966 research outputs found
Electronic Properties of Molecules and Surfaces with a Self\uad-Consistent Interatomic van der Waals Density Functional.
How strong is the effect of van der Waals (vdW) interactions on the electronic properties of molecules
and extended systems? To answer this question, we derived a fully self-consistent implementation of the
density-dependent interatomic vdW functional of Tkatchenko and Scheffler [Phys. Rev. Lett. 102, 073005
(2009)]. Not surprisingly, vdW self-consistency leads to tiny modifications of the structure, stability, and
electronic properties of molecular dimers and crystals. However, unexpectedly large effects were found in
the binding energies, distances, and electrostatic moments of highly polarizable alkali-metal dimers. Most
importantly, vdW interactions induced complex and sizable electronic charge redistribution in the vicinity
of metallic surfaces and at organic-metal interfaces. As a result, a substantial influence on the computed
work functions was found, revealing a nontrivial connection between electrostatics and long-range electron
correlation effects
Positive Solution Curves of Semipositone Problems with Concave Nonlinearities
We consider the positive solutions to the semilinear equation:
-Δu(x) = λf(u(x)) for x ∈ Ω
u(x) = 0 for x ∈ ∂Ω
where Ω denotes a smooth bounded region in RN (N \u3e 1) and λ \u3e 0. Here f :[0, ∞)→R is assumed to be monotonically increasing, concave and such that f(0) \u3c 0 (semipositone). Assuming that f\u27(∞) ≡ lim t→∞ f\u27(t) \u3e 0, we establish the stability and uniqueness of large positive solutions in terms of (f(t)/t)\u27. When Ω is a ball, we determine the exact number of positive solutions for each λ \u3e 0. We also obtain the geometry of the branches of positive solutions completely and establish how they evolve. This work extends and complements that of [3, 7] where f\u27(∞) ≤ 0
Long-range correlation energy calculated from coupled atomic response functions
An accurate determination of the electron correlation energy is an essential prerequisite for describing the structure, stability, and function in a wide variety of systems. Therefore, the development of efficient approaches for the calculation of the correlation energy (and hence the dispersion energy as well) is essential and such methods can be coupled with many density-functional approximations, local methods for the electron correlation energy, and even interatomic force fields. In this work, we build upon the previously developed many-body dispersion (MBD) framework, which is intimately linked to the random-phase approximation for the correlation energy. We separate the correlation energy into short-range contributions that are modeled by semi-local functionals and long-range contributions that are calculated by mapping the complex all-electron problem onto a set of atomic response functions coupled in the dipole approximation. We propose an effective range-separation of the coupling between the atomic response functions that extends the already broad applicability of the MBD method to non-metallic materials with highly anisotropic responses, such as layered nanostructures. Application to a variety of high-quality benchmark datasets illustrates the accuracy and applicability of the improved MBD approach, which offers the prospect of first-principles modeling of large structurally complex systems with an accurate description of the long-range correlation energy
Long-range correlation energy calculated from coupled atomic response functions
An accurate determination of the electron correlation energy is an essential prerequisite for describing the structure, stability, and function in a wide variety of systems. Therefore, the development of efficient approaches for the calculation of the correlation energy (and hence the dispersion energy as well) is essential and such methods can be coupled with many density-functional approximations, local methods for the electron correlation energy, and even interatomic force fields. In this work, we build upon the previously developed many-body dispersion (MBD) framework, which is intimately linked to the random-phase approximation for the correlation energy. We separate the correlation energy into short-range contributions that are modeled by semi-local functionals and long-range contributions that are calculated by mapping the complex all-electron problem onto a set of atomic response functions coupled in the dipole approximation. We propose an effective range-separation of the coupling between the atomic response functions that extends the already broad applicability of the MBD method to non-metallic materials with highly anisotropic responses, such as layered nanostructures. Application to a variety of high-quality benchmark datasets illustrates the accuracy and applicability of the improved MBD approach, which offers the prospect of first-principles modeling of large structurally complex systems with an accurate description of the long-range correlation energy
Minimal immersions of closed surfaces in hyperbolic three-manifolds
We study minimal immersions of closed surfaces (of genus ) in
hyperbolic 3-manifolds, with prescribed data , where
is a conformal structure on a topological surface , and is a holomorphic quadratic differential on the surface . We
show that, for each for some , depending only on
, there are at least two minimal immersions of closed surface
of prescribed second fundamental form in the conformal structure
. Moreover, for sufficiently large, there exists no such minimal
immersion. Asymptotically, as , the principal curvatures of one
minimal immersion tend to zero, while the intrinsic curvatures of the other
blow up in magnitude.Comment: 16 page
On smoothness-asymmetric null infinities
We discuss the existence of asymptotically Euclidean initial data sets to the
vacuum Einstein field equations which would give rise (modulo an existence
result for the evolution equations near spatial infinity) to developments with
a past and a future null infinity of different smoothness. For simplicity, the
analysis is restricted to the class of conformally flat, axially symmetric
initial data sets. It is shown how the free parameters in the second
fundamental form of the data can be used to satisfy certain obstructions to the
smoothness of null infinity. The resulting initial data sets could be
interpreted as those of some sort of (non-linearly) distorted Schwarzschild
black hole. Its developments would be so that they admit a peeling future null
infinity, but at the same time have a polyhomogeneous (non-peeling) past null
infinity.Comment: 13 pages, 1 figur
Action minimizing orbits in the n-body problem with simple choreography constraint
In 1999 Chenciner and Montgomery found a remarkably simple choreographic
motion for the planar 3-body problem (see \cite{CM}). In this solution 3 equal
masses travel on a eight shaped planar curve; this orbit is obtained minimizing
the action integral on the set of simple planar choreographies with some
special symmetry constraints. In this work our aim is to study the problem of
masses moving in \RR^d under an attractive force generated by a potential
of the kind , , with the only constraint to be a simple
choreography: if are the orbits then we impose the
existence of x \in H^1_{2 \pi}(\RR,\RR^d) such that q_i(t)=x(t+(i-1) \tau),
i=1,...,n, t \in \RR, where . In this setting, we first
prove that for every d,n \in \NN and , the lagrangian action
attains its absolute minimum on the planar circle. Next we deal with the
problem in a rotating frame and we show a reacher phenomenology: indeed while
for some values of the angular velocity minimizers are still circles, for
others the minima of the action are not anymore rigid motions.Comment: 24 pages; 4 figures; submitted to Nonlinearit
Multiple solutions to a magnetic nonlinear Choquard equation
We consider the stationary nonlinear magnetic Choquard equation
[(-\mathrm{i}\nabla+A(x))^{2}u+V(x)u=(\frac{1}{|x|^{\alpha}}\ast |u|^{p})
|u|^{p-2}u,\quad x\in\mathbb{R}^{N}%] where is a real valued vector
potential, is a real valued scalar potential ,
and . \ We assume that both and are
compatible with the action of some group of linear isometries of
. We establish the existence of multiple complex valued
solutions to this equation which satisfy the symmetry condition where
is a given group homomorphism into the unit
complex numbers.Comment: To appear on ZAM
Non-radial sign-changing solutions for the Schroedinger-Poisson problem in the semiclassical limit
We study the existence of nonradial sign-changing solutions to the
Schroedinger-Poisson system in dimension N>=3. We construct nonradial
sign-changing multi-peak solutions whose peaks are displaced in suitable
symmetric configurations and collapse to the same point. The proof is based on
the Lyapunov-Schmidt reduction
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