scholarly journals Two-Dimensional Probabilistic Infiltration Analysis in a Hillslope Using First-Order Moment Approach

Ground Water ◽  
2018 ◽  
Vol 57 (2) ◽  
pp. 226-237 ◽  
Author(s):  
Rui-Xuan Tang ◽  
Jing-Sen Cai ◽  
Tian-Chyi Jim Yeh
Keyword(s):  
Order Moment ◽  
Two Dimensional ◽  
First Order ◽  
Moment Approach

scholarly journals On the use of the first-order moment approach for measurements of Heff from LSD profiles

2020 ◽  
Vol 493 (1) ◽  
pp. 1130-1138
Author(s):  
J C Ramírez Vélez
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Measurements ◽  
Moment Equation ◽  
Order Moment ◽  
Depth Limit ◽  
First Order ◽  
Moment Approach ◽  
Stellar Magnetic Fields ◽  
The Magnetic Field

ABSTRACT The big majority of the reported measurements of the stellar magnetic fields that have analysed spectropolarimetric data have employed the least-squares deconvolution method (LSD) and the first-order moment approach. We present a series of numerical tests in which we review some important aspects of this technique. First, we show that the selection of the profile widths, i.e. integration range in the first-order moment equation, is independent of the accuracy of the magnetic measurements, meaning that for any arbitrary profile width it is always possible to properly determine the longitudinal magnetic field. We also study the interplay between the line depth limit adopted in the line mask and the normalization values of the LSD profiles. We finally show that the rotation of the stars has to be considered to correctly infer the intensity of the magnetic field, something that has been neglected up to now. We show that the latter consideration is crucial, and our test shows that the magnetic intensities differ by a factor close to 3 for a moderate fast rotator star with vsini of 50 ${\rm km\, s^{-1}}$. Therefore, it is expected that in general the stellar magnetic fields reported for fast rotators are stronger than what was believed. All the previous results shows that the first-order moment can be a very robust tool for measurements of magnetic fields, provided that the weak magnetic field approximation is secured. We also show that when the magnetic field regime breaks down, the use of the first-order moment method becomes uncertain.

scholarly journals Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clifford V. Johnson ◽  
Felipe Rosso
Keyword(s):  
Phase Structure ◽  
Scalar Potential ◽  
String Equation ◽  
Two Dimensional ◽  
Leading Order ◽  
Classical Analysis ◽  
First Order ◽  
First Order Phase Transition ◽  
Definition Of ◽  
First Order Phase

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1219-1229 ◽  
Author(s):  
D.-A. Becker ◽  
E. W. Richter
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
First Order ◽  
Partially Invariant Solutions ◽  
Quasilinear Systems ◽  
Ideal Mhd ◽  
Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

A Difference Method for Plane Problems in Magnetoelastodynamics

1972 ◽  
Vol 39 (3) ◽  
pp. 689-695 ◽  
Author(s):  
W. W. Recker
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Method ◽  
Difference Method ◽  
Necessary Condition ◽  
Two Dimensional ◽  
Symmetric Hyperbolic System ◽  
Von Neumann ◽  
First Order ◽  
Independent Variables

The two-dimensional equations of magnetoelastodynamics are considered as a symmetric hyperbolic system of linear first-order partial-differential equations in three independent variables. The characteristic properties of the system are determined and a numerical method for obtaining the solution to mixed initial and boundary-value problems in plane magnetoelastodynamics is presented. Results on the von Neumann necessary condition are presented. Application of the method to a problem which has a known solution provides further numerical evidence of the convergence and stability of the method.

TERBIUM MOLYBDATE: GROUP THEORY AND FLUCTUATIONS

1987 ◽  
Vol 01 (05n06) ◽  
pp. 239-244
Author(s):  
SERGE GALAM
Keyword(s):  
Fixed Point ◽  
Group Theory ◽  
Parameter Space ◽  
Landau Theory ◽  
Two Dimensional ◽  
Stable Fixed Point ◽  
Theory Analysis ◽  
Continuous Transition ◽  
Dimensional Parameter ◽  
First Order

A new mechanism to explain the first order ferroelastic—ferroelectric transition in Terbium Molybdate (TMO) is presented. From group theory analysis it is shown that in the two-dimensional parameter space ordering along either an axis or a diagonal is forbidden. These symmetry-imposed singularities are found to make the unique stable fixed point not accessible for TMO. A continuous transition even if allowed within Landau theory is thus impossible once fluctuations are included. The TMO transition is therefore always first order. This explanation is supported by experimental results.

Upstream motions in stratified flow

1988 ◽  
Vol 187 ◽  
pp. 487-506 ◽  
Author(s):  
I. P. Castro ◽  
W. H. Snyder
Keyword(s):  
Body Height ◽  
Three Dimensional ◽  
Time Dependent ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Towing Tank ◽  
First Order ◽  
Density Perturbations ◽  
Small Obstacle ◽  
Obstacle Height

In this paper experimental measurements of the time-dependent velocity and density perturbations upstream of obstacles towed through linearly stratified fluid are presented. Attention is concentrated on two-dimensional obstacles which generate turbulent separated wakes at Froude numbers, based on velocity and body height, of less than 0.5. The form of the upstream columnar modes is shown to be largely that of first-order unattenuating disturbances, which have little resemblance to the perturbations described by small-obstacle-height theories. For two-dimensional obstacles the disturbances are similar to those found by Wei, Kao & Pao (1975) and it is shown that provided a suitable obstacle drag coefficient is specified, the lowest-order modes (at least) are quantitatively consistent with the results of the Oseen inviscid model.Discussion of some results of similar measurements upstream of three-dimensional obstacles, the importance of towing tank endwalls and the relevance of the Foster & Saffman (1970) theory for the limit of zero Froude number is also included.

Steady detonation propagation in a circular arc: a Detonation Shock Dynamics model

2016 ◽  
Vol 807 ◽  
pp. 87-134 ◽  
Author(s):  
Mark Short ◽  
James J. Quirk ◽  
Chad D. Meyer ◽  
Carlos Chiquete
Keyword(s):  
Surface Wave ◽  
Angular Speed ◽  
Order Correction ◽  
Two Dimensional ◽  
Normal Surface ◽  
Circular Arc ◽  
First Order ◽  
Shock Dynamics ◽  
First Order Correction ◽  
Steady Detonation

We study the physics of steady detonation wave propagation in a two-dimensional circular arc via a Detonation Shock Dynamics (DSD) surface evolution model. The dependence of the surface angular speed and surface spatial structure on the inner arc radius ($R_{i}$), the arc thickness ($R_{e}-R_{i}$, where $R_{e}$ is the outer arc radius) and the degree of confinement on the inner and outer arc is examined. We first analyse the results for a linear $D_{n}$–$\unicode[STIX]{x1D705}$ model, in which the normal surface velocity $D_{n}=D_{CJ}(1-B\unicode[STIX]{x1D705})$, where $D_{CJ}$ is the planar Chapman–Jouguet velocity, $\unicode[STIX]{x1D705}$ is the total surface curvature and $B$ is a length scale representative of a reaction zone thickness. An asymptotic analysis assuming the ratio $B/R_{i}\ll 1$ is conducted for this model and reveals a complex surface structure as a function of the radial variation from the inner to the outer arc. For sufficiently thin arcs, where $(R_{e}-R_{i})/R_{i}=O(B/R_{i})$, the angular speed of the surface depends on the inner arc radius, the arc thickness and the inner and outer arc confinement. For thicker arcs, where $(R_{e}-R_{i})/R_{i}=O(1)$, the angular speed does not depend on the outer arc radius or the outer arc confinement to the order calculated. It is found that the leading-order angular speed depends only on $D_{CJ}$ and $R_{i}$, and corresponds to a Huygens limit (zero curvature) propagation model where $D_{n}=D_{CJ}$, assuming a constant angular speed and perfect confinement on the inner arc surface. Having the normal surface speed depend on curvature requires the insertion of a boundary layer structure near the inner arc surface. This is driven by an increase in the magnitude of the surface wave curvature as the inner arc surface is approached that is needed to meet the confinement condition on the inner arc surface. For weak inner arc confinement, the surface wave spatial variation with the radial coordinate is described by a triple-deck structure. The first-order correction to the angular speed brings in a dependence on the surface curvature through the parameter $B$, while the influence of the inner arc confinement on the angular velocity only appears in the second-order correction. For stronger inner arc confinement, the surface wave structure is described by a two-layer solution, where the effect of the confinement on the angular speed is promoted to the first-order correction. We also compare the steady-state arc solution for a PBX 9502 DSD model to an experimental two-dimensional arc geometry validation test.

scholarly journals First-order spatial coherence measurements in a thermalized two-dimensional photonic quantum gas

2017 ◽  
Vol 8 (1) ◽  
Author(s):  
Tobias Damm ◽  
David Dung ◽  
Frank Vewinger ◽  
Martin Weitz ◽  
Julian Schmitt
Keyword(s):  
Spatial Coherence ◽  
Two Dimensional ◽  
Quantum Gas ◽  
First Order
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