Search results for "dynamics."
showing 10 items of 9637 documents
Gradient estimates for solutions to quasilinear elliptic equations with critical sobolev growth and hardy potential
2015
This note is a continuation of the work \cite{CaoXiangYan2014}. We study the following quasilinear elliptic equations \[ -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\, x\in\mathbb{R}^{N}, \] where $1<p<N,0\leq\mu<\left((N-p)/p\right)^{p}$ and $Q\in L^{\infty}(\R^{N})$. Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.
Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry
2017
This work deals with free transport equations with partly diffuse stochastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in $L^{1}$ spaces$.\ $We prove convergence to equilibrium at the rate $O\left( t^{-\frac{k}{2(k+1)+1}}\right) \ (t\rightarrow +\infty )$ for $L^{1}$ initial data $g$ in a suitable subspace of the domain of the generator $T$ where $k\in \mathbb{N}$ depends on the properties of the boundary operators near the tangential velocities to the slab. This result is derived from a quantified version of Ingham's tauberian theorem by showing that $F_{g}(s):=\lim_{\varepsilon \rightarrow 0_{+}}\left( is+\varepsilon -T\right) ^{-1}g$ exists…
Electron crystallography and non-linear optics
1999
Electron crystallography can be used to obtain specific information about molecular parameters such as the polarisability, dipole moment, and hyperpolarisability. In this, work we show how a combination of quantum mechanics and simulation methods can be used to solve several unknown organic structures and how the calculated molecular parameters can be used to predict the corresponding physical properties of the crystals.
Adsorption of hydrogen isotopes in the zeolite NaX: Experiments and simulations
2017
Abstract Among the different methods to separate hydrogen isotopes one is based on the physisorption at low temperature (below 100 K) where quantum effects induce a particular behavior. In the present work, we study the adsorption of single H 2 and D 2 on the zeolite NaX by combining experiments (manometry) from 30 to 150 K and molecular dynamics simulations at 40 and 77 K. Simulations also include the adsorption analysis for T 2 . Adsorption on NaX membranes is simulated and quantum corrections are introduced by using the well-known Feynman–Hibbs approach into the interaction potentials. Experimental adsorption isotherms are reproduced by using the Toth equation and it is shown that the ad…
The Performance of the Gradient-Like Influence Measure in Generalized Linear Mixed Models
2015
A gradient-like statistic, recently introduced as an influence measure, has been proven to work well in large sample, thanks to its asymptotic properties. In this work, through small-scale simulation schemes, the performance of such a diagnostic measure is further investigated in terms of concordance with the main influence measures used for outlier identification. The simulation studies are performed by using generalized linear mixed models (GLMMs).
A further exploration of a nucleophilicity index based on the gas-phase ionization potentials
2008
An empirical nucleophilicity index based on the gas-phase ionization potentials has been recently shown to be useful categorizing and settling the nucleophilicity power of a series of captodative ethylenes reacting in cycloaddition reactions (L.R. Domingo, E. Chamorro, P. Perez, Journal of Organic Chemistry 73 (2008) 4615–4624). In the present work, the applicability of such model is tested within a broader series of substituted alkenes, substituted aromatic compounds and simple nucleophilic molecules. This index obtained within a Koopman’s theorem framework has been evaluated here in both gas and solution phases for several well-known nucleophiles. These results are found to be linearly co…
Integro-differential equation modelling heat transfer in conducting, radiating and semitransparent materials
1998
In this work we analyse a model for radiative heat transfer in materials that are conductive, grey and semitransparent. Such materials are for example glass, silicon, water and several gases. The most important feature of the model is the non-local interaction due to exchange of radiation. This, together with non-linearity arising from the well-known Stefan-Boltzmann law, makes the resulting heat equation non-monotone. By analysing the terms related to heat radiation we prove that the operator defining the problem is pseudomonotone. Hence, we can prove the existence of weak solution in the cases where coercivity can be obtained. In the general case, we prove the solvability of the system us…
Peak capacity estimation in isocratic elution.
2008
Peak capacity (i.e. maximal number of resolved peaks that fit in a chromatographic window) is a theoretical concept with growing interest, but based on a situation rarely met in practice. Real chromatograms tend to have uneven distributions, with overlapped peaks and large gaps. The number of resolved compounds should, therefore, be known from estimations. Several equations have been reported for this purpose based on three perspectives, namely, the intuitive approach (peak capacity as the size of the retention time window measured in peak width units), which assumes peaks with the same width, and the outlines of Giddings and Grushka, which consider changes in peak width with retention time…
The influence of the temperature on the liquid–liquid equlibria of the mixture limonene + ethanol + H2O
2004
Abstract In this work, experimental liquid–liquid equilibria (LLE) of the limonene + ethanol + water system are presented. The LLE of this system has been measured at 293.15, 303.15, 313.15 and 323.15 K. The equilibrium data presented are correlated using NRTL and UNIQUAC equations. Finally, the reliability of these models is tested by comparison with experimental results.
Contribution of mode coupling and phase-mixing of Alfv\'en waves to coronal heating
2017
This research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 647214) and from the UK Science and Technology Facilities Council. This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk. This equipment was funded by a BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/K00087X/1, DiRAC Operations grant ST/K003267/1 and Durham University. Context. Phase-mixing of Alfvén waves in the solar corona has been identified as one possible candid…