Autoparametric resonance in a structure containing a liquid,Part II: Three mode interaction

Autoparametric coupling of the first antisymmetric liquid sloshing mode with two orthogonal structure freedoms in a simple structure containing a liquid is investigated theoretically and experimentally. Asymptotic approximation up to the first order shows four possible conditions of internal resonance. The response of the system is obtained analytically and numerically in the neighbourhood of the internal resonance conditions. Under the principal internal resonance (i.e., when one of the normal mode frequencies is twice one of the other mode frequencies) the system possesses a steady-state response. Under the summed or differenced internal resonance (i.e., when one of the normal mode frequencies equals the sum or difference of two other natural mode frequencies) the system does not achieve a constant amplitude steady-state response.Experimental investigations confirm the possible existence of most of the internal resonance conditions considered in the analytical study; however, theoretical amplitude-frequency response curves are rather higher than the experimental results. Experimental observations showed that other kinds of instabilities occur when the liquid free surface exhibits rotational flow at a forcing frequency just above twice the liquid sloshing frequency.     

Autoparametric resonances in a structure/fluid interaction system carrying a cylindrical liquid tank

The nonlinear-coupled vibrations of an elastic structure and liquid sloshing in a cylindrical container are investigated. The behavior of the liquid surface is governed by a kind of the Mathieu equation because the structure is subjected to a vertical and sinusoidal excitation. Modal equations for liquid sloshing governing the coupled motions are derived when the natural frequency of the structure is equal to twice the natural frequency of an anti-symmetric mode of sloshing. The theoretical resonance curves are determined by using van der Pol's method. The influences of a liquid level and a detuning parameter on the theoretical resonance curves are investigated when only the excitation frequency is selected as a control parameter. The inclination of a frequency response curve depends on the liquid level. Furthermore, a small deviation of the tuning condition may cause amplitude- and phase-modulated motions and chaotic vibrations. This deviation also leads to separate the occurrence region of the coupled vibration into two regions of the excitation frequency. The theoretical resonance curves are quantitatively in agreement with the experimental data. Lastly, the amplitude- and phase-modulated motions and chaotic vibrations were observed in experiments.     

Fluid dynamics of a flow excited resonance,Part II: Flow acoustic interaction

This is the second of two companion papers in which the physics and detailed fluid dynamics of a flow excited resonance are examined. The approach is rather different from those previously used, in which stability theory has been applied to small wavelike disturbances in a linearly unstable shear layer, with an equivalent source driving the sound field which provides the feedback. In the approach used here, the physics of the flow acoustic interaction is explained in terms of the detailed momentum and energy exchanges occurring inside the fluid. Gross properties of the flow and resonance are described in terms of the parameters necessary to determine the behaviour of the feedback system. In this second paper it is shown that two relatively distinct momentum balances can be considered in the resonator neck region. One can be identified with the vortically induced pressure and velocity fluctuations and the other with the reciprocating potential flow. The fluctuating Coriolis force caused by the interaction of the potential and vortical flows is shown to be the only term in the linearized momentum equation which is not directly balanced by a fluctuating pressure gradient. This force provides the mechanism for the exchange of the mean energies associated with the mean and fluctuating momenta, respectively. A source and sink of energy are identified in which mean energy associated with fluctuating momentum is extracted from and returned to the mean flow, respectively. The imbalance between the source and sink is responsible for both the radiated acoustic power and the power carried away by the vortices as they convect downstream. This radiated acoustic power and vortically convected power, and the source and sink powers, are all of the same order of magnitude. With the vortex shedding and reciprocating potential flow “phase locked” the amplitude of the steady state oscillations is determined by the condition that the net power produced in the resonator neck (the source power less the sink power) is equal to the sum of the radiated acoustic power and that carried by the vortices.     

Flow-resonant sound interaction in a duct containing a plate,part I: Semi-circular leading edge

The interaction between flow and flow-induced acoustic resonances near rigid plates with semi-circular leading edges located in a hard-walled duct is described. These plates generate acoustic resonances over flow velocity ranges depending on thickness, chord and trailing edge geometry, together with rigidity, internal dimensions, length of the working section and shape of the terminations of the working section. A potential flow model for the plate with a smooth leading edge is developed, and the acoustic power generated by vortices growing and shedding from the trailing edge is calculated. The rate of growth of the vortices is determined by an instantaneous Kutta condition applied over part of the cycle. This technique simulates the influence of the sound field on vortex growth.     

Nonlinear degenerate resonance interaction of waves on a charged liquid surface

The physics of nonlinear degenerate resonance energy exchange between waves on the flat free charged surface of a conducting liquid is analytically (asymptotically) studied up to the second order of smallness. A set of differential equations for the evolution of the amplitudes of nonlinearly resonantly interacting waves is derived. It turns out that nonlinear computations (taking into account the dependence of the wave frequency on the finite amplitude) yield an infinite number of degenerate resonances, although computations based on frequencies found in the linear theory give a finite number of resonances. In nonlinear computations, the positions of the degenerate resonances depend on the surface charge density (or on the external electric field normal to the free surface of the liquid) in contrast to the results of linear computations (based on frequencies found in the linear theory). It is found that as the wavenumber of an exact degenerate resonance is approached (that is, in the vicinity of this number), the direction of energy transfer changes sign: now the energy is transferred from a shorter wave to a longer one and not the reverse.     

Two interacting particles in a disordered chain I: Multifractality of the interaction matrix elements

For N interacting particles in a one dimensional random potential, we study the structure of the corresponding network in Hilbert space. The states without interaction play the role of the “sites”. The hopping terms are induced by the interaction. When the one body states are localized, we numerically find that the set of directly connected “sites” is multifractal. For the case of two interacting particles, the fractal dimension associated to the second moment of the hopping term is shown to characterize the Golden rule decay of the non interacting states and the enhancement factor of the localization length. Received: 17 April 1998 / Accepted: 14 May 1998     

Adventures of a Theoretical Physicist, Part I: Europe

I was born in Budapest, Hungary, on July 7, 1907, and this first part of my interview with Andor Frenkel focuses on my life and work in Europe. After my elementary and secondary education I studied mathematics at the University of Budapest for two years. I went to the University of G?ttingen in 1928 where I attended Max Born’s lectures on quantum mechanics, which influenced me to change from mathematics to physics, and as a consequence I focused on filling the gaps in my physics background. When ready to turn to research work I followed the advice of my friend Edward Teller and spent three months in Werner Heisenberg’s group at the University of Leipzig in the summer of 1930. That fall I returned to the University of Budapest, where I received my Ph.D.degree in the summer of 1932. Two months later, because I had become entangled in the illegal Communist Party, I was arrested and sentenced to fourteen months in prison. Fifteen months after my release, I joined Lev Landau’s group at the Ukrainian Physical-Technical Institute in Kharkov, passed Landau’s so-called “theorminimum” program on my second attempt, began research on the theory of liquid helium, and lost my faith in communism following Stalin’s repressive measures. I obtained an exit visa through the Hungarian Legation and returned to Budapest in June 1937. That September, again with the help of my friend Edward Teller, I attended a conference in Paris where I met Fritz London and Edmond Bauer, who arranged for me a small scholarship and an association with the Langevin laboratory at the Collège de France. Four months later, in January 1938 Kapitza, and John F. Allen and A. Donald Misener reported their independent discovery of the superfluidity of helium, which London and I explored theoretically and I explained with my two-fluid theory later in 1938. Following the German invasion of France, my wife and I left Paris for Toulouse in June 1940, obtained exit visas to enter Spain and Portugal in February 1941, and boarded a Portuguese ship for New York the following month. The second part of this interview, covering my life and work in America, will appear in the next issue.     

Noiselike magnetic resonance fine structure for ferromagnetic powders: Dipole-dipole interaction effects

A noiselike fine structure of ferromagnetic resonance spectra in magnetic powders was investigated after ultrasonic treatment. Magnetic interactions between particles are proved to have an influence upon the fine structure formation. After decreasing dipole-dipole magnetic interactions in dilute suspension a special order appears in fine-structure spectra, which is generally the same for different systems.     

Annealing effect in glass woven fabric composites,Part I. Mode I and mode II interlaminar fracture behavior

Mode I and mode II interlaminar fracture behavior of plain glass woven fabric composites with different silane concentration was investigated on the basis of a discussion of the effects of annealing on the fracture behavior. The fracture mode changed by annealing from stable to unstable manner in lower silane concentration and from unstable to stable manner in higher silane concentration specimens in mode I fracture. In the mode II fracture, the initiation values of fracture toughness increased by annealing without respect to silane concentration.     

Nonlinear birefringence in fluids containing nonspherical molecules : I. Response and mode coupling theory

The orientation density in nonequilibrium systems is expressed in terms of equilibrium time-correlation functions to quadratic order in the gradients in density, pressure and velocity fields. These are evaluated by mode coupling theory in the reversible bare vertex approximation, at infinite dilution of the nonspherical component and using a two-variable model prediction for the two-point orientation correlations. A very simple nonlinear correction term is found, predicting no nonlinear shear birefringence and a nonlinear acoustic birefringence which scales as ΩI^1/2/Г with respect to the linear birefringence (Ω is the driving frequency, I is a dimensionless acoustic intensity and Г is the equilibrium orientation relaxation rate).     

A simple model of ultrasound propagation in a cavitating liquid. Part I: Theory, nonlinear attenuation and traveling wave generation

The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of each bubble, by thermal diffusion in the gas and viscous friction in the liquid. Both quantities and calculated numerically for a single inertial bubble driven at 20 kHz, and are found to be several orders of magnitude larger than the linear prediction. Viscous dissipation is found to be the predominant cause of energy loss for bubbles small enough. Then, the classical nonlinear Caflish equations describing the propagation of acoustic waves in a bubbly liquid are recast and simplified conveniently. The main harmonic part of the sound field is found to fulfill a nonlinear Helmholtz equation, where the imaginary part of the squared wave number is directly correlated with the energy lost by a single bubble. For low acoustic driving, linear theory is recovered, but for larger drivings, namely above the Blake threshold, the attenuation coefficient is found to be more than 3 orders of magnitude larger then the linear prediction. A huge attenuation of the wave is thus expected in regions where inertial bubbles are present, which is confirmed by numerical simulations of the nonlinear Helmholtz equation in a 1D standing wave configuration. The expected strong attenuation is not only observed but furthermore, the examination of the phase between the pressure field and its gradient clearly demonstrates that a traveling wave appears in the medium.     

Identification of a continuous structure with a geometrical non-linearity. Part I: Conditioned reverse path method

Particular effort has been spent in the field of identification of multi-degree-of-freedom non-linear systems. The newly developed methods permit the structural analyst to consider increasingly complex systems. The aim of this paper and a companion paper is to study, by means of two methods, a continuous non-linear system consisting of an experimental cantilever beam with a geometrical non-linearity. In this paper (Part I), the ability of the conditioned reverse path method, which is a frequency domain technique, to identify the behaviour of this structure is assessed. The companion paper (Part II) is devoted to the application of proper orthogonal decomposition, which is an updating technique, to the test example.     

Nuclear acoustic resonance in a liquid metal

The first observation of direct nuclear acoustic resonance (NAR) in a bulk liquid is reported. The measurements were performed with pure gallium. The line shape and angular dependence of the absorption signal are in good agreement with the theory for spin phonon coupling via the nuclear magnetic dipole moment.     

Development of helical cholesteric structure in a nematic liquid crystal due to the dipole-dipole interaction

A nematic liquid crystalline phase is considered whose rod-like non-centrosymmetric molecules possess a permanent dipole moment. This phase is a “liquid ferroelectric” if all the molecules are oriented along the same “preferred” direction. It is shown that a liquid ferroelectric can not exist in a homogeneous nematic state. It is transformed into a more stable helical structure (the vector of the spontaneous polarization of such a structure rotates aroung the helical axis). There is a variety of domain structures for the specific case when the anisotropy coefficient of the polarization is equal to zero. Since each elementary dipole moment is rigidly bound to its molecule, the “preferred” alignment direction of the rod-like molecules as well as the polarization vector rotates with respect to the same axis in a helical manner. Therefore a nematic phase with a nonzero spontaneous polarization has a cholesteric structure. Its helical pitch is determined by the geometric size of the sample, the absolute value of the spontaneous polarization, and the elastic moduli. Apparently, we can consider some cholesteric phases to be liquid ferroelectrics with helical domain structure.     

Stochastic electrodynamics with particle structure Part I: Zero-point induced Brownian behavior

If ordinary views on particle structure are introduced in a simple classical particle model in replacement of the point particles of standard use in stochastic electrodynamics, it can be shown that an internalZitterbewegung induced by the zero-point field background gives rise to a Brownian movement for the whole particle with a diffusion constant of the form D = /2m_D , where m_D is a modeldependent mass. Since the days of Madeleung and Fuhr brownian behaviour has often been associated with quantization. We discuss this from the viewpoint of stochastic electrodynamics.     

General interaction quenches in a Luttinger liquid

We discuss a general interaction quench in a Luttinger liquid described by a paired bosonic Hamiltonian.By employing su(1,1)Lie algebra,the post-quench time-evolved wavefunctions are obtained analytically,from which the time evolution of the entanglement in momentum space can be investigated.We note that depending on the choice of Bogoliubov quasiparticles,the expressions of wavefunctions,which describe time-evolved paired states,can take different forms.The correspondence between the largest entanglement eigenvalue in momentum space and the wavefunction overlap in quench dynamics is discussed,which generalizes the results of Dora et al(2016,Phys.Rev.Lett.117,010603).A numerical demonstration on an XXZ lattice model is presented via the exact diagonalization method.     

Molecular structure calculations applied to solid state polymer physics: Part I

This review focuses upon the applications of molecular structure calculations to determine the three-dimensional physicochemical features of polymeric solids. In some cases, the structure calculations are used to evaluate expressions arising from specific models or theories. As such, molecular structure calculations are auxillary aides in the illumination of the solid-state properties of polymers.