Very Simple Markov-Perfect Industry Dynamics: Theory: Very Simple Markov-Perfect Industry Dynamics: Theory
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Abbring, Jaap H.↗
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Use of dynamic theory to describe experimental results from volume holography
The general applicability of dynamic theory to the description of the recording and readout characteristics of volume (thick) hologram gratings is indicated. In dynamic theory (as opposed to static theory), the volume nature of the thick holographic grating allows the interference of an incident light beam with its own diffracted beam inside the recording medium. This effect causes the continuous recording of another grating that alters the initial one, producing a resultant grating that is not uniform through the thickness of the recording material and a grating whose writing and reading characteristics may vary dramatically, depending on the recording material and the experimental conditions. A large number of diverse types of writing, reading, and angular-selectivity behavior have been reported. The dynamic theory of thick-hologram writing and reading is shown to predict qualitatively all of these various types of experimental behavior.
Magnusson, R.↗
A dynamical theory of elastic directed curves.
Elastic directed curves dynamic theory, considering Hamilton principle, mass conservation and behavior of action density function under rigid body variations
Desilva, C. N.↗
Nonlinear dynamic theory for photorefractive phase hologram formation
A nonlinear dynamic theory is developed for the formation of photorefractive volume phase holograms. A feedback mechanism existing between the photogenerated field and free-electron density, treated explicitly, yields the growth and saturation of the space-charge field in a time scale characterized by the coupling strength between them. The expression for the field reduces in the short-time limit to previous theories and approaches in the long-time limit the internal or photovoltaic field. Additionally, the phase of the space charge field is shown to be time-dependent.
Kim, D. M.↗
Solar wind flow about the terrestrial planets. II - Comparison with gas dynamic theory and implications for solar-planetary interactions
Bow shock models are employed to determine and compare the solar wind flows about Venus, Mars, and the earth. Initially, gas dynamic theory predictions are compared with the large data base available for the near-earth environment. The observed shape and location of the magnetopause proved sufficient for predicting the average dayside bow shock position to within 2% error. Use of the same gas dynamics theory produced highly disparate results for the flows past Venus and Mars. A variation of 510-1000 km altitude (high) for the solar wind-obstacle interface was found for Mars, thus requiring the presence of an effective magnetic moment of within 0.6 of 1.4 x 10 to the 22nd G/cu cm in the Martian magnetosphere, consistent with Viking data. The Venus bow wave was calculated to be closer to the planet than possible with a purely ionospheric interaction, indicating that solar wind-neutral atmosphere interactions in the lower ionosheath must necessarily be included in a gas dynamic modeling of the Venus obstacle to the solar wind.
Slavin, J. A.↗
Computation of magnetic suspension of maglev systems using dynamic circuit theory
Dynamic circuit theory is applied to several magnetic suspensions associated with maglev systems. These suspension systems are the loop-shaped coil guideway, the figure-eight-shaped null-flux coil guideway, and the continuous sheet guideway. Mathematical models, which can be used for the development of computer codes, are provided for each of these suspension systems. The differences and similarities of the models in using dynamic circuit theory are discussed in the paper. The paper emphasizes the transient and dynamic analysis and computer simulation of maglev systems. In general, the method discussed here can be applied to many electrodynamic suspension system design concepts. It is also suited for the computation of the performance of maglev propulsion systems. Numerical examples are presented in the paper.
He, J. L.↗
Dynamical Theory of X-Ray Diffraction for Restricted Beams: I. Coherent Scattering by a Porous Crystal
A dynamical theory of X-ray coherent scattering of spatially restricted beams in porous crystals has been developed. The solutions have been obtained for the amplitude transmission and reflection coefficients as functions of the beam size and structural characteristics of the crystal. The peculiarities of the formation of reciprocal space maps as well as vertical and transverse cross sections of coherent scattering by porous films, gradient structures, and superlattices have been demonstrated.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Dynamical Theory of X-Ray Diffraction for Restricted Beams: III. Analysis of Experimental Data for a Porous Crystal
Using the dynamical theory of X-ray diffraction for restricted beams, we have performed quantitative analysis of the structure of an InP(001) porous crystal layer on the basis of experimental data obtained by high-resolution X-ray diffractometry. The parameters of the porous crystal have been determined by simulating coherent and diffuse scattering. The influence of the instrumental function and dynamical effects on the results of investigation has been demonstrated.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Dynamical theory of the solar wind.
Dynamical properties of solar wind and solar corona atmosphere with extended temperature bound strongly by gravity
CORONA↗
Excitons in Hematite Fe 2 O 3 : Short-Time Dynamics from TD-DFT and Non-Adiabatic Dynamics Theories
We present a first-principles study of the short-time dynamics of excitons in hematite Fe 2 O 3 . We used time-dependent density functional theory (TD-DFT) with an underlying DFT+U treatment of electron interactions to characterize the electronic structure of excitons and nonadiabatic molecular dynamics theory (NA-MD) to determine their recombination (electronic ground-state recovery) and relaxation dynamics. Decoherence-corrected trajectory surface hopping approaches in NA-MD simulations yielded recovery times of ~1.1 to 1.8 ns and “higher-lying” exciton relaxation times of ~60 to 70 fs, in accord with experimentally derived lifetimes. With hematite phonons in the range of ~100 to 700 cm –1 , higher-lying excitons relax within one or two oscillations of the phonons before getting trapped into an electron–hole pair Exc-3 structure on the first excited state potential energy surface. This structure resembles already a pair of polarons (electron polaron plus hole polaron) with associated lattice distortions three (3) basal planes away. On longer time scales, the electron–hole bipolaronic pair hops to structures Exc-5, then Exc-7, then Exc-9, ... with the electron polaron and hole polaron separated by 5, 7, 9, ... basal planes in a process of charge separation. The largest frequency phonon ~672 cm –1 for the Exc-3 exciton structure is associated with the electron polaron moiety of the exciton. This phonon is a good candidate for giving rise to the recently observed and reported postexcitation transient IR absorption peak.
36 MATERIALS SCIENCE↗
Dynamical Theory of X-Ray Diffraction in a Crystal with a Surface Grating of Another Material
A general theory is developed for dynamical X-ray diffraction in a crystal on the surface of which a lateral periodic structure of thin-film lines (strips) of another material is formed. On the basis of the model of edge forces, the fields of elastic lattice displacements in the substrate are calculated that arise as a result of formation of a lateral surface grating (SG). With the use of the formalism of diffraction of spatially restricted X-ray beams, solutions are obtained for the amplitudes of X-ray waves reflected from a crystal with an SG whose chemical composition differs from the composition of the substrate. A numerical simulation is carried out of X-ray diffraction in a silicon substrate with SGs of tungsten and SiO{sub 2} oxide. It is shown that the angular distributions of the scattering intensity by a silicon crystal with tungsten and oxide lines of identical size differ significantly, and the physical nature of such difference is established.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Chemical Reaction Rate Coefficients from Ring Polymer Molecular Dynamics: Theory and Practical Applications
This Feature Article presents an overview of the current status of ring polymer molecular dynamics (RPMD) rate theory. We first analyze the RPMD approach and its connection to quantum transition-state theory. We then focus on its practical applications to prototypical chemical reactions in the gas phase, which demonstrate how accurate and reliable RPMD is for calculating thermal chemical reaction rate coefficients in multifarious cases. This review serves as an important checkpoint in RPMD rate theory development, which shows that RPMD is shifting from being just one of recent novel ideas to a well-established and validated alternative to conventional techniques for calculating thermal chemical rate coefficients. We also hope it will motivate further applications of RPMD to various chemical reactions.
36 MATERIALS SCIENCE↗
Grating-based holographic diffraction methods for X-rays and neutrons: phase object approximation and dynamical theory
A method dubbed grating-based holography was recently used to determine the structure of colloidal fluids in the rectangular grooves of a diffraction grating from X-ray scattering measurements. Similar grating-based measurements have also been recently made with neutrons using a technique called spin-echo small-angle neutron scattering. The analysis of the X-ray diffraction data was done using an approximation that treats the X-ray phase change caused by the colloidal structure as a small perturbation to the overall phase pattern generated by the grating. In this paper, the adequacy of this weak phase approximation is explored for both X-ray and neutron grating holography. Additionally, it is found that there are several approximations hidden within the weak phase approximation that can lead to incorrect conclusions from experiments. In particular, the phase contrast for the empty grating is a critical parameter. Finally, while the approximation is found to be perfectly adequate for X-ray grating holography experiments performed to date, it cannot be applied to similar neutron experiments because the latter technique requires much deeper grating channels.
36 MATERIALS SCIENCE↗
Microscopic activated dynamics theory of the shear rheology and stress overshoot in ultradense glass-forming fluids and colloidal suspensions
We formulate a particle and force level, activated dynamics-based statistical mechanical theory for the continuous startup nonlinear shear rheology of ultradense glass-forming hard sphere fluids and colloidal suspensions in the context of the elastically collective nonlinear Langevin equation approach and a generalized Maxwell model constitutive equation. Activated structural relaxation is described as a coupled local-nonlocal event involving caging and longer range collective elasticity which controls the characteristic stress relaxation time. Theoretical predictions for the deformation-induced enhancement of mobility, the onset of relaxation acceleration at remarkably low values of stress, strain, or shear rate, apparent power law thinning of the steady-state structural relaxation time and viscosity, a nonvanishing activation barrier in the shear thinning regime, an apparent Herschel–Buckley form of the shear rate dependence of the steady-state shear stress, exponential growth of different measures of a yield or flow stress with packing fraction, and reduced fragility and dynamic heterogeneity under deformation were previously shown to be in good agreement with experiments. The central new question we address here is the defining feature of the transient response—the stress overshoot. In contrast to the steady-state flow regime, understanding the transient response requires an explicit treatment of the coupled nonequilibrium evolution of structure, elastic modulus, and stress relaxation time. We formulate a new quantitative model for this aspect in a physically motivated and computationally tractable manner. Theoretical predictions for the stress overshoot are shown to be in good agreement with experimental observations in the metastable ultradense regime of hard sphere colloidal suspensions as a function of shear rate and packing fraction, and accounting for deformation-assisted activated motion appears to be crucial for both the transient and steady-state responses.
Mechanics↗
Nonlinear mechanisms in physiology and pathophysiology Toward a dynamical theory of health and disease
The application of nonlinear analysis both to normal physiological dynamics and pathophysiological perturbations in a variety of different systems leads to observations not predicted by traditional models. Such analyses may have important implications for diagnostic and prognostic assessment as well as for therapeutics.
Goldberger, A. L.↗
Einstein-aether theory: dynamics of relativistic particles with spin or polarization in a Gödel-type universe
In the framework of the Einstein-aether theory we consider a cosmological model, which describes the evolution of the unit dynamic vector field with activated rotational degree of freedom. We discuss exact solutions of the Einstein-aether theory, for which the space-time is of the Gödel-type, the velocity four-vector of the aether motion is characterized by a non-vanishing vorticity, thus the rotational vectorial modes can be associated with the source of the universe rotation. The main goal of our paper is to study the motion of test relativistic particles with a vectorial internal degree of freedom (spin or polarization), which is coupled to the unit dynamic vector field. The particles are considered as the test ones in the given space-time background of the Gödel-type; the spin (polarization) coupling to the unit dynamic vector field is modeled using exact solutions of three types. The first exact solution describes the aether with arbitrary Jacobson's coupling constants; the second one relates to the case, when the Jacobson's constant responsible for the vorticity is vanishing; the third exact solution is obtained using three constraints for the coupling constants. The analysis of the exact expressions, which are obtained for the particle momentum and for the spin (polarization) four-vector components, shows that the interaction of the spin (polarization) with the unit vector field induces a rotation, which is additional to the geodesic precession of the spin (polarization) associated with the universe rotation as a whole.
79 ASTRONOMY AND ASTROPHYSICS↗