Stationary Dipole Research Articles

Prediction of the acoustic particle velocity in aerodynamic flows and its applications to the boundary element method

The acoustic variables are essential for understanding sound energy transmission and redistribution. The previous methods focused on acoustic pressure without the acoustic particle velocity, which is not enough for acoustic field evaluation. In this paper, an analytical formula for acoustic particle velocity prediction is developed based on the permeable surface integral solution of a vector wave equation. The validation examples are presented with stationary dipole and rotational monopole. The acoustic quantities, pressure, and velocity are solved at the same time and will be applied as input for the boundary element method (BEM) to evaluate the sound scattering problem in the frequency domain. Furthermore, the method is applied to study the acoustic field of flow passing a cylinder. The acoustic pressure shows good agreement with the flow observer. The acoustic particle velocity is also investigated.

Acoustic velocity analogy formulation for sources in quiescent medium

The prediction of near field acoustic velocity is necessary when using equivalent source method and evaluating multi acoustic fields problem. According to the idea of acoustic analogy, this paper induces a vector wave equation of aeroacoustics by rearranging the conservation equations of mass and momentum with a permeable surface. Then, an analytical formulation of the acoustic velocity, called formulation V2A, is derived for sources in a quiescent medium by solving the vector wave equation with the free-space Green’s function. The validity of the formulation is confirmed by numerical results for a stationary monopole, a stationary dipole source, and a rotating monopole source in a quiescent medium. The result indicates that the predication of formulation V2A is nearly identical to the exact solutions no matter in far-field or near-field.

Effects of muscle shortening on single-fiber, motor unit, and compound muscle action potentials

Even under isometric conditions, muscle contractions are associated with some degree of fiber shortening. The effects of muscle shortening on extracellular electromyographic potentials have not been characterized in detail. Moreover, the anatomical, biophysical, and detection factors influencing the muscle-shortening effects have been neither identified nor understood completely. Herein, we investigated the effects of muscle shortening on the amplitude and duration characteristics of single-fiber, motor unit, and compound muscle action potentials. We found that, at the single-fiber level, two main factors influenced the muscle-shortening effects: (1) the electrode position and distance relative to the myotendinous zone and (2) the electrode distance to the maxima of the dipole field arising from the stationary dipole created at the fiber-tendon junction. Besides, at the motor unit and muscle level, two additional factors were involved: (3) the overlapping between the propagating component of some fibers with the non-propagating component of other fibers and (4) the spatial spreading of the fiber-tendon junctions. The muscle-shortening effects depend critically on the electrode longitudinal distance to the myotendinous zone. When the electrode was placed far from the myotendinous zone, muscle shortening resulted in an enlargement and narrowing of the final (negative) phase of the potential, and this enlargement became less pronounced as the electrode approached the fiber endings. For electrode locations close to the myotendinous zone, muscle shortening caused a depression of both the main (positive) and final (negative) phases of the potential. Beyond the myotendinous zone, muscle shortening led to a decrease of the final (positive) phase. The present results provide reference information that will help to identify changes in MUPs and M waves due to muscle shortening, and thus to differentiate these changes from those caused by muscle fatigue.Graphical abstract

Rapid computation of TMS-induced E-fields using a dipole-based magnetic stimulation profile approach

BackgroundTMS neuronavigation with on-line display of the induced electric field (E-field) has the potential to improve quantitative targeting and dosing of stimulation, but present commercially available solutions are limited by simplified approximations. ObjectiveDeveloping a near real-time method for accurate approximation of TMS induced E-fields with subject-specific high-resolution surface-based head models that can be utilized for TMS navigation. MethodsMagnetic dipoles are placed on a closed surface enclosing an MRI-based head model of the subject to define a set of basis functions for the incident and total E-fields that define the subject's Magnetic Stimulation Profile (MSP). The near real-time speed is achieved by recognizing that the total E-field of the coil only depends on the incident E-field and the conductivity boundary geometry. The total E-field for any coil position can be obtained by matching the incident field of the stationary dipole basis set with the incident E-field of the moving coil and applying the same basis coefficients to the total E-field basis functions. ResultsComparison of the MSP-based approximation with an established TMS solver shows great agreement in the E-field amplitude (relative maximum error around 5%) and the spatial distribution patterns (correlation >98%). Computation of the E-field took ~100 ms on a cortical surface mesh with 120k facets. ConclusionThe numerical accuracy and speed of the MSP approximation method make it well suited for a wide range of computational tasks including interactive planning, targeting, dosing, and visualization of the intracranial E-fields for near real-time guidance of coil positioning.

Dipole Approximation for Electrically Small Loop Antennas

An elementary magnetic emitter is considered as an approximation for the variable magnetic field of an electrically small radiating loop antenna. The frequency limits for applicability of the stationary dipole model are studied. Approximate formulas are obtained for characterizing the difference between the magnetic field of a circular loop antenna and the magnetic field of the equivalent point source.

Unveiling the Role of Dopant Polarity in the Recombination and Performance of Organic Light‐Emitting Diodes

AbstractThe recombination of charges is an important process in organic photonic devices, because the process influences the device characteristics such as the driving voltage, efficiency, and lifetime. Here, by using various homoleptic and heteroleptic Ir complexes as dopants, it is reported that the stationary dipole moment (μ0) of the dopant rather than the trap depth (ΔEt) is a major factor determining the recombination mechanism in dye‐doped organic light‐emitting diodes (OLEDs). Dopants with large μ0 (e.g., homoleptic Ir(III) dyes) induce large charge trapping on them, resulting in high driving voltage and trap‐assisted recombination‐dominated emission. On the other hand, dyes with small μ0 (e.g., heteroleptic Ir(III) dyes) show Langevin recombination‐dominated emission characteristics with much less charge trapping on them no matter what ΔEt is, leading to lower driving voltage and higher efficiencies. This finding will be useful in any organic photonic devices such as phosphorescent or thermally assisted delayed fluorescent dye sensitized fluorescent OLEDs where trapping and recombination mechanisms play key roles.

Vacuum source-field correlations and advanced waves in quantum optics

The solution to the wave equation as a Cauchy problem with prescribed fields at an initial timet=0is purely retarded. Similarly, in the quantum theory of radiation the specification of Heisenberg picture photon annihilation and creation operators at timet>0in terms of operators att=0automatically yields purely retarded source-fields. However, we show that two-time quantum correlations between the retarded source-fields of a stationary dipole and the quantum vacuum-field possess advanced wave-like contributions. Despite their advanced nature, these correlations are perfectly consistent with Einstein causality. It is shown that while they do not significantly contribute to photo-detection amplitudes in the vacuum state, they do effect the statistics of measurements involving the radiative force experienced by a point charge in the field of the dipole. Specifically, the dispersion in the charge's momentum is found to increase with time. This entails the possibility of obtaining direct experimental evidence for the existence of advanced waves in physical reality, and provides yet another signature of the quantum nature of the vacuum.

Analytic Time-Domain Formulation for Acoustic Pressure Gradient Prediction in a Moving Medium

This paper presents an analytic time-domain formulation for acoustic pressure gradient prediction in a moving medium, which has significant application potential in evaluating the acoustic scattering boundary condition. Based on the convective Ffowcs Williams–Hawkings equation, a semianalytic time-domain acoustic pressure gradient formulation with a form involving the observer time differentiation outside the integrals is first developed, and then the desired analytic time-domain acoustic pressure gradient formulation is derived. Because the derived formulations are performed directly in the time domain, they are particularly applicable to the moving observer case. Simulation results for a stationary monopole source, a stationary dipole source, as well as a rotating monopole source in a moving medium demonstrate the effectiveness and accuracy of the proposed formulations for both stationary and moving sources with moving observers.

Математическая модель взаимодействия ледового покрова и гидродинамического диполя в канале

In this paper, hydroelastic waves generated by a hydrodynamic dipole in a channel covered with ice are studied. The stationary dipole placed in a flow of a liquid with constant speed and the dipole that moves uniformly along the channel are described. A mathematical model is based on the Kelvin-Voigt differential equation of viscoelastic plate and the Laplace equation for a velocity potential under the ice cover. The velocity potential is equal to the sum of the dipole potential in the channel and a potential of the flow caused by the deflection of the plate. The equation for the dipole potential in the channel is obtained by a method of mirror images for four walls. These equations are supplemented by impermeability boundary conditions on the walls and bottom of the channel, clamped boundary conditions of ice on the walls of the channel, and kinematic and dynamic conditions at the ice-liquid interface. The dynamic condition is described by the linearized Cauchy-Lagrange integral. A formulation of the stationary problem is studied. The solution is sought in the form of a traveling wave, which is independent of time in a coordinate system moving with the dipole. Streamlines of the fluid motion and shapes of the flow are studied for the case of flowing around the dipole in the channel. Obtained results are compared with forms of flow in an unbounded fluid.DOI 10.14258/izvasu(2017)1-30

Investigation of the strong turbulence in the geospace environment

Abstract. Plasma vortices are often detected by spacecraft in the geospace (atmosphere, ionosphere, magnetosphere) environment, for instance in the magnetosheath and in the magnetotail region. Large scale vortices may correspond to the injection scale of turbulence, so that understanding their origin is important for understanding the energy transfer processes in the geospace environment. In a recent work, turbulent state of plasma medium (especially, ionosphere) is overviewed. Experimental observation data from THEMIS mission (Keiling et al., 2009) is investigated and numerical simulations are carried out. By analyzing the THEMIS data for that event, we find that several vortices in the magnetotail are detected together with the main one and these vortices constitute a vortex chain. Such vortices can cause the strong turbulent state in the different media. The strong magnetic turbulence is investigated in the ionsophere as an ensemble of such strongly localized (weakly interacting) vortices. Characteristics of power spectral densities are estimated for the observed and analytical stationary dipole structures. These characteristics give good description of the vortex structures.

Stationary dipole at the fracture tip in a poroelastic medium

This paper presents an analytic self-similar solution describing an equilibrium of a planar semi-infinite hydraulic fracture in a poroelastic medium. The equilibrium of the fracture is sustained by a balance between the pressure of fluid within the fracture and the confining stress due to elasticity of nearby poroelastic material satisfying the Biot model assumptions. Propagation of fluid in the fracture, leakoff through the fracture’s walls and filtration in the poroelastic medium towards the fracture’s tip form a dipole-type pattern of flow. The solution is used for the verification of a numerical algorithm developed earlier for the pressure transient analysis in water injection wells.

Direct Evaluation of Acoustic-Intensity Vector Field Around an Impedance Scattering Body

The paper presents a direct method for predicting the acoustic-intensity vector field around an impedance scattering body. The results obtained from the present method, combined with the equivalent-source method, graphically display the acoustic-intensity vector field around the scattering body, and reveal the effect of surface impedance on the absorption of the acoustic energy. Three test cases (i.e., the plane wave scattered by a rigid sphere, and the sound of the stationary monopole and dipole point sources scattered by an impedance sphere) are carried out to validate the method. From the analysis of the computational error, it is suggested that the maximum length of the surface element should be less than one-tenth of the wavelength to ensure that the relative error is less than 3%.

Remote Manipulation With a Stationary Computer-Controlled Magnetic Dipole Source

In this paper, we examine several magnetic control methods that utilize the fully controllable dipole field generated by the single stationary dipole source. Since the magnetic field generated by a dipole source is nonuniform, it applies both forces and torques to magnetic objects and can be used to manipulate magnetic tools. Recently, the Omnimagnet, a computer-controlled magnetic dipole source capable of varying both its dipole-moment direction and magnitude, was developed to perform magnetic manipulation. The equations and methods are developed generally; therefore, they can be applied to any omnidirectional dipole source, but their effectiveness is demonstrated using the Omnimagnet.

Dynamical pattern formation in two-dimensional fluids and Landau pole bifurcation.

A phenomenological theory is proposed to analyze the asymptotic dynamics of perturbed inviscid Kolmogorov shear flows in two dimensions. The phase diagram provided by the theory is in qualitative agreement with numerical observations, which include three phases depending on the aspect ratio of the domain and the size of the perturbation: a steady shear flow, a stationary dipole, and four traveling vortices. The theory is based on a precise study of the inviscid damping of the linearized equation and on an analysis of nonlinear effects. In particular, we show that the dominant Landau pole controlling the inviscid damping undergoes a bifurcation, which has important consequences on the asymptotic fate of the perturbation.

Effect of metallic walls on dynamos generated by laminar boundary-driven flow in a spherical domain

We present a numerical study of dynamo action in a conducting fluid encased in a metallic spherical shell. Motions in the fluid are driven by differential rotation of the outer metallic shell, which we refer to as "the wall." The two hemispheres of the wall are held in counter-rotation, producing a steady, axisymmetric interior flow consisting of differential rotation and a two-cell meridional circulation with radial inflow in the equatorial plane. From previous studies, this type of flow is known to maintain a stationary equatorial dipole by dynamo action if the magnetic Reynolds number is larger than about 300 and if the outer boundary is electrically insulating. We vary independently the thickness, electrical conductivity, and magnetic permeability of the wall to determine their effect on the dynamo action. The main results are the following: (a) Increasing the conductivity of the wall hinders the dynamo by allowing eddy currents within the wall, which are induced by the relative motion of the equatorial dipole field and the wall. This processes can be viewed as a skin effect or, equivalently, as the tearing apart of the dipole by the differential rotation of the wall, to which the field lines are anchored by high conductivity. (b) Increasing the magnetic permeability of the wall favors dynamo action by constraining the magnetic field lines in the fluid to be normal to the wall, thereby decoupling the fluid from any induction in the wall. (c) Decreasing the wall thickness limits the amplitude of the eddy currents, and is therefore favorable for dynamo action, provided that the wall is thinner than the skin depth. We explicitly demonstrate these effects of the wall properties on the dynamo field by deriving an effective boundary condition in the limit of vanishing wall thickness.

Hidden momentum and black hole kicks

A stationary magnetic dipole immersed in an electric field carries ‘hidden’ mechanical momentum. However, the fate of this momentum if the fields are turned off is unclear. We consider a charge-and-dipole hidden momentum configuration, and turn off the fields by collapsing a null shell onto the system, forming a black hole. In numerical calculations we find that the black hole receives a kick corresponding to 0.1% of the initial stored momentum. When extrapolated to apply to purely gravitational phenomena, this efficiency suggests a role for the hidden momentum kick mechanism in generating the binary black hole ‘superkicks’ observed in numerical simulations of Einstein’s equation.

Dynamics of surface dipole and tripole solitons in nonlocal nonlinear media with optical lattice field

Abstract We find the existence conditions for stationary dipole and tripole surface solitons formed at the interface of a nonlocal nonlinear medium and a lattice with linearly modulated frequency. We investigate how the degree of nonlocality, the depth, and the modulation frequency of the optical lattice field affect on the existence of the surface solitons and their dynamics. The relationship between the power and the model parameters is identified. The stability of the surface dipole and tripole solitons is numerically investigated.

On the mechanism of electromagnetic microwave absorption in superfluid helium

In experiments on electromagnetic (EM) wave absorption in the microwave range in superfluid (SF) helium [1–3], a narrow EM field absorption line with a width on the order of (20–200) kHz was observed against the background of a wide absorption band with a width of 30–40 GHz at frequencies f 0 ≈ 110–180 GHz corresponding to the roton gap energy Δ r (T) in the temperature range 1.4–2.2 K. Using the so-called flexoelectric mechanism of polarization of helium atoms (4He) in the presence of density gradients in SF helium (HeII), we show that nonresonance microwave absorption in the frequency range 170–200 GHz can be due to the existence of time-varying local density gradients produced by roton excitations in the bulk HeII. The absorption bandwidth is determined by the roton-roton scattering time in an equilibrium Boltzmann gas of rotons, which is t r-r ≈ 3.4 × 10−11 s at T = 1.4 K and decreases upon heating. We propose that the anomalously narrow microwave resonance absorption line in HeII at the roton frequency f 0(T) = Δr(T)/2πħ appears due to the following two factors: (i) the discrete structure of the spectrum of the surface EM resonator modes in the form of a periodic sequence of narrow peaks and (ii) the presence of a stationary dipole layer in HeII near the resonator surface, which forms due to polarization of 4He atoms under the action of the density gradient associated with the vanishing of the density of the SF component at the solid wall. For this reason, the relaxation of nonequilibrium rotons generated in such a surface dipole layer is strongly suppressed, and the shape and width of the microwave resonance absorption line are determined by the roton density of states, which has a sharp peak at the edge of the roton gap in the case of weak dissipation. The effective dipole moments of rotons in the dipole layer can be directed either along or across the normal to the resonator surface, which explains the experimentally observed symmetric doublet splitting of the resonance absorption line in an external dc electric field perpendicular to the resonator surface. We show that negative absorption (induced emission) of EM field quanta observed after triggering a Kapitza “heat gun” occurs when the occupation numbers for roton states due to “pumping” of rotons exceed the occupation numbers of EM field photons in the resonator.

Dipole evolution in rotating two-dimensional flow with bottom friction

The evolution of a dipolar vortex in a quasi-two-dimensional rotating flow of barotropic fluid over a flat surface with a no-slip condition in the Ekman bottom layer is considered. The vorticity equation in this case becomes nonlinear. An effect of bottom friction is displayed mainly in cyclone-anticyclone asymmetry, which results in the expansion (diminution) of cyclonic (anticyclonic) local structures and in the stronger decay of positive vorticity. When a lateral viscosity is omitted, the vorticity equation has a solution in the form of vortex patches and hence a contour dynamics method may be used for numerical simulation. An approach of point vortices with decaying strengths is also discussed. In an approximation of two patches of opposite uniform vorticity, a three-parameter family of stationary (in an ideal fluid) orbital dipoles [V. G. Makarov and Z. Kizner, “Stability and evolution of uniform-vorticity dipoles,” J. Fluid Mech. 672, 307 (2011)] https://doi.org/10.1017/S0022112010006026 consisting of patches with unequal areas and absolute values of vorticity is considered. A three-dimensional domain of instability for this family is numerically constructed. It is shown that the evolution of such dipoles in a flow with bottom friction is described with good accuracy by a properly matched trajectory in parameter space of ideal-fluid steady states. Explicit time-dependent formulae for this phase trajectory are obtained. All characteristics (including the patch's shapes) of the evolutionary dipole, and the same characteristics for the corresponding ideal-fluid stationary dipole, almost completely coincide, at least while the phase trajectory remains in the stability region. The evolution of stationary translating dipoles (with zero net circulation) that have continuously distributed vorticity inside a quasi-elliptical finite region is also examined. When the circular Lamb dipole is used as the initial condition, good qualitative agreement is observed between the asymmetric dipoles obtained during evolution and the chain of the exact solutions from the known one-parameter family of non-symmetrical Chaplygin dipoles.

Evanescent field shapes excitation profile under axial epi-illumination

Axial epi-illuminating light transmitting a >1.3-numerical-aperture microscope objective creates an excitation volume at focus with size and shape dictated by diffraction and due to refraction by the objective and by the coverslip interface separating a specimen in aqueous buffer from the oil immersion objective. The evanescent field on the coverslip aqueous side affects primarily the excitation volume axial dimension as the specimen in focus approaches the interface to within a few hundred nanometers. Following excitation, an excited stationary dipole moment emits fluorescence in a spatially varying pattern collected over the large objective aperture. Collected light propagates in parallel rays toward the tube lens that forms a real three-dimensional image that is decoded to identify dipole orientation. An integral representation of the excitation and emitted fields for infinity-corrected optics--including effects of finite conjugate illumination, fluorescence emission near an interface, emitter dipole orientation, spherical aberration, light transmission through a dichroic filter, and for real microscopic specifications--accurately models observed field intensities including the substantial excitation from the evanescent field. The goal is to develop and verify the practical depiction of excitation and emission in a real microscope for quantitative interpretation of the 3-D emission pattern.