For over 25 years the MaxEnt workshops have explored the use of Bayesian probability theory, entr... more For over 25 years the MaxEnt workshops have explored the use of Bayesian probability theory, entropy and information theory in scientific and engineering applications. This volume considers Methods, Applications, and Foundations. Application areas include, but are not limited to: astronomy, physics, chemistry, biology, Earth science and engineering.
... Ariel Caticha National Institute ofStandards and Technology, Gaithersburg, Maryland 20899 and... more ... Ariel Caticha National Institute ofStandards and Technology, Gaithersburg, Maryland 20899 and Institute for Physical Science and Technology, University ofMaryland, College Park, Maryland 20742 Nestor Caticha Instituto de Fssica, UniUersidade deSdo Paulo, Caixa Postal ...
The only known efficient way to reflect x‐rays at large angles is through their diffraction by pe... more The only known efficient way to reflect x‐rays at large angles is through their diffraction by perfect crystals. The conventional theory which describes these phenomena makes use of approximations which fail when θB≂ρ/2. We analyze the origin of this failure, obtain the appropriate approximations and calculate the reflectivity of a semi‐infinite crystal. Linewidths about three orders of magnitude larger than those obtained under normal conditions are found. The effects of absorption and of the orientation of the crystal surface are studied. A careful choice of experimental conditions allows one to stretch the region of anomalously low absorption (Borrmann effect) to a range of several minutes. The high sensitivity of the diffraction profiles to minute changes of lattice parameter may be of use in high precision measurements. This treatment provides the theoretical basis for the design of resonant cavities and other such interferometric devices.
A new thermal neutron Fabry-Perot interferometer (FPI) similar to that proposed for hard X-rays b... more A new thermal neutron Fabry-Perot interferometer (FPI) similar to that proposed for hard X-rays by the same authors is proposed. Both devices consist of two thin parallel crystals separated by a nondiffracting gap. Bragg angles in both cases are very close to π/2. While for X-rays the thickness of the plates is of the order of a few μm, for neutrons it is one to two orders of magnitude larger. Then, the actual construction of the new interferometer should not impose the difficulties found for X-rays. The transmission profile shows the usual FPI transmission resonances. By changing the thickness of the mirrors and the dimensions of the gap, the energy width of these resonances can be controlled from being rather broad, of the order of the Darwin width, ΔE/E ≈ 10−6, to the extremely narrow theoretical limit of ΔE/E ≈ 10−9. The values may be changed within these limits, either by the choice of the crystal or of the reflection involved and by changing the dimensions of the gap and plate thicknesses. The examples calculated here concentrate on silicon crystal slabs which are cheap and relatively easy to cut down to the required thickness. While the numerical results given are valid only for this material, the analysis made points out to various features of more general validity. In order to design an experiment the diffraction profiles are studied (a) for constant plate thickness and varying gap and (b) for constant gap and varying plate thickness. The results are presented in the text. It is shown that within limits, the effect of roughness of the crystal surfaces does not significantly alter the interferometer performance.
The classical Density Functional Theory (DFT) is introduced as an application of entropic inferen... more The classical Density Functional Theory (DFT) is introduced as an application of entropic inference for inhomogeneous fluids in thermal equilibrium. It is shown that entropic inference reproduces the variational principle of DFT when information about the expected density of particles is imposed. This process introduces a family of trial density-parametrized probability distributions and, consequently, a trial entropy from which the preferred one is found using the method of Maximum Entropy (MaxEnt). As an application, the DFT model for slowly varying density is provided, and its approximation scheme is discussed.
For over 25 years the MaxEnt workshops have explored the use of Bayesian probability theory, entr... more For over 25 years the MaxEnt workshops have explored the use of Bayesian probability theory, entropy and information theory in scientific and engineering applications. This volume considers Methods, Applications, and Foundations. Application areas include, but are not limited to: astronomy, physics, chemistry, biology, Earth science and engineering.
... Ariel Caticha National Institute ofStandards and Technology, Gaithersburg, Maryland 20899 and... more ... Ariel Caticha National Institute ofStandards and Technology, Gaithersburg, Maryland 20899 and Institute for Physical Science and Technology, University ofMaryland, College Park, Maryland 20742 Nestor Caticha Instituto de Fssica, UniUersidade deSdo Paulo, Caixa Postal ...
The only known efficient way to reflect x‐rays at large angles is through their diffraction by pe... more The only known efficient way to reflect x‐rays at large angles is through their diffraction by perfect crystals. The conventional theory which describes these phenomena makes use of approximations which fail when θB≂ρ/2. We analyze the origin of this failure, obtain the appropriate approximations and calculate the reflectivity of a semi‐infinite crystal. Linewidths about three orders of magnitude larger than those obtained under normal conditions are found. The effects of absorption and of the orientation of the crystal surface are studied. A careful choice of experimental conditions allows one to stretch the region of anomalously low absorption (Borrmann effect) to a range of several minutes. The high sensitivity of the diffraction profiles to minute changes of lattice parameter may be of use in high precision measurements. This treatment provides the theoretical basis for the design of resonant cavities and other such interferometric devices.
A new thermal neutron Fabry-Perot interferometer (FPI) similar to that proposed for hard X-rays b... more A new thermal neutron Fabry-Perot interferometer (FPI) similar to that proposed for hard X-rays by the same authors is proposed. Both devices consist of two thin parallel crystals separated by a nondiffracting gap. Bragg angles in both cases are very close to π/2. While for X-rays the thickness of the plates is of the order of a few μm, for neutrons it is one to two orders of magnitude larger. Then, the actual construction of the new interferometer should not impose the difficulties found for X-rays. The transmission profile shows the usual FPI transmission resonances. By changing the thickness of the mirrors and the dimensions of the gap, the energy width of these resonances can be controlled from being rather broad, of the order of the Darwin width, ΔE/E ≈ 10−6, to the extremely narrow theoretical limit of ΔE/E ≈ 10−9. The values may be changed within these limits, either by the choice of the crystal or of the reflection involved and by changing the dimensions of the gap and plate thicknesses. The examples calculated here concentrate on silicon crystal slabs which are cheap and relatively easy to cut down to the required thickness. While the numerical results given are valid only for this material, the analysis made points out to various features of more general validity. In order to design an experiment the diffraction profiles are studied (a) for constant plate thickness and varying gap and (b) for constant gap and varying plate thickness. The results are presented in the text. It is shown that within limits, the effect of roughness of the crystal surfaces does not significantly alter the interferometer performance.
The classical Density Functional Theory (DFT) is introduced as an application of entropic inferen... more The classical Density Functional Theory (DFT) is introduced as an application of entropic inference for inhomogeneous fluids in thermal equilibrium. It is shown that entropic inference reproduces the variational principle of DFT when information about the expected density of particles is imposed. This process introduces a family of trial density-parametrized probability distributions and, consequently, a trial entropy from which the preferred one is found using the method of Maximum Entropy (MaxEnt). As an application, the DFT model for slowly varying density is provided, and its approximation scheme is discussed.
Uploads