Results 121 to 130 of about 20,117 (161)

Multiparameter Variational Principles

SIAM Journal on Mathematical Analysis, 1982
Let T and V be self-adjoint operators on a separable Hilbert space H, where V is bounded and T has compact resolvent. Then a spectral theory, including eigenvector completeness, may be given variationally for the eigenvalue problem \[ Tx = \lambda Vx,\quad 0 \ne x \in H\] provided either $T \gg 0$ (i.e., $(x,Tx) \geq \alpha \| x \|^2 $ for some $\alpha
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Complementary variational principles and variational-iterative principles

Journal of Physics A: Mathematical and General, 1981
Complementary variational principles for the solution of certain linear equations are developed. It is shown that these may be used iteratively for the solution of nonlinear equations. Examples are presented with applications in particle theory, electromagnetic theory, communication theory and the Thomas-Fermi statistical theory for atoms.
Burrows, B. L., Perks, A. J.
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Variation Principles of Hydrodynamics

The Physics of Fluids, 1960
It is shown that the Lagrangian equations for the motion of both incompressible and compressible fluids can be derived from variation principles. As has been pointed out by C. C. Lin, an important feature of these principles is the boundary condition: The coordinates of each particle (and not merely the normal component of its velocity) must be ...
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On Schwinger’s variational principle

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1957
Abstract The classical and quantum theories of dynamical systems whose Lagrangians are linear in the co-ordinate derivatives are studied, with a view to clarifying a number of points in relation to Schwinger’s quantum-mechanical variational principle.
Kibble, T. W. B., Polkinghorne, J. C.
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The construction of variational principles

Journal of Applied Mathematics and Mechanics, 1997
The author investigates two classes of problems of continuum mechanics modeled by system of transfer equations in the stationary case and for the problem of the seepage of an incompressible fluid in a deformable medium of complex rheology. For the above mentioned systems of equations proposed is a deduction of variational principles from variational ...
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Variational Principles in Electromagnetism

Physical Review, 1933
The familiar relation between the potentials in electromagnetic theory is regarded as a consequence of the principles of angular momentum and center of mass expressed by the symmetry of the stress-energy tensor. The electromagnetic equations are derived from a Lagrangian function $L$ equal to an arbitrary function of the invariants ${E}^{2}\ensuremath{-
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Variational Principle in Magnetohydrodynamics

The Physics of Fluids, 1969
By using a special set of electromagnetic field potentials and an appropriate Lagrangian density, the momentum equation for a compressible, inviscid, infinitely conducting fluid undergoing isentropic motion in an electromagnetic field is obtained.
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Variational principles, variational identities, and supervariational principles for wavefunctions

Journal of Mathematical Physics, 1975
We develop variational principles and variational identities for bound state and continuum wavefunctions in a general context, paying particular attention to the proper choice of defining equations and boundary conditions which will lead to unique and unambiguous wavefunctions even when these functions are complex.
Gerjuoy, E., Rau, A. R. P., Rosenberg, L., Spruch, Larry   +3 more
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Variational principles in evolution

Bulletin of Mathematical Biology, 1996
For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a ...
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Structure-preserving integrators based on a new variational principle for constrained mechanical systems

Nonlinear Dynamics, 2023
Philipp L Kinon, Peter Betsch, S Schneider   +2 more
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