The exact equation for Brillouin shifts

1965 ◽  
Vol 26 (11) ◽  
pp. 655-658 ◽  
Author(s):  
V. Chandrasekharan
Keyword(s):  
Exact Equation

scholarly journals Single-particle motion under the influence of the perpendicular ponderomotive force

1987 ◽  
Vol 37 (3) ◽  
pp. 497-506
Author(s):  
M. C. Festeau-Barrioz ◽  
M. L. Sawley ◽  
J. Václavík
Keyword(s):  
Electromagnetic Field ◽  
Single Particle ◽  
Particle Motion ◽  
Ponderomotive Force ◽  
Equation Of Motion ◽  
Exact Equation ◽  
Particle Theory ◽  
Magnetostatic Field ◽  
Single Particle Motion

The motion of a single particle under the influence of the ponderomotive force directed perpendicular to the external magnetostatic field is analysed. By solving the exact equation of motion for a specific applied electromagnetic field, the resultant ponderomotive drift is compared with the prediction of a single-particle theory using the oscillation-centre approximation. The regime of validity of this theory is discussed. It is shown that, for certain values of the amplitude and frequency of the electromagnetic field, the particle motion is unstable and therefore the concept of a single-particle ponderomotive force is meaningless.

A High Resolution Simulation of a Single Shock-Accelerated Particle

2021 ◽  
Author(s):  
W. Curtis Maxon ◽  
Tanner Nielsen ◽  
Nicholas Denissen ◽  
Johnathan D. Regele ◽  
Jacob McFarland
Keyword(s):  
Flow Field ◽  
Cost Effective ◽  
Pressure Effects ◽  
Heat Diffusion ◽  
Spherical Particles ◽  
Navier Stokes ◽  
Exact Equation ◽  
Arbitrary Lagrangian Eulerian ◽  
Particle Laden Flows ◽  
Drag Models

Abstract Particle drag models, which capture macro viscous and pressure effects, have been developed over the years for various flow regimes to enable cost effective simulations of particle-laden flows. The relatively recent derivation by Maxey and Riley has provided an exact equation of motion for spherical particles in a flow field based on the continuum assumption. Many models that have been simplified from these equations have provided reasonable approximations; however, the sensitivity of particle-laden flows to particle drag requires a very accurate model to simulate. To develop such a model, a 2D axisymmetric Navier-Stokes direct numerical simulation of a single particle in a transient, shock-driven flow field was conducted using the hydrocode FLAG. FLAG's capability to run arbitrary Lagrangian-Eulerian hydrodynamics coupled with solid mechanic models makes it an ideal code to capture the physics of the flow field around and in the particle as it is shock-accelerated -- a challenging regime to study. The goal of this work is twofold: to provide a validation for FLAG's Navier-Stokes and heat diffusion solutions, and to provide a rationale for recent experimental particle drag measurements.

NONLINEAR DIFFUSION EQUATION WITH A PERTURBED CONVECTIONTERM: POTENTIAL SYMMETRIES WITH RESPECT TO THE SECOND CONSERVATION LAW

2021 ◽  
Vol 10 (5) ◽  
pp. 2611-2624
Author(s):  
O.K. Narain ◽  
F.M. Mahomed
Keyword(s):  
Diffusion Equation ◽  
Conservation Law ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
The Other ◽  
Linear Case ◽  
Exact Equation ◽  
Convection Term ◽  
Potential Symmetries ◽  
Perturbed Equation

We consider the nonlinear diffusion equation with a perturbed convection term. The potential symmetries for the exact equation with respect to the second conservation law are classified. It is found that these exist only in the linear case. It is further shown that no nontrivial approximate potential symmetries of order one exists for the perturbed equation with respect to the other conservation law.

scholarly journals Neural network emulation of a rainfall-runoff model

2007 ◽  
Vol 4 (1) ◽  
pp. 287-326 ◽  
Author(s):  
R. J. Abrahart ◽  
L. M. See
Keyword(s):  
Neural Network ◽  
Transfer Functions ◽  
Network Models ◽  
Exact Equation ◽  
Rainfall Runoff ◽  
Neural Network Models ◽  
Linear Relationships ◽  
Non Linear ◽  
Rainfall Runoff Model ◽  
Runoff Model

Abstract. The potential of an artificial neural network to perform simple non-linear hydrological transformations is examined. Four neural network models were developed to emulate different facets of a recognised non-linear hydrological transformation equation that possessed a small number of variables and contained no temporal component. The modeling process was based on a set of uniform random distributions. The cloning operation facilitated a direct comparison with the exact equation-based relationship. It also provided broader information about the power of a neural network to emulate existing equations and model non-linear relationships. Several comparisons with least squares multiple linear regression were performed. The first experiment involved a direct emulation of the Xinanjiang Rainfall-Runoff Model. The next two experiments were designed to assess the competencies of two neural solutions that were developed on a reduced number of inputs. This involved the omission and conflation of previous inputs. The final experiment used derived variables to model intrinsic but otherwise concealed internal relationships that are of hydrological interest. Two recent studies have suggested that neural solutions offer no worthwhile improvements in comparison to traditional weighted linear transfer functions for capturing the non-linear nature of hydrological relationships. Yet such fundamental properties are intrinsic aspects of catchment processes that cannot be excluded or ignored. The results from the four experiments that are reported in this paper are used to challenge the interpretations from these two earlier studies and thus further the debate with regards to the appropriateness of neural networks for hydrological modelling.

scholarly journals Incidence of Severe Acute Respiratory Syndrome Coronavirus-2 infection among previously infected or vaccinated employees

2021 ◽  
Author(s):  
Noah Kojima ◽  
Arash Roshani ◽  
Matthew Brobeck ◽  
Arthur Baca ◽  
Jeffrey D Klausner
Keyword(s):  
Severe Acute Respiratory Syndrome ◽  
Clinical Laboratory ◽  
Exact Equation ◽  
Previous Infection ◽  
Group 3 ◽  
Group 2 ◽  
Measure Of Association ◽  
Observation Period ◽  
Group 1

Introduction: The protective effect of previous infection versus vaccination is poorly studied. Among a clinical laboratory that has been conducting routine workforce screening since the beginning of the pandemic, we aimed to assess the relative risk of Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) infection among individuals who were SARS-CoV-2 naive, previously infected, or vaccinated. Methods: Using an electronic laboratory information system, employees were divided into three groups: (1) SARS-CoV-2 naive and unvaccinated, (2) previous SARS-CoV-2 infection, and (3) vaccinated. Person-days were measured from the date of the employee first test and truncated at the end of the observation period. SARS-CoV-2 infection was defined as two positive SARS-CoV-2 PCR tests in a 30-day period. Individuals with fewer than 14 days of follow up were excluded. Incidence estimates and the 95% confidence intervals were calculated using the Poisson Exact equation. The incidence rate ratio (IRR) was used as a measure of association between groups. Analyses were performed on StataSE (StataCorp, College Station, TX). Results: We identified 4313, 254 and 739 employee records for groups 1, 2, and 3, respectively. The median age of employees was 29.0 years (interquartile range: 23.6, 39.9). During the observation period, 254, 0, and 4 infections were identified among groups 1, 2, and 3, respectively. Group 1 had an incidence of 25.9 per 100 person-years (95% CI: 22.8-29.3). Group 2 had an incidence of 0 per 100 person-years (95% CI: 0-5.0). Group 3 had an incidence of 1.6 per 100 person-years (95% CI: 0.04-4.2). The IRR of reinfection among those with previous infection compared to SARS-CoV-2 naive was 0 (95% CI: 0-0.19). The IRR of those vaccinated compared to SARS-CoV-2 naive was 0.06 (95% CI: 0.02-0.16). The IRR of those vaccinated compared to prior SARS-CoV-2 was 0 (95% CI: 0-4.98). Conclusion: Previous SARS-CoV-2 infection and vaccination for SARS-CoV-2 were associated with decreased risk for infection or re-infection with SARS-CoV-2 in a routinely screened workforce. The was no difference in the infection incidence between vaccinated individuals and individuals with previous infection. Further research is needed to determine whether our results are consistent with the emergence of new SARS-CoV-2 variants.

scholarly journals A New Analytical Expression for the T.C.R. of Thin Monocrystalline Metal Films

1979 ◽  
Vol 5 (4) ◽  
pp. 209-213 ◽  
Author(s):  
C. R. Tellier
Keyword(s):  
Electrical Conductivity ◽  
Relaxation Time ◽  
Reflection Coefficient ◽  
Grain Boundary ◽  
Metal Film ◽  
Approximate Equation ◽  
Metal Films ◽  
Exact Equation ◽  
Temperature Coefficient Of Resistivity ◽  
Comparison Of The Results

The analysis of electrical conductivity of continuous thin monocrystalline metal film has been treated by assuming that the scattering from other sources than grain-boundaries can be described by an effective relaxation time. This relaxation time method is applied to the temperature coefficient of resistivity and leads to an analytical approximate equation in terms of the grain-boundary reflection coefficientrand the reduced thicknessk.Comparison of the results with those deduced from the exact equation (derived from the Mayadas and Shatzkes theory) shows that they deviate by less than 5% in largek–,p–, andr– ranges.

scholarly journals Possible configurations of the magnetic field in the outer magnetosphere during geomagnetic polarity reversals

2000 ◽  
Vol 18 (1) ◽  
pp. 11-27 ◽  
Author(s):  
D. M. Willis ◽  
A. C. Holder ◽  
C. J. Davis
Keyword(s):  
Magnetic Field ◽  
Spherical Cavity ◽  
Exact Equation ◽  
Outer Magnetosphere ◽  
Special Cases ◽  
Magnetospheric Configuration And Dynamics ◽  
Polarity Reversals ◽  
Field Lines ◽  
Geomagnetic Polarity ◽  
The Magnetic Field

Abstract. Possible configurations of the magnetic field in the outer magnetosphere during geomagnetic polarity reversals are investigated by considering the idealized problem of a magnetic multipole of order m and degree n located at the centre of a spherical cavity surrounded by a boundless perfect diamagnetic medium. In this illustrative idealization, the fixed spherical (magnetopause) boundary layer behaves as a perfectly conducting surface that shields the external diamagnetic medium from the compressed multipole magnetic field, which is therefore confined within the spherical cavity. For a general magnetic multipole of degree n, the non-radial components of magnetic induction just inside the magnetopause are increased by the factor {1 + [(n + 1)/n]} relative to their corresponding values in the absence of the perfectly conducting spherical magnetopause. An exact equation is derived for the magnetic field lines of an individual zonal (m = 0), or axisymmetric, magnetic multipole of arbitrary degree n located at the centre of the magnetospheric cavity. For such a zonal magnetic multipole, there are always two neutral points and n-1 neutral rings on the spherical magnetopause surface. The two neutral points are located at the poles of the spherical magnetopause. If n is even, one of the neutral rings is coincident with the equator; otherwise, the neutral rings are located symmetrically with respect to the equator. The actual existence of idealized higher-degree (n>1) axisymmetric magnetospheres would necessarily imply multiple (n + 1) magnetospheric cusps and multiple (n) ring currents. Exact equations are also derived for the magnetic field lines of an individual non-axisymmetric magnetic multipole, confined by a perfectly conducting spherical magnetopause, in two special cases; namely, a symmetric sectorial multipole (m = n) and an antisymmetric sectorial multipole (m = n-1). For both these non-axisymmetric magnetic multipoles, there exists on the spherical magnetopause surface a set of neutral points linked by a network of magnetic field lines. Novel magnetospheric processes are likely to arise from the existence of magnetic neutral lines that extend from the magnetopause to the surface of the Earth. Finally, magnetic field lines that are confined to, or perpendicular to, either special meridional planes or the equatorial plane, when the multipole is in free space, continue to be confined to, or perpendicular to, these same planes when the perfectly conducting magnetopause is present.Key words. Geomagnetism and paleomagnetism (reversals-process, time scale, magnetostratigraphy) · Magnetospheric physics (magnetopause, cusp, and boundary layers; magnetospheric configuration and dynamics)

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