scholarly journals Variational procedure leading from Davidson potentials to the E(5)and X(5) critical point symmetries

2020 ◽  
Vol 13 ◽  
pp. 10
Author(s):  
Dennis Bonatsos ◽  
D. Lenis ◽  
N. Minkov ◽  
D. Petrellis ◽  
P. P. Raychev ◽  
...  
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Ground State ◽  
Nuclear Energy ◽  
Energy Spectra ◽  
Variational Procedure ◽  
Ground State Band ◽  
Sharp Maximum ◽  
State Band ◽  
Shape Phase Transition

Davidson potentials of the form β^2 + β0^4/β^2, when used in the original Bohr Hamiltonian for γ-independent potentials bridge the U(5) and 0(6) symmetries. Using a variational procedure, we determine for each value of angular momentum L the value of β0 at which the derivative of the energy ratio RL = E(L)/E(2) with respect to β0 has a sharp maximum, the collection of RL values at these points forming a band which practically coincides with the ground state band of the E(5) model, corresponding to the critical point in the shape phase transition from U(5) to Ο(6). The same potentials, when used in the Bohr Hamiltonian after separating variables as in the X(5) model, bridge the U(5) and SU(3) symmetries, the same variational procedure leading to a band which practically coincides with the ground state band of the X(5) model, corresponding to the critical point of the U(5) to SU(3) shape phase transition. A new derivation of the Holmberg-Lipas formula for nuclear energy spectra is obtained as a by-product.

scholarly journals PROBING FOAMY SPACE–TIME WITH VARIATIONAL METHODS

1999 ◽  
Vol 14 (18) ◽  
pp. 2905-2920 ◽  
Author(s):  
REMO GARATTINI
Keyword(s):  
Black Hole ◽  
Variational Methods ◽  
Momentum Space ◽  
Flat Space ◽  
Casimir Energy ◽  
Space Time ◽  
Pair Creation ◽  
Variational Procedure ◽  
Loop Correction ◽  
Quasilocal Energy

A one-loop correction of the quasilocal energy in the Schwarzschild background, with flat space as a reference metric, is performed by means of a variational procedure in the Hamiltonian framework. We examine the graviton sector in momentum space, in the lowest possible state. An application to the black hole pair creation via the Casimir energy is presented. Implications on the foamlike scenario are discussed.

Approximate Analysis of Elastic Stress Distribution in Thin Strip Material

1967 ◽  
Vol 89 (1) ◽  
pp. 81-85 ◽  
Author(s):  
G. C. Feng ◽  
L. E. Goodman
Keyword(s):  
Elastic Stress ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Plate Thickness ◽  
Thin Strip ◽  
Variational Procedure ◽  
Two Dimensional ◽  
Normal Loading ◽  
Variational Equations ◽  
State Of Stress

The general problem of the two-dimensional state of stress in a strip of elastic material under normal loading is considered. A series expansion of displacement functions generated along lines suggested by Mindlin and Medick [1] for dynamical questions arising in plate theory is employed in the solution. The variational procedure generates a set of variational equations of motion. In order to obtain useful results the series is truncated in such a way that the analysis gives an approximate solution valid for ratios of loaded length to plate thickness greater than unity.

Variational estimates for the creep behaviour of polycrystals

1995 ◽  
Vol 448 (1932) ◽  
pp. 121-142 ◽  
Keyword(s):  
Heterogeneous Media ◽  
Creep Behaviour ◽  
The Self ◽  
Polycrystalline Materials ◽  
Variational Procedure ◽  
Constitutive Behaviour ◽  
Effective Potentials ◽  
Self Consistent ◽  
Geometric Arrangements

A variational procedure is developed for estimating the effective constitutive behaviour of polycrystalline materials undergoing high-temperature creep. The procedure is based on a new variational principle allowing the determination of the effective potential function of a given nonlinear polycrystal in terms of the corre­sponding potential for a linear comparison polycrystal with an identical geometric arrangements of its constituent single-crystal grains. As such, it constitutes an extension, to locally anisotropic behaviour, of the variational procedure devel­oped by Ponte Castañeda (1991) for nonlinear heterogeneous media with locally isotropic behaviour. By way of an example, the procedure is applied to the de­termination of bounds of the Hashin-Shtrikman type for the effective potentials of statistically isotropic nonlinear polycrystals. The bounds are computed for the special class of untextured FCC polycrystals with isotropic pure power-law viscous behaviour, first considered by Hutchinson (1976), in the context of a calculation of the self-consistent type. The new bounds are found to be more restrictive than the corresponding classical Taylor-Bishop-Hill bounds, and also more re­strictive, if only slightly so, than related bounds of the Hashin-Shtrikman type by Dendievel et al . (1991). The new procedure has the advantage over the self-consistent procedure of Hutchinson (1976) that it may be applied, without any essential complications, to aggregates of crystals with slip systems exhibiting dif­ferent creep rules - with, for example, different power exponents - and to general loading conditions. However, the distinctive feature of the new variational proce­dure is that it may be used in conjunction with other types of known bounds and estimates for linear polycrystals to generate corresponding bounds and estimates for nonlinear polycrystals.

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