Variational Techniques

2009 ◽  
pp. 301-327 ◽  
Author(s):  
Kenneth Meyer ◽  
Glen Hall ◽  
Dan Offin
Keyword(s):  
Variational Techniques

Periodic Problems with the Scalar p-Laplacian Resonant at any Eigenvalue via Critical Point Methods

2013 ◽  
Vol 13 (3) ◽  
Author(s):  
Sophia Th. Kyritsi ◽  
Donal O’ Regan ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Critical Point ◽  
Morse Theory ◽  
Critical Point Theory ◽  
Smooth Solution ◽  
Point Theory ◽  
Reaction Term ◽  
Variational Techniques ◽  
Periodic Problems

AbstractWe consider nonlinear periodic problems driven by the scalar p-Laplacian with a Carathéodory reaction term. Under conditions which permit resonance at infinity with respect to any eigenvalue, we show that the problem has a nontrivial smooth solution. Our approach combines variational techniques based on critical point theory with Morse theory.

Nowcasting with Data Assimilation: A Case of Global Satellite Mapping of Precipitation

2016 ◽  
Vol 31 (5) ◽  
pp. 1409-1416 ◽  
Author(s):  
Shigenori Otsuka ◽  
Shunji Kotsuki ◽  
Takemasa Miyoshi
Keyword(s):  
Data Assimilation ◽  
Space Time ◽  
Motion Vectors ◽  
The Past ◽  
Variational Techniques ◽  
Alternative Approach ◽  
Ensemble Transform Kalman Filter ◽  
Global Precipitation ◽  
Time Extrapolation ◽  
Satellite Mapping

Abstract Space–time extrapolation is a key technique in precipitation nowcasting. Motions of patterns are estimated using two or more consecutive images, and the patterns are extrapolated in space and time to obtain their future patterns. Applying space–time extrapolation to satellite-based global precipitation data will provide valuable information for regions where ground-based precipitation nowcasts are not available. However, this technique is sensitive to the accuracy of the motion vectors, and over the past few decades, previous studies have investigated methods for obtaining reliable motion vectors such as variational techniques. In this paper, an alternative approach applying data assimilation to precipitation nowcasting is proposed. A prototype extrapolation system is implemented with the local ensemble transform Kalman filter and is tested with the Japan Aerospace Exploration Agency’s Global Satellite Mapping of Precipitation (GSMaP) product. Data assimilation successfully improved the global precipitation nowcasting with the real-case GSMaP data.

scholarly journals On radial stationary solutions to a model of non-equilibrium growth

2013 ◽  
Vol 24 (3) ◽  
pp. 437-453 ◽  
Author(s):  
CARLOS ESCUDERO ◽  
ROBERT HAKL ◽  
IRENEO PERAL ◽  
PEDRO J. TORRES
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stationary Solutions ◽  
Parabolic Partial Differential Equation ◽  
Radial Solutions ◽  
Variational Techniques ◽  
Existence And Multiplicity ◽  
Equilibrium Growth ◽  
Non Equilibrium

We present the formal geometric derivation of a non-equilibrium growth model that takes the form of a parabolic partial differential equation. Subsequently, we study its stationary radial solutions by means of variational techniques. Our results depend on the size of a parameter that plays the role of the strength of forcing. For small forcing we prove the existence and multiplicity of solutions to the elliptic problem. We discuss our results in the context of non-equilibrium statistical mechanics.

SMALL-TO-LARGE POLARON CROSSOVER IN ONE DIMENSION USING VARIATIONAL PHONON-AVERAGING TECHNIQUES

2001 ◽  
Vol 15 (13) ◽  
pp. 1923-1937 ◽  
Author(s):  
P. CHOUDHURY ◽  
A. N. DAS
Keyword(s):  
One Dimension ◽  
Density Matrix Renormalization Group ◽  
Phonon Coupling ◽  
One Dimensional ◽  
Variational Techniques ◽  
Density Matrix Renormalization ◽  
Numerical Studies ◽  
Real Picture ◽  
Analytical Approaches ◽  
Averaging Techniques

The ground-state properties of polarons in a one-dimensional chain is studied analytically within the modified Lang–Firsov (MLF) transformation using various phonon-averaging techniques. The object of the work is to examine how the analytical approaches may be improved to give rise to the real picture of polaronic properties as predicted by extensive numerical studies. The results are compared with those obtained from numerical analyses using the density matrix renormalization group (DMRG) and other variational techniques. It is observed that our results agree well with the numerical results particularly in the low and intermediate range of phonon coupling.

scholarly journals Stable and Unstable Solutions of the Nonlinear Dynamo Problem

1991 ◽  
Vol 130 ◽  
pp. 103-111
Author(s):  
Reinhard Meinel
Keyword(s):  
Fluid Motion ◽  
Dynamo Model ◽  
Back Reaction ◽  
Amplitude Noise ◽  
Variational Techniques ◽  
Dimensional Phase Space ◽  
Unstable Solutions ◽  
Steady Solutions ◽  
The Magnetic Field ◽  
Simple Dynamical System

AbstractA local potential approach to nonlinear dynamo models which allows the use of variational techniques to investigate the problem of stability is introduced. The method applies at least to quasi-kinematic dynamo models, i.e. to models which include the back-reaction of the magnetic field on the fluid motion in a simplified way. A special application leads to a previously investigated one-dimensional dynamo model which shows a coexistence of a periodic solution (limit cycle) with two stable steady solutions of opposite polarities. The inclusion of some small-amplitude noise leads to interesting transition phenomena which may be of relevance to explain the behaviour of astrophysical dynamos. A simple dynamical system with a two-dimensional phase-space is used for illustration.

APPROXIMATE MOLECULAR ORBITALS: III. THE 1sσ AND 2pπ STATES OF HeH++

1967 ◽  
Vol 45 (7) ◽  
pp. 2231-2238 ◽  
Author(s):  
M. Cohen ◽  
R. P. McEachran ◽  
Sheila D. McPhee
Keyword(s):  
Perturbation Theory ◽  
Molecular Orbitals ◽  
Wave Functions ◽  
Variational Techniques ◽  
Approximate Wave ◽  
Schrödinger Perturbation

A combination of Rayleigh–Schrödinger perturbation theory and variational techniques, previously used to calculate the wave functions of the lowest σ and π states of H2+ has been applied to the 1sσ and 2pπ states of HeH++. The accuracy of the resulting approximate wave functions is demonstrated by comparing a number of quantities calculated with them with the corresponding exact values.

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