scholarly journals On physical scattering density fluctuations of amorphous samples

2018 ◽  
Vol 51 (5) ◽  
pp. 1404-1420
Author(s):  
Salvino Ciccariello ◽  
Piero Riello ◽  
Alvise Benedetti
Keyword(s):  
Bounded Function ◽  
Fourier Integral ◽  
Acta Math ◽  
Density Fluctuations ◽  
Invariant Relation ◽  
Rigorous Results ◽  
One Dimensional ◽  
Almost Everywhere ◽  
Angle Scattering ◽  
The Fourier Transform

Using the rigorous results obtained by Wiener [Acta Math. (1930), 30, 118–242] on the Fourier integral of a bounded function and the condition that small-angle scattering intensities of amorphous samples are almost everywhere continuous, the conditions that must be obeyed by a function η(r) for this to be considered a physical scattering density fluctuation are obtained. These conditions can be recast in the following form: the V → ∞ limit of the modulus of the Fourier transform of η(r), evaluated over a cubic box of volume V and divided by V 1/2, exists and its square obeys the Porod invariant relation. Some examples of one-dimensional scattering density functions obeying the aforesaid condition are numerically illustrated.

Small Angle Electron Scattering From Vacuum Condensed Metallic Films

1968 ◽  
Vol 26 ◽  
pp. 380-381
Author(s):  
J. Silcox ◽  
R. H. Wade
Keyword(s):  
Electron Scattering ◽  
Small Angle ◽  
Ring Structure ◽  
Two Dimensional ◽  
Metallic Films ◽  
Micro Structure ◽  
Angle Scattering ◽  
The Fourier Transform ◽  
Source Of Information ◽  
Kinematical Theory

Recent work has drawn attention to the possibilities that small angle electron scattering offers as a source of information about the micro-structure of vacuum condensed films. In particular, this serves as a good detector of discontinuities within the films. A review of a kinematical theory describing the small angle scattering from a thin film composed of discrete particles packed close together will be presented. Such a model could be represented by a set of cylinders packed side by side in a two dimensional fluid-like array, the axis of the cylinders being normal to the film and the length of the cylinders becoming the thickness of the film. The Fourier transform of such an array can be regarded as a ring structure around the central beam in the plane of the film with the usual thickness transform in a direction normal to the film. The intensity profile across the ring structure is related to the radial distribution function of the spacing between cylinders.

scholarly journals Analytical solution of one-dimensional Pennes’ bioheat equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1084-1092
Author(s):  
Hongyun Wang ◽  
Wesley A. Burgei ◽  
Hong Zhou
Keyword(s):  
Analytical Solution ◽  
Radiofrequency Energy ◽  
Bioheat Equation ◽  
Surface Cooling ◽  
One Dimensional ◽  
The Fourier Transform ◽  
The One ◽  
Parameter Values ◽  
Mathematical Derivation ◽  
Effect Of Surface

Abstract Pennes’ bioheat equation is the most widely used thermal model for studying heat transfer in biological systems exposed to radiofrequency energy. In their article, “Effect of Surface Cooling and Blood Flow on the Microwave Heating of Tissue,” Foster et al. published an analytical solution to the one-dimensional (1-D) problem, obtained using the Fourier transform. However, their article did not offer any details of the derivation. In this work, we revisit the 1-D problem and provide a comprehensive mathematical derivation of an analytical solution. Our result corrects an error in Foster’s solution which might be a typo in their article. Unlike Foster et al., we integrate the partial differential equation directly. The expression of solution has several apparent singularities for certain parameter values where the physical problem is not expected to be singular. We show that all these singularities are removable, and we derive alternative non-singular formulas. Finally, we extend our analysis to write out an analytical solution of the 1-D bioheat equation for the case of multiple electromagnetic heating pulses.

Large-density fluctuations for the one-dimensional supercritical contact process

1989 ◽  
Vol 55 (3-4) ◽  
pp. 639-648 ◽  
Author(s):  
Antonio Galves ◽  
Fabio Martinelli ◽  
Enzo Olivieri
Keyword(s):  
Contact Process ◽  
Density Fluctuations ◽  
One Dimensional ◽  
Large Density ◽  
The One

Comparison of iterative desmearing procedures for one-dimensional small-angle scattering data

2011 ◽  
Vol 44 (1) ◽  
pp. 32-42 ◽  
Author(s):  
Thomas Vad ◽  
Wiebke F. C. Sager
Keyword(s):  
Small Angle ◽  
Incident Beam ◽  
Scattering Data ◽  
Data Sets ◽  
Convergence Criteria ◽  
Small Momentum Transfer ◽  
One Dimensional ◽  
Noise Filter ◽  
Large Numbers ◽  
Angle Scattering

Two simple iterative desmearing procedures – the Lake algorithm and the Van Cittert method – have been investigated by introducing different convergence criteria using both synthetic and experimental small-angle neutron scattering data. Implementing appropriate convergence criteria resulted in stable and reliable solutions in correcting resolution errors originating from instrumental smearing,i.e.finite collimation and polychromaticity of the incident beam. Deviations at small momentum transfer for concentrated ensembles of spheres encountered in earlier studies are not observed. Amplification of statistical errors can be reduced by applying a noise filter after desmearing. In most cases investigated, the modified Lake algorithm yields better results with a significantly smaller number of iterations and is, therefore, suitable for automated desmearing of large numbers of data sets.

scholarly journals The canSAS standard for storing reduced one-dimensional small-angle scattering data in XML files

2008 ◽  
Vol 64 (a1) ◽  
pp. C554-C554
Author(s):  
P.R. Jemian ◽  
A.J. Jackson ◽  
S.M. King ◽  
K.C. Littrell ◽  
A.R.J. Nelson ◽  
...  
Keyword(s):  
Small Angle ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
One Dimensional ◽  
Angle Scattering

scholarly journals Probing non-thermal density fluctuations in the one-dimensional Bose gas

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Jacopo De Nardis ◽  
Milosz Panfil ◽  
Andrea Gambassi ◽  
Leticia Cugliandolo ◽  
Robert Konik ◽  
...  
Keyword(s):  
Spatial Dimension ◽  
Bose Gas ◽  
Density Fluctuations ◽  
Dynamical Structure ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Fluctuation Dissipation ◽  
Quantum Integrable Models ◽  
The One

Quantum integrable models display a rich variety of non-thermal excited states with unusual properties. The most common way to probe them is by performing a quantum quench, i.e., by letting a many-body initial state unitarily evolve with an integrable Hamiltonian. At late times these systems are locally described by a generalized Gibbs ensemble with as many effective temperatures as their local conserved quantities. The experimental measurement of this macroscopic number of temperatures remains elusive. Here we show that they can be obtained for the Bose gas in one spatial dimension by probing the dynamical structure factor of the system after the quench and by employing a generalized fluctuation-dissipation theorem that we provide. Our procedure allows us to completely reconstruct the stationary state of a quantum integrable system from state-of-the-art experimental observations.

THE HALDANE GAP IN ANTIFERROMAGNETIC HEISENBERG CHAINS

1994 ◽  
Vol 06 (05a) ◽  
pp. 887-899 ◽  
Author(s):  
IAN AFFLECK
Keyword(s):  
Bose Condensation ◽  
Local Order ◽  
Rigorous Results ◽  
One Dimensional ◽  
Haldane Gap ◽  
Local Order Parameter ◽  
Recent Developments ◽  
Heisenberg Chains ◽  
Non Local ◽  
And Behavior

Integer-spin Heisenberg antiferromagnetic chains are expected to have a singlet groundstate and a gap to the first excited state, as first argued by Haldane. We review rigorous results on this conjecture and discuss experimental realizations. Theoretical and experimental aspects of three recent developments in this field are then reviewed: chainend excitations and the non-local order parameter, a field theory mapping and behavior near zero wave-vector, high-field behavior and one-dimensional Bose condensation.

Maximum-entropy method as a routine tool for determination of particle size distributions by small-angle scattering

2004 ◽  
Vol 37 (1) ◽  
pp. 32-39 ◽  
Author(s):  
Dragomir Tatchev ◽  
Rainer Kranold
Keyword(s):  
Particle Size ◽  
Fourier Transform ◽  
Small Angle ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Angle Scattering ◽  
The Fourier Transform

Several aspects of the application of the maximum-entropy method (MEM) to the determination of particle size distributions by small-angle scattering (SAS) are discussed. The `historic' version of the MEM produces completely satisfying results. Limiting the data error from below (i.e.imposing a minimal relative error) is proposed as a solution of some convergence problems. The MEM is tested against the Fourier transform technique. The size distribution of Pb particles in an Al–Pb alloy is determined by the MEM and the Fourier transform technique. The size distributions obtained by transmission electron microscopy (TEM) and SAXS show partial agreement.

Field of a Uniformly Moving Charge in an Anisotropic Dispersive Medium

1973 ◽  
Vol 28 (6) ◽  
pp. 907-910
Author(s):  
S. Datta Majumdar ◽  
G. P. Sastry
Keyword(s):  
Electromagnetic Field ◽  
Fourier Transform ◽  
Point Charge ◽  
Rest Frame ◽  
Dispersive Medium ◽  
Scalar Potential ◽  
Fourier Integral ◽  
The Third ◽  
Dispersion Formula ◽  
The Fourier Transform

The electromagnetic field of a point charge moving uniformly in a uniaxial dispersive medium is studied in the rest frame of the charge. It is shown that the Fourier integral for the scalar potential breaks up into three integrals, two of which are formally identical to the isotropic integral and yield the ordinary and extraordinary cones. Using the convolution theorem of the Fourier transform, the third integral is reduced to an integral over the isotropic field. Dispersion is explicitly introduced into the problem and the isotropic field is evaluated on the basis of a simplified dispersion formula. The effect of dispersion on the field cone is studied as a function of the cut-off frequency.

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