scholarly journals Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170612 ◽  
Author(s):  
Malena I. Español ◽  
Dmitry Golovaty ◽  
J. Patrick Wilber
Keyword(s):  
Continuum Model ◽  
Domain Walls ◽  
Three Dimensional ◽  
Variational Model ◽  
Dimensional System ◽  
Two Dimensional ◽  
Starting Point ◽  
Continuum Modelling ◽  
Three Dimensional System ◽  
The Continuum

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

Some Problems of Polar Missile Control

1960 ◽  
Vol 64 (596) ◽  
pp. 482-488 ◽  
Author(s):  
D. Best
Keyword(s):  
Control Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Dimensional System ◽  
Two Dimensional ◽  
Special Design ◽  
Design Problems ◽  
Yaw Control ◽  
Homing Missiles ◽  
Three Dimensional System

A polar-controlled missile is one in which manoeuvre is carried out by rotations about roll and pitch axes, that is, in the manner of a conventional aeroplane. This paper discusses some problems in the application of this form of control to homing missiles.In comparison with the alternative Cartesian configuration, this method presents some special design problems. In the former case, it is often possible to resolve the motion into two planes and consider the pitch and yaw control systems as independent two-dimensional problems. This simplification is not possible in the case of polar control and it is usually necessary to consider the whole three-dimensional system. The equations of motion which result are, in general, not susceptible to analysis. Because of this, the design of control systems requires extensive use of simulators.

scholarly journals Bell-shaped dose response for a system with no IFFLs

2020 ◽  
Author(s):  
Eduardo D. Sontag
Keyword(s):  
Steady State ◽  
T Cell Activation ◽  
Dose Response ◽  
Cell Activation ◽  
Three Dimensional ◽  
Dimensional System ◽  
Two Dimensional ◽  
Converse Implication ◽  
Feedforward Loop ◽  
Three Dimensional System

AbstractIt is well known that the presence of an incoherent feedforward loop (IFFL) in a network may give rise to a steady state non-monotonic dose response. This note shows that the converse implication does not hold. It gives an example of a three-dimensional system that has no IFFLs, yet its dose response is bell-shaped. It also studies under what conditions the result is true for two-dimensional systems, in the process recovering, in far more generality, a result given in the T-cell activation literature.

scholarly journals TWO-DIMENSIONAL BOSE GAS AT LOW DENSITY

1993 ◽  
Vol 07 (15) ◽  
pp. 1029-1038 ◽  
Author(s):  
A.A. OVCHINNIKOV
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Scattering Length ◽  
Three Dimensional ◽  
Bose Gas ◽  
Dimensional System ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Three Dimensional System

We propose a new method to describe the interacting bose gas at zero temperature. For three-dimensional system, the correction to the ground state energy in density is reproduced. For the two-dimensional dilute bose gas, the ground state energy in the leading order in the parameter | ln α2ρ|−1, where α is a two-dimensional scattering length, is obtained.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

Inner-product theory calculations for some rational potentials in a three-dimensional system

1996 ◽  
Vol 74 (1-2) ◽  
pp. 4-9
Author(s):  
M. R. M. Witwit
Keyword(s):  
Energy Levels ◽  
Three Dimensional ◽  
Inner Product ◽  
Dimensional System ◽  
Product Technique ◽  
Special Cases ◽  
Wide Range ◽  
Perturbation Parameters ◽  
Three Dimensional System ◽  
Range Of Values

The energy levels of a three-dimensional system are calculated for the rational potentials,[Formula: see text]using the inner-product technique over a wide range of values of the perturbation parameters (λ, g) and for various eigenstates. The numerical results for some special cases agree with those of previous workers where available.

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