MAGNETIZATION OF THE PURE STATES IN THE p-SPIN INTERACTION MODEL

2004 ◽  
Vol 18 (04n05) ◽  
pp. 773-784
Author(s):  
M. TALAGRAND
Keyword(s):  
Low Temperature ◽  
Finite Number ◽  
Interaction Model ◽  
Spin Interaction ◽  
Rigorous Proof ◽  
Pure States ◽  
Number Of Cells

We study the magnetization of the pure states in (a suitable version of) the p-spin interaction model at low temperature. We give a rigorous proof of the phenomenon, discovered in 1 that (very roughly speaking), at a given level of accuracy, the set of sites decomposes in a finite number of cells on which the magnetization of any different pure states are uncorrelated.

SELF ORGANIZATION IN THE LOW TEMPERATURE REGION OF A SPIN GLASS MODEL

2003 ◽  
Vol 15 (01) ◽  
pp. 1-78 ◽  
Author(s):  
MICHEL TALAGRAND
Keyword(s):  
Low Temperature ◽  
External Field ◽  
Temperature Region ◽  
Interaction Model ◽  
Self Organization ◽  
Spin Interaction ◽  
Spin Glass Model ◽  
Glass Model ◽  
One Step ◽  
Pure States

We obtain an almost complete description of the structure of the p-spin interaction model down to temperatures that decrease exponentially with p. We prove in particular the spontaneous creation of pure states, and we describe the distribution of their weights. This confirms the picture of "one step of symmetry breaking" predicted by the physicists. Similar results are obtained when a small external field is added, provided one accepts to add a lower order "generic" perturbation to the Hamiltonian.

Finiteness conditions for CW complexes. Il

1966 ◽  
Vol 295 (1441) ◽  
pp. 129-139 ◽  
Keyword(s):  
Topological Space ◽  
Finite Number ◽  
Simple Form ◽  
Finite Dimension ◽  
Homotopy Equivalent ◽  
Finite Complex ◽  
Finiteness Conditions ◽  
Cw Complexes ◽  
Number Of Cells

A CW complex is a topological space which is built up in an inductive way by a process of attaching cells. Spaces homotopy equivalent to CW complexes play a fundamental role in topology. In the previous paper with the same title we gave criteria (in terms of more-or-less standard invariants of the space) for a CW complex to be homotopy equivalent to one of finite dimension, or to one with a finite number of cells in each dimension, or to a finite complex. This paper contains some simplification of these results. In addition, algebraic machinery is developed which provides a rough classification of CW complexes homotopy equivalent to a given one (the existence clause of the classification is the interesting one). The results would take a particularly simple form if a certain (rather implausible) conjecture could be established.

PCB Layout Design Using a Genetic Algorithm

1996 ◽  
Vol 118 (1) ◽  
pp. 11-15 ◽  
Author(s):  
Sakait Jain ◽  
Hae Chang Gea
Keyword(s):  
Genetic Algorithm ◽  
Optimal Design ◽  
Finite Number ◽  
Layout Design ◽  
Circuit Board ◽  
Heat Sources ◽  
Connectivity Analysis ◽  
Physical Constraints ◽  
Pcb Layout ◽  
Number Of Cells

This paper presents an approach to find the optimal design layout of chips on a circuit board in a manner that minimizes the area covered on the board and the connections between the various chips. In addition, there are no major heat sources next to each other and certain physical constraints are satisfied while finding a layout design. In this approach, the whole circuit board area is divided into a finite number of cells for mapping it into a Genetic Algorithm (GA) chromosome. The mutation and crossover operators have been modified and are applied in conjunction with connectivity analysis for the chips to reduce the creation of a lot of faulty generations. Examples of GA based chip layout are presented to show how each of the objectives are attained separately followed by examples to arrive at layouts using multiple objectives.

scholarly journals A coupled Euler-Lagrange CFD modelling of droplets-to-film

2017 ◽  
Vol 121 (1246) ◽  
pp. 1897-1918 ◽  
Author(s):  
A. A. Adeniyi ◽  
H. P. Morvan ◽  
K. A. Simmons
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Interaction Model ◽  
Film Coating ◽  
Cfd Modelling ◽  
Lagrangian Particles ◽  
Lagrangian Framework ◽  
Computational Fluid Dynamics Cfd ◽  
Model Technique ◽  
Number Of Cells

ABSTRACTIn this paper, a droplet to film interaction model technique is presented. In the proposed approach, the liquid and gas continua are modelled using an enhanced Volume-of-Fluid (VoF) technique while the droplets are tracked using a Lagrangian framework and are coupled to the Eulerian phases using source terms. The eventual target application is an aeroengine bearing chamber in which oil is found as droplets, shed from the bearings, splashing on impact, separated from wall surfaces at obstacles or simply re-entrained, and as a continuum oil film coating the bearing chamber outer walls which it also cools. In finite volume Computational Fluid Dynamics (CFD) techniques, a prohibitively large number of cells would be required to describe the details of the droplet impact phenomenon. Based on published correlations, the splashing droplets are created and tracked as Lagrangian particles. The flowing film and the gas continua are handled with an enhanced VoF technique.

SCALING LIMIT FOR A GENERAL CLASS OF QUANTUM FIELD MODELS AND ITS APPLICATIONS TO NUCLEAR PHYSICS AND CONDENSED MATTER PHYSICS

2007 ◽  
Vol 10 (01) ◽  
pp. 43-65 ◽  
Author(s):  
AKITO SUZUKI
Keyword(s):  
Theoretical Model ◽  
Nuclear Physics ◽  
Nuclear Force ◽  
Condensed Matter ◽  
Scaling Limit ◽  
Interaction Model ◽  
Spin Interaction ◽  
Quantum Field ◽  
Lattice Spin System ◽  
Field Theoretical Model

We consider a scaling limit of the Hamiltonian of the generalized spin-boson (GSB) model which is an abstract quantum field theoretical model of particles interacting with a Bose field. Applying it to a Hamiltonian of the field of the nuclear force with isospin, we obtain an effective potential of the interaction between nucleons. Also, we discuss an application to a Hamiltonian of a lattice spin system interacting with a Bose field and obtain a spin–spin interaction in the vacuum of the Bose field. An interaction model between a Fermi field and a Bose field yields an interaction in the vacuum of the Bose field.

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