scholarly journals Preconditioning for Allen–Cahn variational inequalities with non-local constraints

2012 ◽  
Vol 231 (16) ◽  
pp. 5406-5420 ◽  
Author(s):  
Luise Blank ◽  
Lavinia Sarbu ◽  
Martin Stoll
Keyword(s):  
Variational Inequalities ◽  
Local Constraints ◽  
Non Local

scholarly journals Causation does not explain contextuality

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 63 ◽  
Author(s):  
Sally Shrapnel ◽  
Fabio Costa
Keyword(s):  
Quantum Mechanics ◽  
Causal Structure ◽  
Quantum Correlations ◽  
Global Constraints ◽  
Local Constraints ◽  
The Past ◽  
Interpretations Of Quantum Mechanics ◽  
The World ◽  
Non Local ◽  
Initial States

Realist interpretations of quantum mechanics presuppose the existence of elements of reality that are independent of the actions used to reveal them. Such a view is challenged by several no-go theorems that show quantum correlations cannot be explained by non-contextual ontological models, where physical properties are assumed to exist prior to and independently of the act of measurement. However, all such contextuality proofs assume a traditional notion of causal structure, where causal influence flows from past to future according to ordinary dynamical laws. This leaves open the question of whether the apparent contextuality of quantum mechanics is simply the signature of some exotic causal structure, where the future might affect the past or distant systems might get correlated due to non-local constraints. Here we show that quantum predictions require a deeper form of contextuality: even allowing for arbitrary causal structure, no model can explain quantum correlations from non-contextual ontological properties of the world, be they initial states, dynamical laws, or global constraints.

The unified method for the heat equation: I. non-separable boundary conditions and non-local constraints in one dimension

2013 ◽  
Vol 24 (6) ◽  
pp. 857-886 ◽  
Author(s):  
DIONYSSIOS MANTZAVINOS ◽  
ATHANASSIOS S. FOKAS
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Spatial Dimension ◽  
Local Constraints ◽  
Transform Methods ◽  
Linear Evolution ◽  
Non Local ◽  
Spectral Representations ◽  
The Unified Method ◽  
Unified Method

We use the heat equation as an illustrative example to show that the unified method introduced by one of the authors can be employed for constructing analytical solutions for linear evolution partial differential equations in one spatial dimension involving non-separable boundary conditions as well as non-local constraints. Furthermore, we show that for the particular case in which the boundary conditions become separable, the unified method provides an easier way for constructing the relevant classical spectral representations avoiding the classical spectral analysis approach. We note that the unified method always yields integral expressions which, in contrast to the series or integral expressions obtained by the standard transform methods, are uniformly convergent at the boundary. Thus, even for the cases that the standard transform methods can be implemented, the unified method provides alternative solution expressions which have advantages for both numerical and asymptotic considerations. The former advantage is illustrated by providing the numerical evaluation of typical boundary value problems.

The use of non-local constraints in maximum-entropy electron density reconstruction

1986 ◽  
Vol 42 (4) ◽  
pp. 212-223 ◽  
Author(s):  
J. Navaza
Keyword(s):  
Maximum Entropy ◽  
Electron Density ◽  
Configurational Entropy ◽  
Super Resolution ◽  
General Purpose ◽  
Local Constraints ◽  
Electron Density Function ◽  
Density Maps ◽  
Resolution Model ◽  
Non Local

Different expressions of the maximum-entropy estimates of the electron density function, corresponding to different prior information are obtained. They show that no general-purpose configurational entropy of density maps exists. Some universal properties of the modellings are discussed. In particular, the meaning of super-resolution is clarified. The information of lower and upper bounds of the electron density is not in general strong enough to produce atomic maps. Atomicity is then introduced as non-local constraints and applied to the problem of phase extension using experimental data and low-resolution model phases. In all cases, the knowledge of phases up to 3.5-3 Å and observed moduli up to 1.5-1 Å allows an estimate of the electron density of roughly the same quality as the 1 Å map obtained from a Fourier summation to be produced.

Sign in / Sign up

Export Citation Format

Share Document