Search results for "Asymptotic"
showing 10 items of 230 documents
Matched asymptotic solution for the solute boundary layer in a converging axisymmetric stagnation point flow
2007
Abstract A novel boundary-layer solution is obtained by the method of matched asymptotic expansions for the solute distribution at a solidification front represented by a disk of finite radius R 0 immersed in an axisymmetric converging stagnation point flow. The detailed analysis reveals a complex internal structure of the boundary layer consisting of eight subregions. The development of the boundary layer starts from the rim region where the concentration, according to the obtained similarity solution, varies with the radius r along the solidification front as ∼ln 1/3 ( R 0 / r ). At intermediate radii, where the corresponding concentration is found to vary as ∼ln( R 0 / r ), the boundary …
Solutions for parametric double phase Robin problems
2021
We consider a parametric double phase problem with Robin boundary condition. We prove two existence theorems. In the first the reaction is ( p − 1 )-superlinear and the solutions produced are asymptotically big as λ → 0 + . In the second the conditions on the reaction are essentially local at zero and the solutions produced are asymptotically small as λ → 0 + .
Multiplicity of solutions of Dirichlet problems associated with second-order equations in ℝ2
2009
AbstractWe study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinity.
Uniqueness of positive radial solutions to singular critical growth quasilinear elliptic equations
2015
In this paper, we prove that there exists at most one positive radial weak solution to the following quasilinear elliptic equation with singular critical growth \[ \begin{cases} -\Delta_{p}u-{\displaystyle \frac{\mu}{|x|^{p}}|u|^{p-2}u}{\displaystyle =\frac{|u|^{\frac{(N-s)p}{N-p}-2}u}{|x|^{s}}}+\lambda|u|^{p-2}u & \text{in }B,\\ u=0 & \text{on }\partial B, \end{cases} \] where $B$ is an open finite ball in $\mathbb{R}^{N}$ centered at the origin, $1<p<N$, $-\infty<\mu<((N-p)/p)^{p}$, $0\le s<p$ and $\lambda\in\mathbb{R}$. A related limiting problem is also considered.
Testing for goodness rather than lack of fit of an X–chromosomal SNP to the Hardy-Weinberg model
2019
The problem of checking the genotype distribution obtained for some diallelic marker for compatibility with the Hardy-Weinberg equilibrium (HWE) condition arises also for loci on the X chromosome. The possible genotypes depend on the sex of the individual in this case: for females, the genotype distribution is trinomial, as in the case of an autosomal locus, whereas a binomial proportion is observed for males. Like in genetic association studies with autosomal SNPs, interest is typically in establishing approximate compatibility of the observed genotype frequencies with HWE. This requires to replace traditional methods tailored for detecting lack of fit to the model with an equivalence test…
On the moments of Cochran's Q statistic under the null hypothesis, with application to the meta-analysis of risk difference.
2011
W. G. Cochran's Q statistic was introduced in 1937 to test for equality of means under heteroscedasticity. Today, the use of Q is widespread in tests for homogeneity of effects in meta-analysis, but often these effects (such as risk differences and odds ratios) are not normally distributed. It is common to assume that Q follows a chi-square distribution, but it has long been known that this asymptotic distribution for Q is not accurate for moderate sample sizes. In this paper, the effect and weight for an individual study may depend on two parameters: the effect and a nuisance parameter. We present expansions for the first two moments of Q without any normality assumptions. Our expansions w…
Higgs mass predicted from the standard model with asymptotically safe gravity
2016
Tässä Pro Gradu -tutkielmassa tavoitteena on ennustaa Higgsin bosonin massa ottaen lähtökohdaksi hiukkasfysiikan standardimalli, johon on kytketty gravitaatio ns. asymptoottisesti turvallisena teoriana. Ennusteen laskemiseksi selvitetään Higgsin bosonin itseiskytkennän ja neljän muun standardimallin kytkinvakion juokseminen, eli kytkinvakioiden käyttäytyminen energiaskaalan funktiona, johtavassa kertaluvussa MS-skeemassa. Standardimallista saatuihin β-funktioihin lisätään asymptoottisesti turvallisen gravitaation antamat korjaukset suurilla energiaskaaloilla, jonka jälkeen β-funktioiden muodostama differentiaaliyhtälöryhmä ratkaistaan numeerisesti. Standardimallin osittainen äärellinen remo…
Entropy Production during Asymptotically Safe Inflation
2011
The Asymptotic Safety scenario predicts that the deep ultraviolet of Quantum Einstein Gravity is governed by a nontrivial renormalization group fixed point. Analyzing its implications for cosmology using renormalization group improved Einstein equations we find that it can give rise to a phase of inflationary expansion in the early Universe. Inflation is a pure quantum effect here and requires no inflaton field. It is driven by the cosmological constant and ends automatically when the renormalization group evolution has reduced the vacuum energy to the level of the matter energy density. The quantum gravity effects also provide a natural mechanism for the generation of entropy. It could eas…
The metric on field space, functional renormalization, and metric-torsion quantum gravity
2015
Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein-Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and "tetrad-only" gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an addition…
Bimetric truncations for quantum Einstein gravity and asymptotic safety
2010
In the average action approach to the quantization of gravity the fundamental requirement of "background independence" is met by actually introducing a background metric but leaving it completely arbitrary. The associated Wilsonian renormalization group defines a coarse graining flow on a theory space of functionals which, besides the dynamical metric, depend explicitly on the background metric. All solutions to the truncated flow equations known to date have a trivial background field dependence only, namely via the classical gauge fixing term. In this paper we analyze a number of conceptual issues related to the bimetric character of the gravitational average action and explore a first no…