scholarly journals Threshold Effects for the Generalized Friedrichs Model with the Perturbation of Rank One

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Saidakhmat Lakaev ◽  
Arsmah Ibrahim ◽  
Shaxzod Kurbanov
Keyword(s):  
Threshold Effects ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Rank One ◽  
Friedrichs Model ◽  
Unique Eigenvalue ◽  
Generalized Friedrichs Model

A familyHμ(p),μ>0,p∈𝕋2of the Friedrichs models with the perturbation of rank one, associated to a system of two particles, moving on the two-dimensional latticeℤ2is considered. The existence or absence of the unique eigenvalue of the operatorHμ(p)lying below threshold depending on the values ofμ>0andp∈Uδ(0)⊂𝕋2is proved. The analyticity of corresponding eigenfunction is shown.

scholarly journals Sharp Rank-One Convexity Conditions in Planar Isotropic Elasticity for the Additive Volumetric-Isochoric Split

2021 ◽  
Vol 143 (2) ◽  
pp. 301-335
Author(s):  
Jendrik Voss ◽  
Ionel-Dumitrel Ghiba ◽  
Robert J. Martin ◽  
Patrizio Neff
Keyword(s):  
Differential Inequalities ◽  
Two Dimensional ◽  
Ellipticity Condition ◽  
One Dimensional ◽  
Suitable Sense ◽  
Precise Analysis ◽  
Rank One ◽  
Isotropic Elasticity ◽  
Convexity Conditions

AbstractWe consider the volumetric-isochoric split in planar isotropic hyperelasticity and give a precise analysis of rank-one convexity criteria for this case, showing that the Legendre-Hadamard ellipticity condition separates and simplifies in a suitable sense. Starting from the classical two-dimensional criterion by Knowles and Sternberg, we can reduce the conditions for rank-one convexity to a family of one-dimensional coupled differential inequalities. In particular, this allows us to derive a simple rank-one convexity classification for generalized Hadamard energies of the type $W(F)=\frac{\mu }{2} \hspace{0.07em} \frac{\lVert F \rVert ^{2}}{\det F}+f(\det F)$ W ( F ) = μ 2 ∥ F ∥ 2 det F + f ( det F ) ; such an energy is rank-one convex if and only if the function $f$ f is convex.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

Deposition of particles in a two-dimensional lattice gas flow

1992 ◽  
Vol 68 (13) ◽  
pp. 2027-2030 ◽  
Author(s):  
Jean-Christophe Toussaint ◽  
Jean-Marc Debierre ◽  
Loïc Turban
Keyword(s):  
Gas Flow ◽  
Lattice Gas ◽  
Two Dimensional ◽  
Dimensional Lattice
Sign in / Sign up

Export Citation Format

Share Document