The Method of Boundary States with Perturbations in the Problems of Body Elastostatics Under the Action of Follower Load

Author(s):  
Viktor Borisovich Penkov ◽  
Lyubov Vladimirovna Levina ◽  
Evgeniy Aleksandrovich Novikov
2001 ◽  
Vol 16 (22) ◽  
pp. 3659-3671 ◽  
Author(s):  
A. N. SCHELLEKENS ◽  
N. SOUSA

We construct explicitly the open descendants of some exceptional automorphism invariants of U (2N) orbifolds. We focus on the case N = p1 × p2, p1 and p2 prime, and on the automorphisms of the diagonal and charge conjugation invariants that exist for these values of N. These correspond to orbifolds of the circle with radius R2 = 2p1/p2. For each automorphism invariant we find two consistent Klein bottles, and for each Klein bottle we find a complete (and probably unique) set of boundary states. The two Klein bottles are in each case related to each other by simple currents, but surprisingly for the automorphism of the charge conjugation invariant neither of the Klein bottle choices is the canonical (symmetric) one.


1982 ◽  
Vol 25 (1) ◽  
pp. 67-71 ◽  
Author(s):  
H.C. de Graaff ◽  
M. Huybers ◽  
J.G. de Groot

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
A. Ramesh Chandra ◽  
Jan de Boer ◽  
Mario Flory ◽  
Michal P. Heller ◽  
Sergio Hörtner ◽  
...  

Abstract We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the gravitational action. The optimal circuit minimizes the gravitational action. This is a generalization of both the “complexity equals volume” conjecture to unoptimized circuits, and path integral optimization to finite cutoffs. Using tools from holographic $$ T\overline{T} $$ T T ¯ , we find that surfaces of constant scalar curvature play a special role in optimizing quantum circuits. We also find an interesting connection of our proposal to kinematic space, and discuss possible circuit representations and gate counting interpretations of the gravitational action.


2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Philip Boyle Smith ◽  
David Tong

Abstract We study boundary states for Dirac fermions in d = 1 + 1 dimensions that preserve Abelian chiral symmetries, meaning that the left- and right-moving fermions carry different charges. We derive simple expressions, in terms of the fermion charge assignments, for the boundary central charge and for the ground state degeneracy of the system when two different boundary conditions are imposed at either end of an interval. We show that all such boundary states fall into one of two classes, related to SPT phases supported by (−1)F , which are characterised by the existence of an unpaired Majorana zero mode.


Author(s):  
D.A. Ivanychev ◽  
E.Yu. Levina

In this work, we studied the axisymmetric elastic equilibrium of transversely isotropic bodies of revolution, which are simultaneously under the influence of surface and volume forces. The construction of the stress-strain state is carried out by means of the boundary state method. The method is based on the concepts of internal and boundary states conjugated by an isomorphism. The bases of state spaces are formed, orthonormalized, and the desired state is expanded in a series of elements of the orthonormal basis. The Fourier coefficients, which are quadratures, are calculated. In this work, we propose a method for forming bases of spaces of internal and boundary states, assigning a scalar product and forming a system of equations that allows one to determine the elastic state of anisotropic bodies. The peculiarity of the solution is that the obtained stresses simultaneously satisfy the conditions both on the boundary of the body and inside the region (volume forces), and they are not a simple superposition of elastic fields. Methods are presented for solving the first and second main problems of mechanics, the contact problem without friction and the main mixed problem of the elasticity theory for transversely isotropic finite solids of revolution that are simultaneously under the influence of volume forces. The given forces are distributed axisymmetrically with respect to the geometric axis of rotation. The solution of the first main problem for a non-canonical body of revolution is given, an analysis of accuracy is carried out and a graphic illustration of the result is given


2012 ◽  
Vol 17 (3) ◽  
pp. 232-242 ◽  
Author(s):  
Prasath Mageswaran ◽  
Fernando Techy ◽  
Robb W. Colbrunn ◽  
Tara F. Bonner ◽  
Robert F. McLain

Object The object of this study was to evaluate the effect of hybrid dynamic stabilization on adjacent levels of the lumbar spine. Methods Seven human spine specimens from T-12 to the sacrum were used. The following conditions were implemented: 1) intact spine; 2) fusion of L4–5 with bilateral pedicle screws and titanium rods; and 3) supplementation of the L4–5 fusion with pedicle screw dynamic stabilization constructs at L3–4, with the purpose of protecting the L3–4 level from excessive range of motion (ROM) and to create a smoother motion transition to the rest of the lumbar spine. An industrial robot was used to apply continuous pure moment (± 2 Nm) in flexion-extension with and without a follower load, lateral bending, and axial rotation. Intersegmental rotations of the fused, dynamically stabilized, and adjacent levels were measured and compared. Results In flexion-extension only, the rigid instrumentation at L4–5 caused a 78% decrease in the segment's ROM when compared with the intact specimen. To compensate, it caused an increase in motion at adjacent levels L1–2 (45.6%) and L2–3 (23.2%) only. The placement of the dynamic construct at L3–4 decreased the operated level's ROM by 80.4% (similar stability as the fusion at L4–5), when compared with the intact specimen, and caused a significant increase in motion at all tested adjacent levels. In flexion-extension with a follower load, instrumentation at L4–5 affected only a subadjacent level, L5–sacrum (52.0%), while causing a reduction in motion at the operated level (L4–5, −76.4%). The dynamic construct caused a significant increase in motion at the adjacent levels T12–L1 (44.9%), L1–2 (57.3%), and L5–sacrum (83.9%), while motion at the operated level (L3–4) was reduced by 76.7%. In lateral bending, instrumentation at L4–5 increased motion at only T12–L1 (22.8%). The dynamic construct at L3–4 caused an increase in motion at T12–L1 (69.9%), L1–2 (59.4%), L2–3 (44.7%), and L5–sacrum (43.7%). In axial rotation, only the placement of the dynamic construct at L3–4 caused a significant increase in motion of the adjacent levels L2–3 (25.1%) and L5–sacrum (31.4%). Conclusions The dynamic stabilization system displayed stability characteristics similar to a solid, all-metal construct. Its addition of the supraadjacent level (L3–4) to the fusion (L4–5) did protect the adjacent level from excessive motion. However, it essentially transformed a 1-level lumbar fusion into a 2-level lumbar fusion, with exponential transfer of motion to the fewer remaining discs.


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