Wavenumber In Terms Research Articles

A comparative study of circularity of artefact detecting circle using CMM and form tester with different filters

This paper presents a study of circularity of the different workpiece using CMM for smooth functioning of manufactured parts. The present work to study of roundness of different artefact using different algorithm and filters. For the present study have been conducted on RA-2200CNC form tester and LEGEX 9106 CMM by selecting two filters and four types of algorithm with different range of spectral wave numbers in terms of undulations per revolution (UPR) and fitting software techniques. Instrument data set help the designer and operator to satisfy the best fit for roundness in nano scale metrology.

Pattern formation in the wake of triggered pushed fronts

Pattern-forming fronts are often controlled by an external stimulus which progresses through a stable medium at a fixed speed, rendering it unstable in its wake. By controlling the speed of excitation, such stimuli, or ‘triggers’, can mediate pattern forming fronts which freely invade an unstable equilibrium and control which pattern is selected. In this work, we analytically and numerically study when the trigger perturbs an oscillatory pushed free front. In such a situation, the resulting patterned front, which we call a pushed trigger front, exhibits a variety of phenomenon, including snaking, non-monotonic wave-number selection, and hysteresis. Assuming the existence of a generic oscillatory pushed free front, we use heteroclinic bifurcation techniques to prove the existence of trigger fronts in an abstract setting motivated by the spatial dynamics approach. We then derive a leading order expansion for the selected wave-number in terms of the trigger speed. Furthermore, we show that such a bifurcation curve is governed by the difference of certain strong-stable and weakly-stable spatial eigenvalues associated with the decay of the free pushed front. We also study prototypical examples of these phenomena in the cubic-quintic complex Ginzburg Landau equation and a modified Cahn–Hilliard equation.

Atlantic sea surface height and velocity spectra inferred from satellite altimetry and a hierarchy of numerical simulations

AbstractFrequency and wavenumber spectra of sea surface height (SSH) and surface geostrophic velocity are presented, as they result for the Atlantic Ocean from a 23 year long altimeter data set and from a hierarchy of ocean model simulations with spatial resolutions of 16, 8, and 4 km. SSH frequency spectra follow a spectral decay of roughly f−1 on long periods; toward higher frequencies a spectral decay close to f−2 is found. For geostrophic velocity spectra, a somewhat similar picture emerges, albeit with flatter spectral relations. In terms of geostrophic velocity wavenumber spectra, we find a general relation close to k−3 in the high‐resolution model results. Outside low‐energy regions all model spectra come close to observed spectra at low frequencies and wavenumbers in terms of shape and amplitude. However, the highest model resolution appears essential for reproducing the observed spectra at high frequencies and wavenumbers. This holds especially for velocity spectra in mid and high latitudes, suggesting that eddy resolving ocean models need to be run at a resolution of 1/24° or better if one were to fully resolve the observed mesoscale eddy field. Causes for remaining discrepancies between observed and simulated results can be manifold. At least partially, they can be rationalized by taking into account an aliasing effect of unresolved temporal variability in the altimetric observations occurring on periods smaller than the 20 days Nyquist period of the altimetric data, thereby leading to an overestimate of variability in the altimetric estimates, roughly on periods below 100 days.

Improved Tropical-Cyclone Flight-Level Wind Estimates Using Routine Infrared Satellite Reconnaissance

AbstractA new and improved method for estimating tropical-cyclone (TC) flight-level winds using globally and routinely available TC information and infrared (IR) satellite imagery is presented. The developmental dataset is composed of aircraft reconnaissance (1995–2012) that has been analyzed to a 1 km × 10° polar grid that extends outward 165 km from the TC center. The additional use of an azimuthally average tangential wind at 500 km, based on global model analyses, allows the estimation of winds at larger radii. Analyses are rotated to a direction-relative framework, normalized by dividing the wind field by the observed maximum, and then decomposed into azimuthal wavenumbers in terms of amplitudes and phases. Using a single-field principal component method, the amplitudes and phases of the wind field are then statistically related to principal components of motion-relative IR images and factors related to the climatological radius of maximum winds. The IR principal components allow the wind field to be related to the radial and azimuthal variability of the wind field. Results show that this method, when provided with the storm location, the estimated TC intensity, the TC motion vector, and a single IR image, is able to estimate the azimuthal wavenumber 0 and 1 components of the wind field. The resulting wind field reconstruction significantly improves on the method currently used for satellite-based operational TC wind field estimates. This application has several potential uses that are discussed within.

Optimal perturbations of gravitationally unstable, transient boundary layers in porous media

AbstractWe study the linear stability of gravitationally unstable, transient, diffusive boundary layers in porous media using non-modal stability theory. We first perform a classical optimization procedure, using an adjoint-based method, to obtain the perturbations at the initial time $t= {t}_{p} $ that have a maximum amplification at a final time $t= {t}_{f} $. We then investigate the sensitivity of the optimal perturbations to the initial time, ${t}_{p} $, and the final time, ${t}_{f} $, as well as different measures of perturbation amplification. Due to the transient nature of the base state, we demonstrate that there is an optimal initial perturbation time, ${ t}_{p}^{o} $. By rescaling the problem, we develop analytical relationships for the optimal initial time and wavenumber in terms of aquifer properties. We also demonstrate that the classical optimization procedure essentially recovers the dominant perturbation structures predicted by a quasi-steady modal analysis. Although the classical optimal perturbations are mathematically valid, we observe that due to physical constraints, they are unlikely to reflect analogous laboratory experiments. Therefore, we propose a modified optimization procedure (MOP) that constrains the optimization to physically admissible initial perturbation fields. We compare the results of the classical and modified optimization procedures with quasi-steady modal analyses and initial value problems commonly used in the literature. Finally, we validate the predictions of the modified optimization scheme by performing direct numerical simulations (DNS) that emulate the onset of convection in physical systems.

On the linear stability of a scalar-field with exponential potential in a flat Robertson-Walker background

We study covariant and gauge-invariant linear scalar perturbations of a scalar-field with positive exponential potential in a flat Robertson-Walker background. By applying a dynamical systems approach we investigate how the phase of the perturbations evolves, finding bounds on the wave-number in terms of the slope parameter, for which the perturbations decays when approaching the inflationary solution.

Onset of coherent electromagnetic structures in the REB–DT fuel interaction of fast ignition interest

This paper focuses on the combinations of swiftly growing electromagnetic instabilities arising from the interaction of relativistic electron beams (REBs) with precompressed deuterium+tritium (DT) fuels of fast ignition interest for ICF. The REB–target system is taken as neutral in charge and current with distribution functions including target and beam temperatures. We also stress the significant impact, on the modes' growth rates (GRs), of mode–mode-coupling and intrabeam scattering. Collisional damping is documented at large wavenumbers in terms of inverse skin depth. A quasi-linear approach yields lower GR than linear ones. One of the most conspicuous outputs of the linear analysis are 3D broken ridges featuring the largest GR above k-space for an oblique propagation w.r.t. initial particle beam direction. The given modes are seen immune to any temperature-induced damping. Those novel patterns are easily produced by considering simultaneously Weibel, filamentation and two-stream instabilities. This behavior persists in the presence of smooth density gradients or strong applied magnetic fields. Moreover, in the very early propagation stage with no current neutralization in the presence of large edge density gradients, REBs demonstrate a characteristic ring-like and regularly spiked pattern in agreement with recent experimental results and previous simulations.

Onset of Coherent electromagnetic structures in the relativistic electron beam deuterium-tritium fuel interaction of fast ignition concern

We focus attention on the combinations of swiftly growing electromagnetic instabilities (EMI) arising in the interaction of relativistic electron beams (REB) with precompressed deuterium-tritium (DT) fuels of fast ignition interest for inertial confinement fusion (ICF). REB-target system is taken neutral in charge and current with distribution functions including target and beam temperatures. We stress also the significant impact on modes growth rates (GR) of mode-mode coupling and intrabeam scattering. Collisional damping is documented at large wave numbers in terms of inverse skin depth. A quasi-linear approach yields lower GR than linear ones. One of the most conspicuous output of the linear analysis are three-dimensional (3D) broken ridges featuring the largest GR above k-space for an oblique propagation w.r.t initial particle beam direction. The given modes are seen immune to any temperature induced damping. Those novel patterns are easily produced by considering simultaneously Weibel, filamentation and two-stream instabilities. The behaviors persist in the presence of smooth density gradients or strong applied magnetic fields. Moreover, in the very early propagation stage with no current neutralization in the presence of large edge density gradients, REB demonstrate a characteristics ringlike and regularly spiked pattern in agreement with recent experimental results and previous simulations.

Onset of coherent electromagnetic structures in the relativistic electron beam deuterium-tritium fuel interaction of fast ignition concern

AbstractWe focus attention on the combinations of swiftly growing electromagnetic instabilities (EMI) arising in the interaction of relativistic electron beams (REB) with precompressed deuterium-tritium (DT) fuels of fast ignition interest for inertial confinement fusion (ICF). REB-target system is taken neutral in charge and current with distribution functions including target and beam temperatures. We stress also the significant impact on modes growth rates (GR) of mode-mode coupling and intrabeam scattering. Collisional damping is documented at large wave numbers in terms of inverse skin depth. A quasi-linear approach yields lower GR than linear ones. One of the most conspicuous output of the linear analysis are three-dimensional (3D) broken ridges featuring the largest GR above k-space for an oblique propagation w.r.t initial particle beam direction. The given modes are seen immune to any temperature induced damping. Those novel patterns are easily produced by considering simultaneously Weibel, filamentation and two-stream instabilities. The behaviors persist in the presence of smooth density gradients or strong applied magnetic fields. Moreover, in the very early propagation stage with no current neutralization in the presence of large edge density gradients, REB demonstrate a characteristics ringlike and regularly spiked pattern in agreement with recent experimental results and previous simulations.

Band structures of coupled electromagnetic slow waves

In this paper, a modified transfer matrix method is applied for the analysis of electromagnetic slow wave propagation in Kronig–Penny photonic crystals. Analytic expressions for Bloch wavenumbers in terms of normalized frequency are derived and the asymptotic behaviour of electromagnetic slow wave propagation in these structures is investigated at different regimes. The tight binding method is also used for the analysis of electromagnetic slow wave propagation in Kronig–Penny photonic crystals and analytic expressions are given. It has been shown that forbidden wavenumbers rather than forbidden frequencies can be observed under specific circumstances.

Optical properties of poly 2-methoxy-5-hexyloxy phenylenevinylene and related copolymers

We have measured the dielectric function of poly 2-methoxy-5-hexyloxy phenylenevinylene and the alternating copolymers with N-hexylphenothiazine grown on glass using variable angle spectroscopic ellipsometry and Raman spectroscopy at room temperature. Using the parametric optical constant model, we estimated the dielectric function of each polymer and also determined the band gap parameters, such as threshold energy, broadening, and amplitude. We also determined the band gap parameters by performing lineshape curve-fitting on the second derivative of the fit dielectric function using standard critical point model, and compared to those of the parametric optical constant model. We discussed the shift of band gap parameters and phonon wave numbers in terms of the chemical structures.

Estimation of the electromagnetic field created at the earth’s surface by an overhead line current

The electromagnetic field that an overhead infinitely line current produces at the surface of the earth can be expressed as inverse Fourier integrals over a horizontal wave number in terms of the Neumann and Struve functions. These functions have known mathematical properties, including the series expansions. The latter are utilized in this work to derive expressions for the electromagnetic field. The integrals of the electromagnetic field are solved and the results are represented graphically.

Is Relativistic Quantum Mechanics Compatible with Special Relativity?

Abstract The transformation from a time-dependent random walk to quantum mechanics converts a modi­fied Bessel function into an ordinary one together with a phase factor e,ir/2 for each time the electron flips both direction and handedness. Causality requires the argument to be greater than the order of the Bessel function. Assuming equal probabilities for jumps ± 1 , the normalized modified Bessel function of an imaginary argument is the solution of the finite difference differential Schrödinger equation whereas the same function of a real argument satisfies the diffusion equation. In the nonrelativistic limit, the stability condition of the difference scheme contains the mass whereas in the ultrarelativistic limit only the velocity of light appears. Particle waves in the nonrelativistic limit become elastic waves in the ultrarelativistic limit with a phase shift in the frequency and wave number of 7r/2. The ordinary Bessel function satisfies a second order recurrence relation which is a finite difference differential wave equation, using non-nearest neighbors, whose solutions are the chirality components of a free-particle in the zero fermion mass limit. Reintroducing the mass by a phase transformation transforms the wave equation into the Klein-Gordon equation but does not admit a solution in terms of ordinary Bessel functions. However, a sign change of the mass term permits a solution in terms of a modified Bessel function whose recurrence formulas produce all the results of special relativity. The Lorentz transformation maximizes the integral of the modified Bessel function and determines the paths of steepest descent in the classical limit. If the definitions of frequency and wave number in terms of the phase were used in special relativity, the condition that the frame be inertial would equate the superluminal phase velocity with the particle velocity in violation of causality. In order to get surfaces of constant phase to move at the group velocity, an integrating factor is required which determines how the intensity decays in time. The phase correlation between neighboring sites in quantum mechanics is given by the phase factor for the electron to reverse its direction, whereas, in special relativity, it is given by the Doppler shift.

Harmonic wave propagation in viscoelastic heterogeneous materials Part II: Effective complex moduli

The effective complex moduli of a heterogeneous periodic viscoelastic medium has been determined through its dispersion and damping curves. These curves give the values of complex wave numbers in terms of frequencies and wave direction. The solution of Christoffel's equations of an equivalent viscoelastic homogeneous medium for judiciously selected wave directions provides us simple relations between complex wave numbers belonging to the heterogeneous medium and its effective complex moduli. Based on this method two examples have been treated. The one, a viscoelastic homogeneous material, to show the accuracy of this method. The other, a fiber composite material, to illustrate the applicability of the method.

Receptivity of boundary layers: asymptotic theory and experiment

The sources of disturbance (vibrators, small jets, vortices, sound waves) in a boundary layer are considered, emphasizing their ability to provoke the onset of eigenoscillations with exponentially growing amplitude. Harmonic sources give rise to the Tollmien–Schlichting waves, whereas impulsive sources excite wave packets. General requirements are stated for the temporal and spatial characteristics of the signals emitted by the devices causing disturbance, as well as for obstacles met by signals when propagating. To scale the frequencies and wavenumbers in terms of the Reynolds number taking on indefinitely large values, the asymptotic theory of an interacting boundary layer with the triple-deck structure is used. The conclusions from the asymptotic analysis are in line with the results of measurements in wind tunnels when the Reynolds numbers were moderate.

The effect of geometry on the gravitational instability of a buoyant region of viscous fluid

The low-Reynolds-number stability of a region of buoyant fluid surrounded by denser fluid is analysed in two situations. In the first study, the buoyant fluid lies in a thin layer sandwiched between two denser and much deeper layers. The growth rate and wavelength of the most unstable sinusoidal perturbation are calculated and the effects of the viscosity ratios and density differences between the fluids are investigated. It is found that if the buoyant fluid is much less viscous than the overlying fluid then, in quite general circumstances, both the most unstable wavelength and the corresponding growth rate are inversely proportional to the cube root of the viscosity of the buoyant fluid. A physical explanation of this result is given by scaling analysis of the total dissipation. In the second study, the buoyant fluid takes the form of a cylinder rising through a uniform environment. The eigenmodes of small perturbation about this state of motion are found for each axial wavenumber in terms of Fourier series of separable solutions to the Stokes equations. In contrast to the first study, it is found that the most unstable wavelength and growth rate are asymptotically independent of the viscosity of the buoyant fluid when this viscosity is small.The difference between the results of the two studies is of importance, particularly for geophysical applications in which viscosity ratios are very large. Previous models of linear regions of volcanism at mid-ocean ridges and at island arcs have assumed that results obtained in simple two-layered systems can be generalized to other geometries. The conclusions of these models are discussed in the light of the stability results for a cylindrical (and hence linea.

Dynamical processes in hard-sphere fluids.

For a classical fluid of hard spheres the nine hydrodynamic time-correlation functions between the microscopic density, longitudinal velocity, and temperature are calculated theoretically on the basis of the revised Enskog theory for all densities and wave numbers. It appears that a simplified description of these correlation functions is possible for small wave numbers in terms of extended hydrodynamic modes and for large wave numbers in terms of free streaming and a single binary collision.

Satellite Generation of Electron Plasma Waves form Low Frequency Oscillations in Plasmas

Experiments demonstrating that the satellite generation of a stable electrostatic wave in the presence of an electron density oscillation in a bounded plasma and that the satellite generation of the unstable plasma wave in a modulated electron beam-plasma system are described. The spatially periodic energy transfer among the satellite modes and the primary mode is observed, which results in an enhanced damping of the stable primary mode in the former case and a decrease in a growth rate of the unstable primary mode in the latter. These results are compared with the theoretical prediction derived by expanding the wave number in terms of fluctuating plasma parameters as well as by using the coupled mode equations.

Plane Wave Propagation in Kinetic Theory

A number of results for plane wave propagation in kinetic theory are obtained. Among these are the following. It is shown that the Boltzmann equation for bounded collision operator has a cutoff frequency beyond which plane waves cease to exist. The analytic continuation of the dispersion relation is discussed and asymptotic results beyond the critical frequency are obtained. Using a kinetic model it is shown that the low-frequency formal power series for complex wavenumber in terms of frequency (and vice versa) are divergent. The last is contrary to the recent result obtained for the rigid sphere Boltzmann equation.