraction of a shock wave over edges with discontinuous profiles in the flow direction. However, these studies have only considered the diffraction of a shock wave travelling over a single, plane surface initially. The current study extends this to consider the dynamics of a plane shock wave travelling simultaneously over two orthogonal surfaces, analogous to a shock wave travelling over the roof and wall of a rectangular building. The flow field bears similarity to the diffraction of a shock wave over a convex diffraction edge whereby there is thickening of the vortex tube formed at the axis defined by the common edge of the two surfaces with outboard thinning. However, as the Mach number of the incident shock wave increases, the vortex tubes shed from the two diffraction edges no longer merge into a single tube but rather each terminates in the downstream face. This also results in curvature of these vortex tubes away from the face rather than remaining approximately parallel to the downstream face as seen in most cases. These results were derived experimentally and computationally for a Mach number in the range M1.3–M1.6.

Dynamics of laser-induced shock wave by optical probe in air

The results of computer blast-hole experiments with copper wire electro-explosion in the polyethylene-concrete media has been analyzed with shock and pressure wave dynamics depending on the spatiotemporal distribution of electrical power deposition in plasma channel. Pressure and stress-wave dynamics of tensely-deformed material state has been analysed by means of physical and mathematical model, which consistently describes the operation of the discharge circuit, plasma channel expansion, generation and propagation of the shock and pressure waves in the condensed media1. It has been shown the significant dependence of the stress-wave profile on the pressure pulse wave shape on the borehole wall which is determined by the rate of electrical energy release in the plasma channel and is weakly depended on the time of energy release (at given rate of its release). Analysis of stress-wave dynamics have been shown that the rapid power deposition results to the higher amplitude of compressive stresses in the wave. The lower energy deposition rate in plasma channel leads to the higher amplitude of tensile stresses both in radial and tangential direction.

A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium.