Oscillatory Decay Research Articles

Dynamics of Gas Bubbles Inside a Ball-like Area at the Nodes of a Uniform Cubic Mesh Under Sudden Liquid Pressure Rise

The influence of hydrodynamic interaction between spherical gas bubbles inside a ball-like area at the nodes of a uniform cubic mesh on their dynamics under sudden liquid pressure rise has been investigated. Main attention is payed to the dynamics of a bubble located in the center of such a cluster of cubic structure. Prior to the pressure rise, the liquid and the bubbles are at rest, the liquid pressure is 1 bar, the radii of the bubbles are 0.25 mm, the size of the cubic mesh cells is 5 mm. The increase in the liquid pressure is 3 bar. For the sake of comparison, ball-like clusters with spherical and stochastic structures are also considered, with similar position of the central bubble and with initial minimum distance between the centers of bubbles not exceeding 5 mm. In the clusters of spherical structure, the non-central bubbles are located on concentric spheres with radii of 5 and 10 mm at the nodes of equally-oriented regular polyhedra (icosahedra and dodecahedra). In the clusters of stochastic structure, the non-central bubbles are distributed stochastically in a sphere with radius of 10 mm. A mathematical model is applied, in which the dynamics of bubbles is governed by the ordinary differential equations in the radii of bubbles and the position-vectors of their centers. It is shown that in the case of a cluster with cubic structure, the interaction between the bubbles leads to strengthening the collapse rate of the central bubble and to non-monotonic decay of oscillations of their pressure. Similar features are characteristic of the clusters with spherical and stochastic structures.

THE ION ENERGY IN A PLASMA RESONATOR EXCITED BY A POWERFUL MICROWAVE PULSE AT ECR FREQUENCY

The possibility of heating argon plasma ions with a density of ≈1013 cm-3 to 2 keV in a resonator placed in a magnetic field of a plug configuration when oscillations were excited at an electron-cyclotron resonance frequency with an electric field strength of up to 12 kV/cm in a pulse with a duration of 1.8 μs was shown experimentally. Ions acquire high energy in the fields of stochastic low-frequency ion oscillations due to the development of a modified decay of microwave oscillations.

Friedel oscillations of one-dimensional correlated fermions from perturbation theory and density functional theory

We study the asymptotic decay of the Friedel density oscillations induced by an open boundary in a one-dimensional chain of lattice fermions with a short-range two-particle interaction. From Tomonaga-Luttinger liquid theory it is known that the decay follows a power law, with an interaction dependent exponent, which, for repulsive interactions, is larger than the noninteracting value $-1$. We first investigate if this behavior can be captured by many-body perturbation theory for either the Green function or the self-energy in lowest order in the two-particle interaction. The analytic results of the former show a logarithmic divergence indicative of the power law. One might hope that the resummation of higher order terms inherent to the Dyson equation then leads to a power law in the perturbation theory for the self-energy. However, the numerical results do not support this. Next we use density functional theory within the local-density approximation and an exchange-correlation functional derived from the exact Bethe ansatz solution of the translational invariant model. While the numerical results are consistent with power-law scaling if systems of $10^4$ or more lattice sites are considered, the extracted exponent is very close to the noninteracting value even for sizeable interactions.

Anomalous Decay of Quantum Resistance Oscillations of 2D Helical Electrons in Magnetic Field

Shubnikov de Haas resistance oscillations of highly mobile two dimensional helical electrons propagating on a conducting surface of strained HgTe 3D topological insulator are studied in magnetic fields B tilted by angle θ from the normal to the conducting layer. Strong decrease of oscillation amplitude A is observed with the tilt: {boldsymbol{A}}sim {boldsymbol{e}}{boldsymbol{x}}{boldsymbol{p}}(,-,{boldsymbol{xi }}/{boldsymbol{c}}{boldsymbol{o}}{boldsymbol{s}}({boldsymbol{theta }})), where ξ is a constant. Evolution of the oscillations with temperature T shows that the parameter {boldsymbol{xi }} contains two terms: {boldsymbol{xi }}={{boldsymbol{xi }}}_{1}+{{boldsymbol{xi }}}_{2}{boldsymbol{T}}. The temperature independent term, {{boldsymbol{xi }}}_{{bf{1}}}, signals possible reduction of electron mean free path {l}_{q} and/or enhancement of in-homogeneous broadening of the oscillations in magnetic field B. The temperature dependent term, {{boldsymbol{xi }}}_{{bf{2}}}{boldsymbol{T}}, indicates increase of the reciprocal velocity of 2D helical electrons: delta ({v}_{F}^{-1})sim B suggesting modification of the electron spectrum in magnetic fields. Results are found in good agreement with proposed phenomenological model.

Synthetic mean-field interactions in photonic lattices

Photonic lattices are usually considered to be limited by their lack of methods to include interactions. We address this issue by introducing mean-field interactions through optical components which are external to the photonic lattice. The proposed technique to realise mean-field interacting photonic lattices relies on a Suzuki-Trotter decomposition of the unitary evolution for the full Hamiltonian. The technique realises the dynamics in an analogous way to that of a step-wise numerical implementation of quantum dynamics, in the spirit of digital quantum simulation. It is a very versatile technique which allows for the emulation of interactions that do not only depend on inter-particle separations or do not decay with particle separation. We detail the proposed experimental scheme and consider two examples of interacting phenomena, self-trapping and the decay of Bloch oscillations, that are observable with the proposed technique.Graphical abstract

Impact of damping on decay time of free oscillations in metal structures

The problem of increase of durability of the bearing thin walled metal structures of hoisting - and - transport machines maybe solved by means of structural damping which allows to increase the logarithmic decrement of the damped oscillations. In the work there are given the results of modelling and experimental check of the advantages of usage low-modulus foam materials as fillers at a structural damping of thin walled elements of metal structures. With the help of computational package SolidWorks there was conducted a numerical study to define amplitude-frequency characteristic of laboratory machine and then there were run the tests of model structure with building vibrorecord. As a result if research there was revealed a significant increase of the logarithmic decrement and reduction of the time of decay of natural oscillation of the foamed structure. Consequently, there are shown the advantages of the further researches to use energy-intensive foam materials to dampen the elements of the structures of handling machinery.

Modeling and Verification of a Parasitic Nonlinear Energy Storage Effect Due To High-Power Electromagnetic Excitation

The analysis of nonlinear effects in electromagnetic compatibility can reveal unexpected system behavior. This article examines the response of nonlinearly loaded receiving structures with respect to high-power electromagnetic pulses. It is observed that induced voltages may exhibit dc components, which are retained after the decay of the usual transient oscillations. These dc components are attributed to stored electric field energy and can considerably be increased by the application of several pulses. This a priori surprising effect can both be predicted by modeling and confirmed by measurement.

Finite-difference simulation of coreflooding based on a reconstructed CT scan; modeling transient oscillating and pulse decay permeability experiment

Numerical simulation and experimental research of fluid flow in porous media enhance the practices of petroleum reservoirs' management. Experiments on acquired reservoir-rock samples are conducted for accurate characterization and realization of the insitu hydrocarbon reserves. Implementing precise numerical simulation of those experiments is crucial to acquire accurate conclusions from the obtained experimental results. Coreflooding experiments quantify reservoir rock's storage capacity, measure its transport connectivity, and evaluate recovery methods' effectiveness for that rock. In this paper, a reconstruction image-processing workflow of cores' CT scan is developed to build a finite difference numerical model for simulating coreflooding experiments. In a transient coreflooding experiment, a controlled pressure pulse with a known frequency and amplitude is transmitted to the rock sample. Rock permeability can be quantified by analytically solving the diffusivity flow equation for that experiment. Simulating the transient permeability experiment is very sensitive to the level of details of the pores' structure described in the numerical model. A transient permeability experiment with two different transient modes, sinusoidal oscillation, and pulse decay, was conducted on a standard Berea core sample. The Berea CT scan was image-processed to reconstruct the static porosity and permeability model in Petrel software using a 3D variogram geostatistical population. Injection and production sources were assigned to the finite gridblock, which correspond to flow nozzles of injection and production coreflooding setup's heads. Scheduled flow and controlled-pressure boundary-conditions were imposed on the dynamic model. Eclipse simulator was used to solve the dynamic model and calculate the pressure in each gridblock. The outlet pressure was calculated at each time step by three different realization approaches for porosity and permeability, i.e., from experiments, from statistical analysis for the CT scan, and by the proposed image processing workflow. The simulated outlet pressure from the prosed workflow matched ideally, with a Pearson correlation coefficient of 0.98 and 0.99, the recorded one in the two experiments compared to underestimated or overestimated outlet pressure from the other two traditional realization approaches, i.e., statistical or experimental.

Transition from Exponentially Damped to Finite-Time Arrest Liquid Oscillations Induced by Contact Line Hysteresis.

To clarify the role of wetting properties on the damping of liquid oscillations, we studied the decay of oscillations of liquid columns in a U-shaped tube with controlled surface conditions. In the presence of sliding triple lines, oscillations are strongly and nonlinearly damped, with a finite-time arrest and a dependence on initial amplitude. We reveal that contact angle hysteresis explains and quantifies this solidlike friction.

An efficient numerical treatment for the asymptotic behaviour of the nonlinear Airy-type problems

This study focuses on symplectic integrators for numerical evaluation of the asymptotic solutions of the nonlinear Airy-type equations obtained by reducing the nonlinear dispersive equations. Since the nature of Airy-type equations has both highly oscillatory slow decay and exponential fast decay, most of classical integrators are not able to correctly exhibit challenging physical behaviour. We use specially designed symplectic integrators combining splitting methods with Magnus integrators to catch asymptotic behaviour of nonlinear Airy-type equations efficiently, even for large step sizes. Efficiency of the proposed methods for given problems is discussed. Moreover, numerical results obtained by the proposed methods are compared with the existing results in the literature.

Global Navier–Stokes Flows for Non-decaying Initial Data with Slowly Decaying Oscillation

Consider the Cauchy problem of incompressible Navier–Stokes equations in $$\mathbb {R}^3$$ with uniformly locally square integrable initial data. If the square integral of the initial datum on a ball vanishes as the ball goes to infinity, the existence of a time-global weak solution has been known. However, such data do not include constants, and the only known global solutions for non-decaying data are either for perturbations of constants, or when the velocity gradients are in $$L^p$$ with finite p. In this paper, we construct global weak solutions for non-decaying initial data whose local oscillations decay, no matter how slowly.

On Helmholtz Equations and Counterexamples to Strichartz Estimates in Hyperbolic Space

AbstractIn this paper, we study nonlinear Helmholtz equations (NLH)$$ \begin{equation} \tag{(NLH)} -\Delta_{\mathbb{H}^N} u - \frac{(N-1)^2}{4} u -\lambda^2 u = \Gamma|u|^{p-2}u \quad\text{in}\ \mathbb{H}^N, \;N\geq 2, \end{equation}$$where $\Delta _{\mathbb {H}^N}$ denotes the Laplace–Beltrami operator in the hyperbolic space $\mathbb {H}^N$ and $\Gamma \in L^\infty (\mathbb {H}^N)$ is chosen suitably. Using fixed point and variational techniques, we find nontrivial solutions to (NLH) for all $\lambda>0$ and $p>2$. The oscillatory behaviour and decay rate of radial solutions is analyzed, with extensions to Cartan–Hadamard manifolds and Damek–Ricci spaces. Our results rely on a new limiting absorption principle for the Helmholtz operator in $\mathbb {H}^N$. As a byproduct, we obtain simple counterexamples to certain Strichartz estimates.

Особенности когерентной спиновой динамики двумерного электронного газа в режиме холловского ферромагнетика

By means of the time-resolved Kerr rotation technique, a spin-depolarized electron system at a filling factor ν = 1 in a GaAs quantum well was studied. At temperatures above 5 K, a transition from a new spin-correlated state to a state with low spin stiffness characteristic of a single-particle electron system was found. A nonlinear contribution to the decay of Larmor oscillations arising at low temperatures, when spin-spin correlations determine the ground state of a two-dimensional electron system, is highlighted. The parameters of the fluctuating magnetic field acting on individual electron spins are estimated.

Excitation of decay-less transverse oscillations of coronal loops by random motions

Context. The relatively large-amplitude decaying regime of transverse oscillations of coronal loops has been known for two decades and has been interpreted in terms of magnetohydrodynamic kink modes of cylindrical plasma waveguides. In this regime oscillations decay in several cycles. Recent observational analysis has revealed so-called decay-less, small-amplitude oscillations, in which a multi-harmonic structure has been detected. Several models have been proposed to explain these oscillations. In particular, decay-less oscillations have been described in terms of standing kink waves driven with continuous mono-periodic motions of loop footpoints, in terms of a simple oscillator model of forced oscillations due to harmonic external force, and as a self-oscillatory process due to the interaction of a loop with quasi-steady flows. However, an alternative mechanism is needed to explain the simultaneous excitation of several longitudinal harmonics of the oscillation. Aims. We study the mechanism of random excitation of decay-less transverse oscillations of coronal loops. Methods. With a spatially one-dimensional and time-dependent analytical model taking into account effects of the wave damping and kink speed variation along the loop, we considered transverse loop oscillations driven by random motions of footpoints. The footpoint motions were modelled by broad-band coloured noise. Results. We found the excitation of loop eigenmodes and analysed their frequency ratios as well as the spatial structure of the oscillations along the loop. The obtained results successfully reproduce the observed properties of decay-less oscillations. In particular, excitation of eigenmodes of a loop as a resonator can explain the observed quasi-monochromatic nature of decay-less oscillations and the generation of multiple harmonics detected recently. Conclusions. We propose a mechanism that can interpret decay-less transverse oscillations of coronal loops in terms of kink waves randomly driven at the loop footpoints.

Non-linear effects in the oscillating drop method for viscosity measurements

The contribution of non-linear fluid flow effects to the damping of surface oscillations in the oscillation drop method was investigated in a series of experiments in an electromagnetic levitation device installed on the International Space station, ISS-EML. In order to correctly evaluate the damping time constant from measured surface oscillation decays the effect of a modulated signal response on measured surface oscillation decay curves was investigated. It could be shown that various experimentally observed signal patterns could be well represented by a modulated response. The physical origin of such modulations is seen in rotation and precession. Over a temperature range of 220 K covered by different surface oscillation excitation pulses with an initial sample shape deformation of 5 – 10% the amplitude of surface oscillations as a function of time could be very well represented by a Lamb type damping with a temperature dependent viscosity. A direct comparison of surface oscillation decay times measured in the same temperature range but for different oscillation amplitudes showed no non-linear contribution to the damping time constant with a confidence level better 10%.

Effect of the fractional oscillator noise in the overdamped linear oscillator with the presence of a periodic force

The overdamped linear oscillator with periodic external force driven by the fractional oscillator (FO) noise is considered and investigated. The correlation function of the FO noise presents power-law-like function, exponential-like function and oscillatory decays similar to those of the harmonic noise. The amplitude of the stationary state of the first moment is obtained and analyzed in relation to the parameters of the system; it presents non-monotonic behaviors which are related to the resonance phenomenon.

Mesoscopic theory for systems with competing interactions near a confining wall.

Mesoscopic theory for self-assembling systems near a planar confining surface is developed. Euler-Lagrange equations and the boundary conditions (BCs) for the local volume fraction and the correlation function are derived from the density functional theory expression for the grand thermodynamic potential. Various levels of approximation can be considered for the obtained equations. The lowest-order nontrivial approximation [generic model (GM)] resembles the Landau-Brazovskii-type theory for a semi-infinite system. Unlike in the original phenomenological theory, however, all coefficients in our equations and BCs are expressed in terms of the interaction potential and the thermodynamic state. Analytical solutions of the linearized equations in the GM are presented and discussed on a general level and for a particular example of the double-Yukawa potential. We show exponentially damped oscillations of the volume fraction and the correlation function in the direction perpendicular to the confining surface. The correlations show oscillatory decay in directions parallel to this surface too, with the decay length increasing significantly when the system boundary is approached. The framework of our theory allows for a systematic improvement of the accuracy of the results.

Chiral p -wave superconductors have complex coherence and magnetic field penetration lengths

We show that in superconductors that break time reversal symmetry and have anisotropy, such as p+ip materials, all order parameters and magnetic modes are mixed. Excitation of the gap fields produces an excitation of the magnetic field and vice versa. Correspondingly the long-range decay of the magnetic field and order parameter are in general given by the same exponent. Thus one cannot characterize p+ip superconductors by the usual coherence and magnetic field penetration lengths. Instead the system has normal modes that are associated with linear combinations of magnetic fields, moduli of and phases of the order parameter components. Each such normal mode has its own decay length that plays the role of a hybridized coherence/magnetic field penetration length. On a large part of the parameter space these exponents are complex. Therefore the system in general has damped oscillatory decay of the magnetic field accompanied by damped oscillatory variation of the order parameter fields.

Revealing Signs and Hidden 1H NMR Coupling Constants in Three-Spin Systems Using Long-Lived Coherences.

Long-lived coherences (LLCs) in a pair of coupled protons have long lifetimes and hence decreased line width and increased spectral resolution. Fourier transformation of the damped oscillatory decay of the LLC also provides coupling information on the spin system. In a three-spin system, unlike in the two-spin case, the peaks in an LLC spectrum are observed at combinations of the coupling constants. This attribute is used to determine the relative signs of the coupling constants in weakly and strongly coupled model systems. In addition, it is shown that a coupling constant in a three-spin system that is unobservable in the 1H NMR spectrum, as is the case in bispidinone, a molecule of significance in peptidomimetics, may be determined from the LLC spectrum.

Simulation of flows with phase transitions and heat transfer using mesoscopic methods

We use mesoscopic lattice Boltzmann and phase-field methods to simulate the growth of crystals from supercooled melt in the presence of melt convection and the behavior of a pinned droplet under the action of the electric field. In the first problem, the flow influences significantly the shape and the stability of growing patterns, leading to the enhanced development of fingers in the direction opposite to the flow. In the second problem, after the application of the electric field, the droplet begins to elongate in the field direction and the oscillations are produced. These oscillations decay in time due to a viscosity of a fluid. After several oscillations, the droplet acquires its equilibrium shape. The contact angle is essentially reduced compared to the case without an electric field.