Three-Dimensional Lattice Walks in the Upper Half-Space: 10795

International audience We continue the investigations of lattice walks in the three-dimensional lattice restricted to the positive octant. We separate models which clearly have a D-finite generating function from models for which there is no reason to expect that their generating function is D-finite, and we isolate a small set of models whose nature remains unclear and requires further investigation. For these, we give some experimental results about their asymptotic behaviour, based on the inspection of a large number of initial terms. At least for some of them, the guessed asymptotic form seems to tip the balance towards non-D-finiteness.

Download Full-text

DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732391004140 ◽

1991 ◽

Vol 06 (39) ◽

pp. 3591-3600 ◽

Cited By ~ 40

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).

Download Full-text

Restoring isotropy in a three-dimensional lattice model: The Ising universality class

Physical Review B ◽

10.1103/physrevb.104.014426 ◽

2021 ◽

Vol 104 (1) ◽

Author(s):

Martin Hasenbusch

Keyword(s):

Lattice Model ◽

Three Dimensional ◽

Universality Class ◽

Dimensional Lattice

Download Full-text

Guided Surface Waves on an Elastic Half Space

Journal of Applied Mechanics ◽

10.1115/1.3408973 ◽

1971 ◽

Vol 38 (4) ◽

pp. 899-905 ◽

Cited By ~ 5

Author(s):

L. B. Freund

Keyword(s):

Wave Propagation ◽

Surface Wave ◽

Surface Waves ◽

Half Space ◽

Body Wave ◽

Three Dimensional ◽

Elastic Half Space ◽

Normal Displacement ◽

Rigid Barrier ◽

Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

Download Full-text