The lagrangian approach to stochastic variational principles on curved manifolds

1992 ◽  
Vol 26 (3) ◽  
pp. 219-236 ◽  
Author(s):  
Ettore Aldrovandi ◽  
Daniela Dohrn ◽  
Francesco Guerra
Keyword(s):  
Variational Principles ◽  
Lagrangian Approach ◽  
Curved Manifolds ◽  
Stochastic Variational Principles

Two Methods for Analyzing Waves in Composites with Random Microstructure

1991 ◽  
Vol 253 ◽  
Author(s):  
John R. Willis
Keyword(s):  
Variational Principle ◽  
Variational Principles ◽  
Statistical Information ◽  
Random Microstructure ◽  
Self Consistent ◽  
The Mean ◽  
Stochastic Variational Principles

ABSTRACTThe problem of calculating the mean wave in a composite with random microstructure is addressed. Exact characterizations of the problem can be given, in the form of stochastic variational principles. Substitution of simple configuration-dependent trial fields into these generates approximations which are, in a sense, ‘optimal’. It is necessary in practice to employ only trial fields which will generate, in the variational principle, no more statistical information than is actually available. Trial fields that require knowledge of two-point statistics generate equations that can also be obtained directly, through use of the QCA. The same fields can be substituted into an alternative variational principle to yield an approximation that makes use of three-point statistics – this approximation is less easy to obtain by direct reasoning. When not even two-point information is available, some more elementary approximation is needed. One such approximation, which is simple and direct in its application, is an extension to dynamics of a “self-consistent embedding” scheme which is widely used in static problems. This is also discussed, together with some illustrative results for a matrix containing inclusions and for a polycrystal.

scholarly journals Semi-martingale driven variational principles

2021 ◽  
Vol 477 (2247) ◽  
pp. 20200957
Author(s):  
O. D. Street ◽  
D. Crisan
Keyword(s):  
Variational Principles ◽  
Geophysical Fluid Dynamics ◽  
Deterministic Theory ◽  
Stochastic Fluid Models ◽  
Pressure Term ◽  
General Constraints ◽  
Stochastic Variational Principles ◽  
Dynamics Models ◽  
Stochastic Fluid ◽  
Special Case

Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a general framework for introducing stochasticity into variational principles through the concept of a semi-martingale driven variational principle and constraining the component variables to be compatible with the driving semi-martingale. Within this framework and the corresponding choice of constraints, the Euler–Poincaré equation can be easily deduced. We show that the deterministic theory is a special case of this class of stochastic variational principles. Moreover, this is a natural framework that enables us to correctly characterize the pressure term in incompressible stochastic fluid models. Other general constraints can also be incorporated as long as they are compatible with the driving semi-martingale.

VARIATIONAL PRINCIPLES IN IMAGE PROCESSING AND THE REGULARIZATION OF ORIENTATION FIELDS

2009 ◽  
Vol 19 (08) ◽  
pp. 2705-2716 ◽  
Author(s):  
JAIME CISTERNAS ◽  
MARCELO GÁLVEZ ◽  
BRAM STIELTJES ◽  
FREDERIK B. LAUN
Keyword(s):  
Mathematical Modeling ◽  
Image Processing ◽  
Free Energy ◽  
Variational Principles ◽  
Scalar Fields ◽  
Energy Functional ◽  
Curved Manifolds ◽  
Free Energy Functional ◽  
Orientation Fields ◽  
Magnetic Gradients

Variational principles and partial differential equations have proved to be fundamental elements in the mathematical modeling of extended systems in physics and engineering. Of particular interest are the equations that arise from a free energy functional. Recently variational principles have begun to be used in Image Processing to perform basic tasks such as denoising, debluring, etc. Great improvements can be achieved by selecting the most appropriate form for the functional. In this article we show how these ideas can be applied not just to scalar fields (i.e. grayscale images) but also to curved manifolds such as the space of orientations. This work is motivated by the denoising of images acquired with Magnetic Resonance scanners using diffusion-sensitized magnetic gradients.

scholarly journals Stochastic variational principles for the collisional Vlasov–Maxwell and Vlasov–Poisson equations

2021 ◽  
Vol 477 (2252) ◽  
pp. 20210167
Author(s):  
Tomasz M. Tyranowski
Keyword(s):  
Maxwell Equations ◽  
Variational Principles ◽  
Particle Method ◽  
Variational Characterization ◽  
Particle In Cell ◽  
Poisson Equations ◽  
Stochastic Variational Principles ◽  
Further Development ◽  
Stochastic Particle

In this work, we recast the collisional Vlasov–Maxwell and Vlasov–Poisson equations as systems of coupled stochastic and partial differential equations, and we derive stochastic variational principles which underlie such reformulations. We also propose a stochastic particle method for the collisional Vlasov–Maxwell equations and provide a variational characterization of it, which can be used as a basis for a further development of stochastic structure-preserving particle-in-cell integrators.

scholarly journals SI “Deterministic and Stochastic Variational Principles and Applications”. December 2015

2015 ◽  
Vol 167 (3) ◽  
pp. 781-782
Author(s):  
Wilfried Grecksch ◽  
Akhtar Khan ◽  
Hannelore Lisei ◽  
Christiane Tammer
Keyword(s):  
Variational Principles ◽  
Stochastic Variational Principles

Discrete stochastic variational principles and quantum mechanics

1984 ◽  
Vol 29 (8) ◽  
pp. 1647-1655 ◽  
Author(s):  
Francesco Guerra ◽  
Rossana Marra
Keyword(s):  
Quantum Mechanics ◽  
Variational Principles ◽  
Stochastic Variational Principles

Variational Principles in Mathematical Physics, Geometry, and Economics

2009 ◽  
Author(s):  
Alexandru Kristaly ◽  
Vicentiu D. Radulescu ◽  
Csaba Varga
Keyword(s):  
Variational Principles ◽  
Mathematical Physics
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