The self-assembly of flat organic molecules on metal surfaces is controlled, apart from the kinetic factors, by the interplay between the molecule-molecule and molecule-surface interactions. These are typically calculated using standard density functional theory within the generalized gradient approximation, which significantly underestimates nonlocal correlations, i.e. van der Waals (vdW) cont...

Abstract. In this paper we present the first results on substructuring methods for nonlocal operators, specifically, an instance of the nonlocal p-Laplace operator. We present a nonlocal variational formulation of this operator, proving a nonlocal Poincaré inequality and upper bound to establish a spectral equivalence. We then introduce a nonlocal two-domain variational formulation utilizing no...

In this paper, we focus on stationary (ergodic) mean-field games (MFGs). These arise in the study of long-time behavior finite-horizon MFGs. Motivated by a prior scheme for Hamilton–Jacobi equations introduced Aubry–Mather's theory, introduce discrete approximation to Relying Kakutani's fixed-point theorem, prove existence and uniqueness (up additive constant) solutions problem. Moreover, show ...

in this research, the buckling and bending behaviour of smart nanocomposite plate reinforced by single- walled carbon nanotubes (swcnts) under electro-magneto-mechanical loadings is studied. the extended mixture rule approach is used to determine the elastic properties of nanocomposite plate. equilibrium equations of smart nanocomposite plate are derived using the hamilton’s principle based on ...

A construction of W-symmetries is given only in terms of the nonlocal fields (parafermions ψ α), which take values on the homogeneous space G/U (1) r , where G is a simply connected compact Lie group manifold (its accompanying Lie algebra G is a simple one of rank r). Only certain restriction of the root set of Lie algebra on which the parafermionic fields take values are satisfied, then a cons...

Parameters of Gasser Leutwyler chiral Lagrangian are proved saturated by dynamical quark self energy Σ(k2) in a gauge invariant, nonlocal, dynamical quark model. Much of low-energy QCD can be encoded into a series parameters appearing in a chiral Lagrangian, expanded to some finite order of low energy expansion. Attempts have been made to understand these parameters: it is shown that low lying ...

We construct Euclidean Liouville conformal field theories in odd number of dimensions. The are nonlocal and non-unitary with a log-correlated field, ${\cal Q}$-curvature background, an exponential Liouville-type potential. study the classical quantum properties these including finite entanglement entropy part sphere partition function $F$, boundary anomaly vertex operators' correlation function...

European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coup...

We calculate the electronic structure of several atoms and small molecules by direct minimization of the Self-Interaction Corrected Local Density Approximation (SIC-LDA) functional. To do this we rst derive an expression for the gradient of this functional under the constraint that the orbitals be orthogonal and show that previously given expressions do not correctly incorporate this constraint...

The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of nonlinear, ordinary differential equation with derivative fractional variable order Gerasimov–Caputo type. questions approximation, convergence, and stability this are studied. It is shown that conditionally stable converges to first order. Using Riccati as an example, computational accuracy method a...