1,464 research outputs found

### Comparison of planted soil infiltration systems for treatment of log yard runoff

Treatment of log yard runoff is required to avoid
contamination of receiving watercourses. The research aim was to assess
if infiltration of log yard runoff through planted soil systems is successful
and if different plant species affect the treatment performance at a fieldscale
experimental site in Sweden (2005 to 2007). Contaminated runoff
from the log yard of a sawmill was infiltrated through soil planted with
Alnus glutinosa (L.) GaÂ¨rtner (common alder), Salix schwerinii3viminalis
(willow variety â€˜â€˜Gudrunâ€™â€™), Lolium perenne (L.) (rye grass), and Phalaris
arundinacea (L.) (reed canary grass). The study concluded that there were
no treatment differences when comparing the four different plants with
each other, and there also were no differences between the tree and the
grass species. Furthermore, the infiltration treatment was effective in
reducing total organic carbon (55%) and total phosphorus (45%)
concentrations in the runoff, even when the loads on the infiltration
system increased from year to year

### A Holder Continuous Nowhere Improvable Function with Derivative Singular Distribution

We present a class of functions $\mathcal{K}$ in $C^0(\R)$ which is variant
of the Knopp class of nowhere differentiable functions. We derive estimates
which establish \mathcal{K} \sub C^{0,\al}(\R) for 0<\al<1 but no $K \in
\mathcal{K}$ is pointwise anywhere improvable to C^{0,\be} for any \be>\al.
In particular, all $K$'s are nowhere differentiable with derivatives singular
distributions. $\mathcal{K}$ furnishes explicit realizations of the functional
analytic result of Berezhnoi.
Recently, the author and simulteously others laid the foundations of
Vector-Valued Calculus of Variations in $L^\infty$ (Katzourakis), of
$L^\infty$-Extremal Quasiconformal maps (Capogna and Raich, Katzourakis) and of
Optimal Lipschitz Extensions of maps (Sheffield and Smart). The "Euler-Lagrange
PDE" of Calculus of Variations in $L^\infty$ is the nonlinear nondivergence
form Aronsson PDE with as special case the $\infty$-Laplacian.
Using $\mathcal{K}$, we construct singular solutions for these PDEs. In the
scalar case, we partially answered the open $C^1$ regularity problem of
Viscosity Solutions to Aronsson's PDE (Katzourakis). In the vector case, the
solutions can not be rigorously interpreted by existing PDE theories and
justify our new theory of Contact solutions for fully nonlinear systems
(Katzourakis). Validity of arguments of our new theory and failure of classical
approaches both rely on the properties of $\mathcal{K}$.Comment: 5 figures, accepted to SeMA Journal (2012), to appea

### Convexity criteria and uniqueness of absolutely minimizing functions

We show that absolutely minimizing functions relative to a convex Hamiltonian
$H:\mathbb{R}^n \to \mathbb{R}$ are uniquely determined by their boundary
values under minimal assumptions on $H.$ Along the way, we extend the known
equivalences between comparison with cones, convexity criteria, and absolutely
minimizing properties, to this generality. These results perfect a long
development in the uniqueness/existence theory of the archetypal problem of the
calculus of variations in $L^\infty.$Comment: 34 page

### Overdetermined Steady-State Initialization Problems in Object-Oriented Fluid System Models

The formulation of steady-state initialization problems for fluid systems is a non-trivial task. If steady-state equations are specified at the component level, the corresponding system of initial equations at the system level might be overdetermined,
if index reduction eliminates some states. On the other hand, steady-state equations are not sufficient to uniquely identify one equilibrium state in the case of closed systems, so additional equations are required. The paper shows how these problems
might be solved in an elegant way by formulating overdetermined initialization problems, which have more equations than unknowns and a unique solution, then solving them using a least-squares minimization algorithm. The concept is tested on a
representative test case using the OpenModelica compiler

### A nonhomogeneous boundary value problem in mass transfer theory

We prove a uniqueness result of solutions for a system of PDEs of
Monge-Kantorovich type arising in problems of mass transfer theory. The results
are obtained under very mild regularity assumptions both on the reference set
$\Omega\subset\mathbf{R}^n$, and on the (possibly asymmetric) norm defined in
$\Omega$. In the special case when $\Omega$ is endowed with the Euclidean
metric, our results provide a complete description of the stationary solutions
to the tray table problem in granular matter theory.Comment: 22 pages, 2 figure

### A Maturity Assessment Framework for Conversational AI Development Platforms

Conversational Artificial Intelligence (AI) systems have recently
sky-rocketed in popularity and are now used in many applications, from car
assistants to customer support. The development of conversational AI systems is
supported by a large variety of software platforms, all with similar goals, but
different focus points and functionalities. A systematic foundation for
classifying conversational AI platforms is currently lacking. We propose a
framework for assessing the maturity level of conversational AI development
platforms. Our framework is based on a systematic literature review, in which
we extracted common and distinguishing features of various open-source and
commercial (or in-house) platforms. Inspired by language reference frameworks,
we identify different maturity levels that a conversational AI development
platform may exhibit in understanding and responding to user inputs. Our
framework can guide organizations in selecting a conversational AI development
platform according to their needs, as well as helping researchers and platform
developers improving the maturity of their platforms.Comment: 10 pages, 10 figures. Accepted for publication at SAC 2021:
ACM/SIGAPP Symposium On Applied Computin

### Boron Isotope Effect in Superconducting MgB$_2$

We report the preparation method of, and boron isotope effect for MgB$_2$, a
new binary intermetallic superconductor with a remarkably high superconducting
transition temperature $T_c$($^{10}$B) = 40.2 K. Measurements of both
temperature dependent magnetization and specific heat reveal a 1.0 K shift in
$T_c$ between Mg$^{11}$B$_2$ and Mg$^{10}$B$_2$. Whereas such a high transition
temperature might imply exotic coupling mechanisms, the boron isotope effect in
MgB$_2$ is consistent with the material being a phonon-mediated BCS
superconductor.Comment: One figure and related discussion adde

### The eigenvalue problem for the âˆž-Bilaplacian

We consider the problem of finding and describing minimisers of the Rayleigh quotient
Î›âˆž:=infuâˆˆW2,âˆž(Î©)âˆ–{0}âˆ¥Î”uâˆ¥Lâˆž(Î©)âˆ¥uâˆ¥Lâˆž(Î©),
Î›âˆž:=infuâˆˆW2,âˆž(Î©)âˆ–{0}â€–Î”uâ€–Lâˆž(Î©)â€–uâ€–Lâˆž(Î©),
where Î©âŠ†RnÎ©âŠ†Rn is a bounded C1,1C1,1 domain and W2,âˆž(Î©)W2,âˆž(Î©) is a class of weakly twice differentiable functions satisfying either u=0u=0 on âˆ‚Î©âˆ‚Î© or u=|Du|=0u=|Du|=0 on âˆ‚Î©âˆ‚Î© . Our first main result, obtained through approximation by LpLp -problems as pâ†’âˆžpâ†’âˆž , is the existence of a minimiser uâˆžâˆˆW2,âˆž(Î©)uâˆžâˆˆW2,âˆž(Î©) satisfying
{Î”uâˆžâˆˆÎ›âˆžSgn(fâˆž)Î”fâˆž=Î¼âˆž a.e. in Î©, in Dâ€²(Î©),
{Î”uâˆžâˆˆÎ›âˆžSgn(fâˆž) a.e. in Î©,Î”fâˆž=Î¼âˆž in Dâ€²(Î©),
for some fâˆžâˆˆL1(Î©)âˆ©BVloc(Î©)fâˆžâˆˆL1(Î©)âˆ©BVloc(Î©) and a measure Î¼âˆžâˆˆM(Î©)Î¼âˆžâˆˆM(Î©) , for either choice of boundary conditions. Here Sgn is the multi-valued sign function. We also study the dependence of the eigenvalue Î›âˆžÎ›âˆž on the domain, establishing the validity of a Faberâ€“Krahn type inequality: among all C1,1C1,1 domains with fixed measure, the ball is a strict minimiser of Î©â†¦Î›âˆž(Î©)Î©â†¦Î›âˆž(Î©) . This result is shown to hold true for either choice of boundary conditions and in every dimension

### Quasivariational solutions for first order quasilinear equations with gradient constraint

We prove the existence of solutions for an evolution quasi-variational
inequality with a first order quasilinear operator and a variable convex set,
which is characterized by a constraint on the absolute value of the gradient
that depends on the solution itself. The only required assumption on the
nonlinearity of this constraint is its continuity and positivity. The method
relies on an appropriate parabolic regularization and suitable {\em a priori}
estimates. We obtain also the existence of stationary solutions, by studying
the asymptotic behaviour in time. In the variational case, corresponding to a
constraint independent of the solution, we also give uniqueness results

### Nonlinear Dynamics of Aeolian Sand Ripples

We study the initial instability of flat sand surface and further nonlinear
dynamics of wind ripples. The proposed continuous model of ripple formation
allowed us to simulate the development of a typical asymmetric ripple shape and
the evolution of sand ripple pattern. We suggest that this evolution occurs via
ripple merger preceded by several soliton-like interaction of ripples.Comment: 6 pages, 3 figures, corrected 2 typo

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