scholarly journals Extended Scaling Relations for Planar Lattice Models

2009 ◽  
Vol 292 (2) ◽  
pp. 569-605 ◽  
Author(s):  
G. Benfatto ◽  
P. Falco ◽  
V. Mastropietro
Keyword(s):  
Lattice Models ◽  
Scaling Relations ◽  
Planar Lattice

Lattice models in micromechanics

2002 ◽  
Vol 55 (1) ◽  
pp. 35-60 ◽  
Author(s):  
Martin Ostoja-Starzewski
Keyword(s):  
Lattice Models ◽  
Network Models ◽  
Type Systems ◽  
Functionally Graded ◽  
Attractive Alternative ◽  
Planar Lattice ◽  
Fiber Network ◽  
Computational Aspects ◽  
Discrete Counterpart ◽  
Planar Systems

This review presents the potential that lattice (or spring network) models hold for micromechanics applications. The models have their origin in the atomistic representations of matter on one hand, and in the truss-type systems in engineering on the other. The paper evolves by first giving a rather detailed presentation of one-dimensional and planar lattice models for classical continua. This is followed by a section on applications in mechanics of composites and key computational aspects. We then return to planar lattice models made of beams, which are a discrete counterpart of non-classical continua. The final two sections of the paper are devoted to issues of connectivity and rigidity of networks, and lattices of disordered (rather than periodic) topology. Spring network models offer an attractive alternative to finite element analyses of planar systems ranging from metals, composites, ceramics and polymers to functionally graded and granular materials, whereby a fiber network model of paper is treated in considerable detail. This review article contains 81 references.

TIME-REVERSAL DUALITY AND PLANAR LATTICE DUALITY IN NON-EQUILIBRIUM LATTICE MODELS

Fractals ◽  
1996 ◽  
Vol 04 (03) ◽  
pp. 285-292
Author(s):  
MAKOTO KATORI
Keyword(s):  
Phase Transitions ◽  
Time Reversal ◽  
Nearest Neighbor ◽  
Contact Process ◽  
Detailed Balance ◽  
Equilibrium Phase ◽  
Lattice Models ◽  
Dimensional System ◽  
Planar Lattice ◽  
Non Equilibrium

The contact process (CP) is a simple mathematical model for the spread of infection of a contagious disease. Though it has only nearest-neighbor interactions, phase transitions occur even in the one-dimensional system and non-equilibrium stationary states appear in supercritical phase. This implies violation of detailed balance. The appearance of such non-equilibrium states is related to directed percolation problems on the spatiotemporal plane. In the present paper, we study discretetime versions of the CP, the two-neighbor stochastic cellular automata (SCA), and clarify this viewpoint. We use two kinds of duality relations, the time-reversal duality and the planar lattice duality on the spatio-temporal plane, and give a good lower bound for the critical line of non-equilibrium phase transitions in the two-neighbor SCA.

Kinematic analysis and deformation of a planar lattice with an arbitrary number of panels

2020 ◽  
pp. 15-19
Author(s):  
M.N. Kirsanov
Keyword(s):  
Exact Solution ◽  
Kinematic Analysis ◽  
Arbitrary Number ◽  
Design Parameters ◽  
Lattice Deformation ◽  
Planar Lattice ◽  
Force Loading

Formulae are obtained for calculating the deformations of a statically determinate lattice under the action of two types of loads in its plane, depending on the number of panels located along one side of the lattice. Two options for fixing the lattice are analyzed. Cases of kinematic variability of the structure are found. The distribution of forces in the rods of the lattice is shown. The dependences of the force loading of some rods on the design parameters are obtained. Keywords: truss, lattice, deformation, exact solution, deflection, induction, Maple system. [email protected]

Computation of Natural Frequencies of Planar Lattice Structure.

1987 ◽  
Author(s):  
James H. Williams ◽  
Nagem Jr. ◽  
Raymond J.
Keyword(s):  
Natural Frequencies ◽  
Lattice Structure ◽  
Planar Lattice

scholarly journals Parafermionization, bosonization, and critical parafermionic theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yuan Yao ◽  
Akira Furusaki
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Degrees Of Freedom ◽  
Lattice Models ◽  
Partition Functions ◽  
Minimal Models ◽  
Fermionic Model ◽  
Conformal Field ◽  
Critical Theories ◽  
Wigner Transformation

AbstractWe formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality atk= 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory whenk >2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.

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