Function Of Wavenumber Research Articles

Modelling of magnetic data for scaling geology

ABSTRACTInterpretation of magnetic data can be carried out either in the space or frequency domain. The interpretation in the frequency domain is computationally convenient because convolution becomes multiplication. The frequency domain approach assumes that the magnetic sources distribution has a random and uncorrelated distribution. This approach is modified to include random and fractal distribution of sources on the basis of borehole data. The physical properties of the rocks exhibit scaling behaviour which can be defined as P(k) = Ak−β, where P(k) is the power spectrum as a function of wave number (k), and A and β are the constant and scaling exponent, respectively. A white noise distribution corresponds to β = 0. The high resolution methods of power spectral estimation e.g. maximum entropy method and multi‐taper method produce smooth spectra. Therefore, estimation of scaling exponents is more reliable. The values of β are found to be related to the lithology and heterogeneities in the crust. The modelling of magnetic data for scaling distribution of sources leads to an improved method of interpreting the magnetic data known as the scaling spectral method. The method has found applicability in estimating the basement depth, Curie depth and filtering of magnetic data.

Halo stochasticity from exclusion and nonlinear clustering

The clustering of galaxies in ongoing and upcoming galaxy surveys contains a wealth of cosmological information, but extracting this information is a nontrivial task since galaxies and their host haloes are stochastic tracers of the nonlinear matter density field. This stochasticity is usually modeled as the Poisson shot noise, which is constant as a function of wave number with amplitude given by $1/\overline{n}$, where $\overline{n}$ is the number density of galaxies. Here we use dark matter haloes in $N$-body simulations to show evidence for deviations from this simple behavior and develop models that explain the behavior of the stochasticity on large scales. First, haloes are extended, nonoverlapping objects, i.e., their correlation function needs to go to $\ensuremath{-}1$ on small scales. This leads to a negative correction to the stochasticity relative to the Poisson value at low wave number $k$, decreasing to zero for wave numbers large compared to the inverse exclusion scale. Second, haloes show a nonlinear enhancement of clustering outside the exclusion scale, leading to a positive stochasticity correction. Both of these effects go to zero for high $k$, making the stochasticity scale dependent even for $k<0.1h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$. We show that the corrections in the low-$k$ regime are the same in Eulerian and Lagrangian space, but that the transition scale is pushed to smaller scales for haloes observed at present time (Eulerian space), relative to the initial conditions (Lagrangian space). These corrections vary with halo mass, and we present approximate scalings with halo mass and redshift. We also discuss simple applications of these effects to galaxy samples with nonvanishing satellite fraction, where the stochasticity can again deviate strongly from the fiducial Poisson expectation. Overall, these effects affect the clustering of galaxies at a level of a few percent even on very large scales and need to be modeled properly if we want to extract high precision cosmological information from the upcoming galaxy redshift surveys.

Master equation in phase space applied to the quantum Brownian motion in a tilted periodic potential

Quantum effects in the Brownian motion in a tilted cosine potential are treated in the high temperature and weak bath–particle coupling limit via the semiclassical master equation for the time evolution of the reduced Wigner function in phase space. The differential recurrence relation generated from the master equation by expanding the periodic Wigner function expressed as a function of wave number k in Fourier series via Floquet's theorem is solved for bounded periodic initial conditions using matrix-continued fractions yielding both the time-independent and the time-dependent bounded periodic solutions. Just as the classical problem, the non-periodic solution is determined from the recurrence relation by integrating w.r.t. k over the first Brillouin zone with the initial conditions generated by the non-periodic Wigner distribution corresponding to zero probability current. The time-independent periodic (locked) solution is used to estimate quantum effects in the dc current–voltage characteristic of a Josephson junction including the capacitance, while the time-dependent non-periodic (running) solution is used to determine the dynamic structure factor and ultimately via integration over the first Brillouin zone the lifetime of the zero-voltage state. The current–voltage characteristics displayed as average velocity versus tilt reproduce in the high damping limit those from the semiclassical Smoluchowski equation, while the decrease in the lifetime of the zero-voltage state due to (the barrier lowering) quantum effects appears to be very sensitive to the tilt.

Phonon relaxation and heat conduction in one-dimensional Fermi-Pasta-Ulam β lattices by molecular dynamics simulations

The phonon relaxation and heat conduction in one-dimensional Fermi-Pasta-Ulam (FPU) β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence of the FPU β lattice, is first calculated from the energy autocorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. We find that the relaxation rate as a function of wave number k is proportional to k1.688, which leads to a N0.41 divergence of the thermal conductivity in the framework of Green—Kubo relation. This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415. Our results confirm the N2/5 divergence in one-dimensional FPU β lattices. The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices. We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions. It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.

Theoretical analysis on the role of annular metallic shapes for microwave processing of food dielectric cylinders with various irradiations

A theoretical analysis has been carried out to analyze efficient microwave assisted heating processes of food cylinders with various shapes of metallic annuli in presence of lateral and radial irradiation. Lateral irradiation represents the sample incident at one direction with source at infinity whereas the radial irradiation represents the situation where the sample is incident with microwave radiations from co-axial cylindrical cavity at infinity. A generic finite element method has been used to obtain computational mesh for all shapes of metallic annulus and Galerkin finite element method has been used to solve electric field and energy balance equations. Influence of metallic annulus has been illustrated for three representative sample lengths or regimes (I, II and III) as a function of wave number ( N w ). Sample radius with regime I is smallest and largest sample radius corresponds to regime III. In general, power absorption due to lateral irradiation is larger for regime I whereas identical power with lateral or radial irradiation or larger power absorption with radial irradiation corresponds to regime II in absence of metallic annulus. The metallic annuli are found to enhance power absorption or heating rate for specific aspect ratios of both bread and beef samples. The aspect ratios are defined as the ratio of the dimension of metallic annulus and outer radius of the food sample. Lateral irradiation is found to give larger heating rates especially for regimes II and III for bread samples (low dielectric loss), but radial irradiation gives smaller degree of thermal runaway. On the other hand, radial irradiation gives significantly large heating rates with minimal thermal runaway for beef samples (high dielectric loss) with all regimes. It is interesting to observe that the metallic annuli enhance two to three times microwave power for beef samples involving regimes II and III. Various shapes of metallic annuli are also found to play dominant role either to focus or to optimize heating effects.

Spectral analysis of line edge and line-width roughness with long-range correlation

Large-scale integrations (LSIs) are facing an ever-growing problem of device variability. One of the origins that cause the variability is line-width roughness (LWR) caused by line edge roughness (LER). Accurate characterization of the LWR plays an essential role in controlling the LWR. To do this, we report a methodology, named the “assembly method,” that enables to analyze LWR statistics beyond the conventional correlation length limit, basing on the previous “patchwork” method and recent discrete power spectral density (PSD) method. The methodology virtually assembles a long line by gathering line segments that are randomly scattered on a single line or equally processed different lines. The virtual lines are repeatedly assembled by randomly changing the combination of the segments and the order of the gathered segments while permitting overlaps of the segments between the assembled lines. Squared Fourier transforms of their widths are averaged over the assembled lines to obtain the PSD. By these steps, the statistical noise, which is inherent to experimental PSDs, is markedly reduced. Furthermore, to extract LWR statistics by comparing experimental and theoretical PSDs, we derived an analytic formula of the assembled-line PSD. In the derivation, the randomness of the segment collections played a key role. The PSDs calculated using the formula almost completely fitted experimental PSDs that were obtained by the assembly method. The parameters used in the best-fitted calculation revealed that the photoresist LWR of this study contained a component that had a correlation length of 2780 nm in addition to the previously reported LWR of 35 nm. The LWR variance of the component accounted for approximately 10% of the total variance. The formula also enabled us to evaluate the accuracy of experimentally obtained averages of widths. We find two distinct features in the PSDs by the assembly method. One is the oscillatory structure that shows up in the case when the correlation length is larger than half the length of the segments. A trace of this structure was actually observed in the experimental PSDs of this study. The other is the spikes that are periodically observed as a function of wave number. The spikes originate from a nonstochastic width variation that exists in all the segments in common. Their intensity is proportional to the number of gathered segments in the assembled lines. Because the spikes are excluded from the analysis, the LWR parameters determined by the assembly method are not affected by the nonstochastic variation, unlike the conventional methods. By all these results, we confirm that the assembly method of this study extends the upper limit of analyzable correlation lengths by a factor of approximately 20 and enhances the accuracy as well. This feature also has a practical significance that the widely observed LWR with a correlation length of approximately 35 nm can be analyzed by the assembly method using a conventional critical-dimension scanning-electron-microscope, without resorting to a specially designed one. Accordingly, the method will be a key tool for investigating LER and LWR in developing and manufacturing LSIs. It will also help analyze other stochastic processes in many research and development settings.

Hydroelastic analysis of the floating plate optimized for maximum radiation damping

In previous work, the problem of optimizing the shape of a thin floating plate to maximize radiation damping was investigated. The plate was modelled with zero draft and floated on the surface of an irrotational, incompressible ocean of infinite extent. For simplicity, only rigid heave motions were considered and the damping coefficient at one wave number was maximized. In the present work, the hydroelastic properties of the optimized plate are determined and compared with those of circular and square plates. The added mass, damping, and diffraction force coefficients in each mode are determined as a function of wave number. The amplitude responses of the plate deflection and bending moments are also presented. The finite element method is used to determine the vibration mode shapes and the flow problem is analysed using the Chen and Mei variational principle wherein the potential field inside a hemisphere surrounding the plate is represented using a spherical harmonic expansion and matched on the hemisphere to an outer field described by distributing sources on the hemisphere.

A reassessment of spectralTeestimation in continental interiors: The case of North America

Conventional spectralTestudies use the real part of the admittance between gravity anomalies and topography or, alternatively, the square of the magnitude of the coherency (i.e., coherence). Here we show the utility of treating both the admittance and coherency as complex quantities. Inverting the real parts to estimateTe, we use the imaginary parts to tell if the inversion is biased by noise. One method inverts the square of the real coherency, with the internal‐to‐total load ratioFderived (as a function of wave number) directly from the gravity and topography. The other method inverts the real part of the admittance assuming thatFis wave number‐independent. We test the methods using synthetic elastic plate models loaded at the surface and Moho in such a way that the final relief is the actual North American topography. In some of the models we add gravity noise generated by a model having both surface and internal loads such that the final topography is zero and find that both methods are susceptible to noise. Application of the two methods to North America givesTemaps showing substantial agreement except in regions affected by noise, but these are not a dominant part of the total area. Given the suggested mechanisms by which noise might arise, it is not surprising that it is not a more widespread feature of the North American craton. Importantly, both methods show that large parts of the Canadian Shield are characterized byTe> 100 km.

Propagation of waves in an electro-microstretch generalized thermoelastic semi-space

The present investigation is concerned with wave propagation in an electro-microstretch generalized thermoelastic solid half space. Two different cases have been discussed: (i) reflection of plane wave at the free surface of an electro-microstretch generalized thermoelastic solid; and (ii) propagation of Rayleigh waves in an electro-microstretch generalized thermoelastic solid half space. In case (i), the amplitude ratios of the various reflected waves have been computed numerically and depicted graphically against angle of incidence. In case (ii), the frequency equation is derived and dispersion curves giving phase velocity and attenuation coefficient as a function of wave number, have been plotted graphically for a specific model. Some special cases of interest are also deduced, for both the cases.

MHD aspect of current sheet oscillations related to magnetic field gradients

Abstract. One-fluid ideal MHD model is applied for description of current sheet flapping disturbances appearing due to a gradient of the normal magnetic field component. The wave modes are studied which are associated to the flapping waves observed in the Earth's magnetotail current sheet. In a linear approximation, solutions are obtained for model profiles of the electric current and plasma densities across the current sheet, which are described by hyperbolic functions. The flapping eigenfrequency is found as a function of wave number. For the Earth's magnetotail conditions, the estimated wave group speed is of the order of a few tens kilometers per second. The current sheet can be stable or unstable in dependence on the direction of the gradient of the normal magnetic field component. The obtained dispersion function is used for calculation of the flapping wave disturbances, which are produced by the given initial Gaussian perturbation at the center of the current sheet and propagating towards the flanks. The propagating flapping pulse has a smooth leading front, and a small scale oscillating trailing front, because the short wave oscillations propagate much slower than the long wave ones.

Vibrational modes of nanolines**This paper is a contribution of the National Institute of Standards and Technology and isnot subject to copyright in the United States.

Brillouin-light-scattering spectra previously have been shown to provide information onacoustic modes of polymeric lines fabricated by nanoimprint lithography. Finite-elementmethods for modeling such modes are presented here. These methods provide atheoretical framework for determining elastic constants and dimensions of nanolinesfrom measured spectra in the low gigahertz range. To make the calculationsfeasible for future incorporation in inversion algorithms, two approximations ofthe boundary conditions are employed in the calculations: the rigidity of thenanoline/substrate interface and sinusoidal variation of displacements along thenanoline length. The accuracy of these approximations is evaluated as a functionof wavenumber and frequency. The great advantage of finite-element methodsover other methods previously employed for nanolines is the ability to model anycross-sectional geometry. Dispersion curves and displacement patterns are calculated formodes of polymethyl methacrylate nanolines with cross-sectional dimensions of65 nm × 140 nm and rectangular or semicircular tops. The vibrational displacements and dispersion curvesare qualitatively similar for the two geometries and include a series of flexural,Rayleigh-like, and Sezawa-like modes.

Transverse-velocity fluctuations in a liquid under steady shear

We present an analysis of the transverse-velocity fluctuations in an isothermal liquid layer with a uniform shear rate between two parallel horizontal boundaries as a function of the wave number and the Reynolds number. The results were obtained by solving a stochastic version of the Orr-Sommerfeld equation subject to no-slip boundary conditions in a second-order Galerkin approximation. We find that the spatial Fourier transform of the transverse-velocity fluctuations exhibits a maximum as a function of the (horizontal) wave number q(parallels). This maximum is associated with a crossover from a q(parallels)(-4) dependence for larger q(parallels) to a q(parallels)(2) dependence for small q(parallels). The q(parallels)(-4) dependence at larger wave numbers is independent of the boundary conditions, but the small- q(parallels) behavior is strongly affected by the boundary conditions. The nonequilibrium enhancement of the intensity of the transverse-velocity fluctuations remains finite for all values of the Reynolds number, but increases approximately with the square of the Reynolds number. The relation between our results and those obtained by previous authors in the absence of boundary conditions is elucidated.

Direct evidence of lipid translocation between adipocytes and prostate cancer cells with imaging FTIR microspectroscopy

Various epidemiological studies show a positive correlation between high intake of dietary FAs and metastatic prostate cancer (CaP). Moreover, CaP metastasizes to the bone marrow, which harbors a rich source of lipids stored within adipocytes. Here, we use Fourier transform infrared (FTIR) microspectroscopy to study adipocyte biochemistry and to demonstrate that PC-3 cells uptake isotopically labeled FA [deuterated palmitic acid (D(31)-PA)] from an adipocyte. Using this vibrational spectroscopic technique, we detected subcellular locations in a single adipocyte enriched with D(31)-PA using the upsilon(as+s)(C-D)(2+3) (D(31)-PA): upsilon(as+s)(C-H)(2+3) (lipid hydrocarbon) signal. In addition, larger adipocytes were found to consist of a higher percentage of D(31)-PA of the total lipid found within the adipocyte. Following background subtraction, the upsilon(as)(C-D)(2+3) signal illuminated starved PC-3 cells cocultured with D(31)-PA-loaded adipocytes, indicating translocation of the labeled FA. This study demonstrates lipid-specific translocation between adipocytes and tumor cells and the use of FTIR microspectroscopy to characterize various biomolecular features of a single adipocyte without the requirement for cell isolation and lipid extraction.

Abnormal long wave dispersion phenomena in a slightly compressible elastic plate with non-classical boundary conditions

A two parameter asymptotic analysis is employed to investigate some unusual long wave dispersion phenomena in respect of symmetric motion in a nearly incompressible elastic plate. The plate is not subject to the usual classical traction free boundary conditions, but rather has its faces fixed, precluding any displacement on the boundary. The abnormal long wave behaviour results in the derivation of non-local approximations for symmetric motion, giving frequency as a function of wave number. Motivated by these approximations, the asymptotic forms of displacement components established and long wave asymptotic integration is carried out.

Towards implicit subgrid-scale modeling by particle methods

The numerical truncation error of vortex-in-cell methods is analyzed a-posteriori through the effective spectral numerical viscosity for simulations of three-dimensional isotropic turbulence. The interpolation kernels used for velocity-smoothing and re-meshing are identified as the most relevant components affecting the shape of the spectral numerical viscosity as a function of wave number. A linear combination of well-known standard kernels leads to new kernels assigned to the specific use for implicit large-eddy simulation of turbulent flows, i.e. their truncation errors acts as subgrid- scale model. Numerical results are provided to show the potential and drawbacks of the approach.

Energy Transfer in Spectra of the d-Dimensional Past Grid Turbulence

Free decay theory of the homogeneous and isotropic developed turbulence isconsidered in the d-dimensional case. The basic quantities under our consideration are the kinetic energy spectrum E(k,t) and energy transfer spectrum T(k,t) as functions of wave number k and decay time t. Starting point for studying E and T represents their adaptation from the stationary model which predicts the Kolmogorov spectrum which is multiplicatively dependent on an unknown scaling function F. In order to study the spectra of decaying turbulence both parameters l and eɛ are supposed to be dependent on t. Formerly derived basic integro–differential equation for F (by Adzhemyan, et al., 1998) has been here solved numerically in the dimension interval d∈(2, 3) for two cases of the Saffman invariant and the Loitsyansky integral fixing an arbitrary theor parameter α (α ⩵ 2 and 4, correspondingly). The energy transfer spectrum T(k) has been analyzed for several dimensions d≤3 showing the presence of integration regions in the wavenumber space where an inverse energy cascade can occur.

Two-dimensional measurement of birefringence dispersion using spectroscopic polarized light

This paper describes a method and system for the measuring the two-dimensional distribution of birefringence dispersion. An optical arrangement consists of a white light source, parallel polarizers, a CCD camera, and an acousto-optic tunable filter for selecting wavelength of the incident light. The intensity of spectroscopic polarized light changes sinusoidally as a function of wave number, and its period changes slightly because of birefringence dispersion. The fast Fourier transform method is used to analyze the birefringence dispersion from the spectroscopic polarized light. One hundred twenty-eight captured images are used for the analysis. Some experimental results on 2-D birefringence dispersion distributions are shown for the demonstration of this method.

Two-dimensional motion in a Bell-constrained plate

The so-called Bell constraint has been used for several years in plasticity theory and has additionally been the subject to several investigations within an elastic context. In this paper the effects of the Bell constraint on the propagation of harmonic waves in a finitely deformed elastic plate are considered. Strong ellipticity conditions are first derived for the unbounded case, and are shown to be dependent on the scalar multiplier associated with the Bell constraint. The dispersion relation, associated with harmonic wave propagation in a plate composed of such a material with zero incremental surface traction, is derived in respect of an arbitrary strain energy function. Asymptotic expansions are then obtained for high and low wave number. These expansions, which give phase speed as a function of wave number, harmonic number and pre-stress, are shown to give excellent agreement with numerical solutions.

Density profiles of temperature-sensitive microgel particles

We have performed small angle neutron scattering measurements (SANS) on dilute aqueous dispersions of polymer microgel particles as a function of temperature, T . The microgel particles are spherical crosslinked assemblies of a loose gel network of a poly-N-isopropylacrylamide (NIPAM) polymer. When the temperature is raised beyond a critical temperature, T(lc) approximately 32 degrees C , the polymer becomes more strongly attracted to itself than the solvent, and the microgel particles contract. The measured form factor, F (q) , for dilute suspensions of uniform microgel particles exhibits many peaks that are characteristic of solid polymer nanospheres. The position and amplitude of the peaks as a function of wave number, q , provide insight into the density profile of poly-NIPAM within the microgels. These peaks can be described well over a wide range of temperature by a model of the polymer density within the particles that is constant up to an inner radius, R1 , and decreases linearly to zero at an outer radius, R2 .

Impedance description of coherent synchrotron radiation with account of bunch deformation

We are concerned with coherent longitudinal motion in a storage ring, especially with situations in which coherent synchrotron radiation (CSR) can in∞uence stability of the beam. The collective force from CSR is usually described by an or a wake function in such a way that the force depends only on the charge distribution at the present time. This description is exact only for a rigid bunch, since causality demands that the force depend on the prior history of the bunch. We show how to treat a deforming bunch by applying the \complete impedance Z(n;!), a function of wave number and frequency. We derive this and study its analytic properties for a special model: radiation from circular orbits shielded by parallel plates representing the metallic vacuum chamber. We analyze the corresponding collective force, obtaining the usual formula as a flrst approximation, plus easily computed corrections that depend on present and prior values of the time derivative of the charge density. In related papers we have applied these results in numerical simulations of instabilities induced by CSR. PACS numbers: Valid PACS appear here