Computer simulation of a biaxial nematogenic model on a three-dimensional lattice and based on a recently proposed interaction potential

2004 ◽  
Vol 337 (3-4) ◽  
pp. 505-519 ◽  
Author(s):  
Silvano Romano
Keyword(s):  
Computer Simulation ◽  
Interaction Potential ◽  
Three Dimensional ◽  
Dimensional Lattice

THE FINITENESS OF THE NUMBER OF EIGENVALUES OF THE FOUR-PARTICLE SCHRÖDINGER OPERATOR WITH THREE-PARTICLE CONTACT INTERACTION

2021 ◽  
Vol 10 (7) ◽  
pp. 2933-2946
Author(s):  
I. Bozorov ◽  
U. Shadiev ◽  
G. Yodgorov
Keyword(s):  
Essential Spectrum ◽  
Contact Interaction ◽  
Interaction Potential ◽  
Three Dimensional ◽  
Schrodinger Operator ◽  
Dimensional Lattice ◽  
Quasi Momentum ◽  
Particle Contact ◽  
Quantum Particles ◽  
Arbitrary Quantum

In this paper, we consider the four-particle Schr\"{o}dinger operator corresponding to the Hamiltonian of a system of four arbitrary quantum particles via a three-particle contact interaction potential on a three-dimensional lattice. The finiteness of the number of eigenvalues of the Schr\"{o}dinger operator lying to the left of the essential spectrum for zero value of the total quasi-momentum is proved.

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).

Three-dimensional predator–prey interactions: a computer simulation of bird flocks and aircraft

1986 ◽  
Vol 64 (11) ◽  
pp. 2624-2633 ◽  
Author(s):  
Peter F. Major ◽  
Lawrence M. Dill ◽  
David M. Eaves
Keyword(s):  
Computer Simulation ◽  
Prey Species ◽  
Three Dimensional ◽  
Aircraft Engine ◽  
Aquatic Environments ◽  
Aircraft Engines ◽  
Predator Prey ◽  
Simulation Techniques ◽  
Computer Simulation Techniques ◽  
Individual Prey

Three-dimensional interactions between grouped aerial predators (frontal discs of aircraft engines), either linearly arrayed or clustered, and flocks of small birds were studied using interactive computer simulation techniques. Each predator modelled was orders of magnitude larger than an individual prey, but the prey flock was larger than each predator. Expected numbers of individual prey captured from flocks were determined for various predator speeds and trajectories, flock–predator initial distances and angles, and flock sizes, shapes, densities, trajectories, and speeds. Generally, larger predators and clustered predators caught more prey. The simulation techniques employed in this study may also prove useful in studies of predator–prey interactions between schools or swarms of small aquatic prey species and their much larger vertebrate predators, such as mysticete cetaceans.The study also provides a method to study problems associated with turbine aircraft engine damage caused by the ingestion of small flocking birds, as well as net sampling of organisms in open aquatic environments.

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