Functional Boundary Conditions Research Articles

How Good is Fluorine as a Hydrogen‐Bond Acceptor in Fluorinated Single‐Walled Carbon Nanotubes?

Ab initio (RI-MP2/TZVPP) computations were employed to investigate the interaction between hydrogen-bond donors H2O and CH3OH and covalently bound fluorine in organofluorine compounds. While the CFHO interaction energy is around 3 kcal mol(-1) for unstrained systems, the linear correlation between pyramidalization angle at the carbon atom and the interaction energy suggests that increased binding can be obtained in strained systems. This is confirmed for the dihydrodifluoropyrene-methanol pair, but a large portion of the binding energy is due to the interaction of the pi system with the oxygen atom. Density functional periodic boundary condition computations (PBC-PBE/6-31G*) of the structures of (5,5) and (10,10) armchair (C2F)n fluorinated SWNTs (F-SWNTs) indicate that the pyramidalization at the fluorine-binding carbon atoms are too similar to that of CH3F to enhance the hydrogen-bond acceptor properties of fluorine significantly. The solubility of F-SWNTs in alcohols therefore could be due to a combination of hydrogen bonds and van der Waals interactions with the pi systems.

Non-perturbative improvement of the axial current for dynamical Wilson fermions

A non-perturbative determination of the axial current improvement coefficient cA is performed with two flavors of dynamical improved Wilson fermions and plaquette gauge action. The improvement condition is formulated with Schroedinger functional boundary conditions and enforced at constant physical volume. Large sensitivity is obtained by using two different pseudo-scalar states in the PCAC relation. We estimate the resulting correction to F_PS at beta=5.2 to be around 10%.

Schrödinger functional formalism with Ginsparg-Wilson fermion

We propose a new method to impose the Schrodinger functional Dirichlet boundary condition generally on the fermion fields including the Ginsparg-Wilson fermion. This is accomplished by an orbifolding projection in temporal direction and is applicable to the system which has both the temporal reflection and the chiral symmetry on lattice.

Extremal solutions of [formula omitted]-Laplacian–diffusion scalar problems with nonlinear functional boundary conditions in a unified way

The aim of this paper is to ensure the existence of extremal solutions lying between a pair of lower and upper solutions for a second-order differential equation that includes both the φ -Laplacian and some classes diffusion equations. The results hold from a suitable change of variables. An example is given to expose the applicability of the obtained results.

Sodium atoms and clusters on graphite by density functional theory

Sodium atoms and clusters $(N<~5)$ on graphite (0001) are studied using density functional theory, pseudopotentials and periodic boundary conditions. A single Na atom is observed to bind at a hollow site 2.45 \AA{} above the surface with an adsorption energy of 0.51 eV. The small diffusion barrier of 0.06 eV indicates a flat potential energy surface. Increased Na coverage results in a weak adsorbate-substrate interaction, which is evident in the larger separation from the surface in the cases of ${\mathrm{Na}}_{3},$ ${\mathrm{Na}}_{4},$ ${\mathrm{Na}}_{5},$ and the $(2\ifmmode\times\else\texttimes\fi{}2)$ Na overlayer. The binding is weak for ${\mathrm{Na}}_{2},$ which has a full valence electron shell. The presence of substrate modifies the structures of ${\mathrm{Na}}_{3},$ ${\mathrm{Na}}_{4},$ and ${\mathrm{Na}}_{5}$ significantly, and both ${\mathrm{Na}}_{4}$ and ${\mathrm{Na}}_{5}$ are distorted from planarity. The calculated formation energies suggest that clustering of atoms is energetically favorable, and that the open shell clusters (e.g., ${\mathrm{Na}}_{3}$ and ${\mathrm{Na}}_{5})$ can be more abundant on graphite than in the gas phase. Analysis of the lateral charge density distributions of Na and ${\mathrm{Na}}_{3}$ shows a charge transfer of $\ensuremath{\sim}0.5$ electrons in both cases.

Simulating the Schrodinger functional with two pseudo-fermions: algorithmic study and the running mass

We present an algorithmic study for the simulation of two massless flavors of O(a) improved Wilson quarks with Schrödinger functional boundary conditions. The algorithm used is Hybrid Monte Carlo with two pseudo-fermion fields as proposed by M. Hasenbusch. A gain in CPU cost of a factor two is reached when compared to one pseudo-fermion field due to the larger possible step-size. This study is integrated in the ALPHA project for the computation of the running of the renormalized quark mass. We include an update on these physics results.

Simulating the Schrödinger functional with two pseudo-fermions

We report on simulations with two flavors of O( a) improved degenerate Wilson fermions with Schrödinger functional boundary conditions. The algorithm which is used is Hybrid Monte Carlo with two pseudo-fermion fields as proposed by M. Hasenbusch. We investigate the numerical precision and sensitivity to reversibility violations of this algorithm. A gain of a factor two in CPU cost is reached compared with one pseudo-fermion field due to the larger possible step-size.

Nonresonance conditions and extremal solutions for first-order impulsive problems under weak assumptions

AbstractIn this work we shall study the existence of extremal solutions for an impulsive problem with functional-boundary conditions and weak regularity assumptions, not only on the right-hand side of the equation and on the functions that define the boundary conditions, but also on the impulse functions, which will be required to be nondecreasing, but not continuous as well, as is customary in the literature.Moreover, in order to prove one of our results we shall study a general impulsive linearproblem, giving a complete characterisation of resonance for it.

Linear stochastic differential equations with functional boundary conditions

We consider linear nth order stochastic differential equations on $[0,1]$, with linear boundary conditions supported by a finite subset of $[0,1]$. We study some features of the solution to these problems, and especially its conditional independence properties of Markovian type.

Image-based computational fluid dynamics modeling in realistic arterial geometries.

Local hemodynamics are an important factor in atherosclerosis, from the development of early lesions, to the assessment of stroke risk, to determining the ultimate fate of a mature plaque. Until recently, our understanding of arterial fluid dynamics and their relationship to atherosclerosis was limited by the use of idealized or averaged artery models. Recent advances in medical imaging, computerized image processing, and computational fluid dynamics (CFD) now make it possible to computationally reconstruct the time-varying, three-dimensional blood flow patterns in anatomically realistic models. In this paper we review progress, made largely within the last five years, towards the routine use of anatomically realistic CFD models, derived from in vivo medical imaging, to elucidate the role of local hemodynamics in the development and progression of atherosclerosis in large arteries. In addition to describing various image-based CFD studies carried out to date, we review the medical imaging and image processing techniques available to acquire the necessary geometric and functional boundary conditions. Issues related to accuracy, precision, and modeling assumptions are also discussed.

Two Functional Boundary-Value Problems with Singularities in Phase Variables

We consider the differential equation x″ = f(txx′) with two functional boundary conditions. Here, f(txy) is a local Caratheeodory function that may be singular at the points x = 0 and y = 0 of the phase variables x and y. The main common feature of these two singular problems is the fact that any solution or the derivative of any solution “passes through” the singularities of f somewhere inside [0, T].$ Existence results are proved using the regularization and sequential techniques, Borsuk antipodal theorem, Leray–Schauder degree, and Vitali convergence theorem.

The Influence of Boundaries on Young Children's Searching and Gathering

Two experiments were conducted to examine how boundaries influence the organization of the gathering and searching of 3- and 4-year-olds. In Experiment 1, children retrieved miniature carrots that were in plain view from a dollhouse that was divided in half by a visual, a functional, or a visual-functional boundary. There was also a control condition in which no boundary was present. Children exhibited more organized gathering in the visual and visual-functional boundary conditions than in the functional boundary and no-boundary conditions. This suggests that visual rather than functional properties of boundaries influenced the organization of young children's gathering behavior. In Experiment 2, we increased task difficulty by requiring children to search for carrots that were out of sight. Unlike in Experiment 1, children produced more organized searching in the visual, visual-functional, and the functional boundary conditions than in the no-boundary condition. Our discussion focuses on the role of the physical environment in organizing behavior.

Extremal solutions for the difference φ-Laplacian problem with nonlinear functional boundary conditions

In this paper, we study the existence and approximation of the extremal solutions for the φ-Laplacian problem lying between a pair of a lower solution α and an upper solution β such that α ≤ β. We consider general boundary functional conditions that include classical ones as separated or periodic.

Non-perturbative scaling tests of twisted mass QCD

We present a scaling study of lattice QCD with O( a) improved Wilson fermions and a chirally twisted mass term. In order to get precise results with a moderate computational effort, we have considered a system of physical size of 0.75 3 × 1.5 fm 4 with Schrödinger functional boundary conditions in the quenched approximation. Looking at meson observables in the pseudoscalar and vector channels, we find that O( a) improvement is effective and residual cutoff effects are fairly small.

Extremal solutions of strongly nonlinear discontinuous second-order equations with nonlinear functional boundary conditions

Extremal solutions of strongly nonlinear discontinuous second-order equations with nonlinear functional boundary conditions

SSOR preconditioning in simulations of the QCD Schrödinger functional

We report on a parallelized implementation of locally-lexicographic SSOR preconditioning for O(a) improved lattice QCD with Schrödinger functional boundary conditions. Numerical simulations in the quenched approximation at parameters in the light quark mass region demonstrate that a performance gain of a factor ∼1.5 over even–odd preconditioning can be achieved.

Multiple solutions of nonlinear functional boundary value problems

A class of nonlinear functional boundary conditions for the system of functional differential equations \(x''(t)=(F(x,y))(t)\), \(y''(t)=(H(x,y))(t)\) is introduced. Here \(F,\,H:C^1([a,b]) \times C^1([a,b]) \rightarrow L_1([a,b])\) are nonlinear continuous operators. Sufficient conditions for the existence of at least four solutions are given. Results are proved by the Bihari lemma, the Leray-Schauder degree theory and the Borsuk theorem.

Low energy physics from the QCD Schrödinger functional

We review recent work by the ALPHA and UKQCD Collaborations where masses and matrix elements were computed in lattice QCD using Schrödinger functional boundary conditions and where the strange quark mass was determined in the quenched approximation. We emphasize the general concepts and our strategy for the computation of quark masses.

Hadron masses and matrix elements from the QCD Schrödinger functional

We explain how masses and matrix elements can be computed in lattice QCD using Schr"odinger functional boundary conditions. Numerical results in the quenched approximation demonstrate that good precision can be achieved. For a statistical sample of the same size, our hadron masses have a precision similar to what is achieved with standard methods, but for the computation of matrix elements such as the pseudoscalar decay constant the Schr"odinger functional technique turns out to be much more efficient than the known alternatives.

Scaling investigation of renormalized correlation functions in O( a) improved quenched lattice QCD

We present a scaling investigation of some correlation functions in O( a) improved quenched lattice QCD. In particular, as one observable the renormalized PCAC quark mass is considered. Others are constructed such that they become the vector meson mass and the pseudoscalar meson decay constant when the volume is large. For the present discussion we remain in intermediate volume, (0.75 3 × 1.5) fm 4 with Schrödinger functional boundary conditions. By fixing the ‘pion mass’ and the spatial lattice size in units of the hadronic scale r 0, we simulated four lattices with resolutions ranging from 0.1 to 0.05 fm and performed the extrapolation to the continuum limit. The maximal scaling violation found in the improved theory is a ∼ 6% effect at a ≅ 0.1 fm.